Fractal Approach to the Regional Seismic Event Discrimination Problem

DTIC Science & Technology

2000-01-01

some H > 0 and this formula might be modified as X(t) = r-HX(rt),t E R (2) where H is the Hurst exponent . Traditionally it is estimated by the...2 3 IogT Figure 2. Hurst exponent H curves for different seismic events: Pakl - nuclear explosion 30.05.98 (Pakistan), ind - nuclear explosion...seismic discrimination. Our findings are summarized in the conclusion section. 261 2 Hurst’s exponents of seismograms We started from the study of self

Characterization of turbulence stability through the identification of multifractional Brownian motions

NASA Astrophysics Data System (ADS)

Lee, K. C.

2013-02-01

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

Bayesian estimation of self-similarity exponent

NASA Astrophysics Data System (ADS)

Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

2011-08-01

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

On the Topological Changes of Local Hurst Exponent in Polar Regions

NASA Astrophysics Data System (ADS)

Consolini, G.; De Michelis, P.

2014-12-01

Geomagnetic activity during magnetic substorms and storms is related to the dinamical and topological changes of the current systems flowing in the Earth's magnetosphere-ionosphere. This is particularly true in the case of polar regions where the enhancement of auroral electrojet current system is responsible for the observed geomagnetic perturbations. Here, using the DMA-technique we evaluate the local Hurst exponent (H"older exponent) for a set of 46 geomagnetic observatories, widely distributed in the northern hemisphere, during one of the most famous and strong geomagnetic storm, the Bastille event, and reconstruct a sequence of polar maps showing the dinamical changes of the topology of the local Hurst exponent with the geomagnetic activity level. The topological evolution of local Hurst exponent maps is discussed in relation to the dinamical changes of the current systems flowing in the polar ionosphere. G. Consolini has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant agreement no. 313038/STORM for this research.

Relation between the Hurst Exponent and the Efficiency of Self-organization of a Deformable System

NASA Astrophysics Data System (ADS)

Alfyorova, E. A.; Lychagin, D. V.

2018-04-01

We have established the degree of self-organization of a system under plastic deformation at different scale levels. Using fractal analysis, we have determined the Hurst exponent and correlation lengths in the region of formation of a corrugated (wrinkled) structure in [111] nickel single crystals under compression. This has made it possible to single out two (micro-and meso-) levels of self-organization in the deformable system. A qualitative relation between the values of the Hurst exponent and the stages of the stress-strain curve has been established.

Fractal analysis of the short time series in a visibility graph method

NASA Astrophysics Data System (ADS)

Li, Ruixue; Wang, Jiang; Yu, Haitao; Deng, Bin; Wei, Xile; Chen, Yingyuan

2016-05-01

The aim of this study is to evaluate the performance of the visibility graph (VG) method on short fractal time series. In this paper, the time series of Fractional Brownian motions (fBm), characterized by different Hurst exponent H, are simulated and then mapped into a scale-free visibility graph, of which the degree distributions show the power-law form. The maximum likelihood estimation (MLE) is applied to estimate power-law indexes of degree distribution, and in this progress, the Kolmogorov-Smirnov (KS) statistic is used to test the performance of estimation of power-law index, aiming to avoid the influence of droop head and heavy tail in degree distribution. As a result, we find that the MLE gives an optimal estimation of power-law index when KS statistic reaches its first local minimum. Based on the results from KS statistic, the relationship between the power-law index and the Hurst exponent is reexamined and then amended to meet short time series. Thus, a method combining VG, MLE and KS statistics is proposed to estimate Hurst exponents from short time series. Lastly, this paper also offers an exemplification to verify the effectiveness of the combined method. In addition, the corresponding results show that the VG can provide a reliable estimation of Hurst exponents.

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion.

PubMed

Makarava, Natallia; Menz, Stephan; Theves, Matthias; Huisinga, Wilhelm; Beta, Carsten; Holschneider, Matthias

2014-10-01

Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

Spectrum-based estimators of the bivariate Hurst exponent

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav

2014-12-01

We discuss two alternate spectrum-based estimators of the bivariate Hurst exponent in the power-law cross-correlations setting, the cross-periodogram and local X -Whittle estimators, as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration during estimation, a simulation study showing performance of the estimators under varying bandwidth parameter as well as correlation between processes and their specification is provided as well. These estimators are less biased than the already existent averaged periodogram estimator, which, however, has slightly lower variance. The spectrum-based estimators can serve as a good complement to the popular time domain estimators.

Developing and Validating a Synthetic Teammate

DTIC Science & Technology

2010-01-31

reveals the stability of team coordination dynamics, the Hurst exponent , was also analyzed to determine if there was a coordination stability...difference between communication groups. An independent samples Mest on the average Hurst exponents across teams revealed that text-comm teams were, on

Relationship between efficiency and predictability in stock price change

NASA Astrophysics Data System (ADS)

Eom, Cheoljun; Oh, Gabjin; Jung, Woo-Sung

2008-09-01

In this study, we evaluate the relationship between efficiency and predictability in the stock market. The efficiency, which is the issue addressed by the weak-form efficient market hypothesis, is calculated using the Hurst exponent and the approximate entropy (ApEn). The predictability corresponds to the hit-rate; this is the rate of consistency between the direction of the actual price change and that of the predicted price change, as calculated via the nearest neighbor prediction method. We determine that the Hurst exponent and the ApEn value are negatively correlated. However, predictability is positively correlated with the Hurst exponent.

Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

NASA Astrophysics Data System (ADS)

Morales, Raffaello; Di Matteo, T.; Gramatica, Ruggero; Aste, Tomaso

2012-06-01

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.

Estimation of Hurst Exponent for the Financial Time Series

NASA Astrophysics Data System (ADS)

Kumar, J.; Manchanda, P.

2009-07-01

Till recently statistical methods and Fourier analysis were employed to study fluctuations in stock markets in general and Indian stock market in particular. However current trend is to apply the concepts of wavelet methodology and Hurst exponent, see for example the work of Manchanda, J. Kumar and Siddiqi, Journal of the Frankline Institute 144 (2007), 613-636 and paper of Cajueiro and B. M. Tabak. Cajueiro and Tabak, Physica A, 2003, have checked the efficiency of emerging markets by computing Hurst component over a time window of 4 years of data. Our goal in the present paper is to understand the dynamics of the Indian stock market. We look for the persistency in the stock market through Hurst exponent and fractal dimension of time series data of BSE 100 and NIFTY 50.

Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps

NASA Astrophysics Data System (ADS)

Tarnopolski, Mariusz

2018-01-01

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this space. A tight correlation between the HEs and mLEs is found, with the Spearman rank ρ = 0 . 83 and ρ = 0 . 75 for the Chirikov and 2D Froeschlé maps, respectively. Based on this relation, a machine learning (ML) procedure, using the nearest neighbor algorithm, is performed to reproduce the HE distribution based on the mLE distribution alone. A few thousand HE and mLE values from the mixed spaces were used for training, and then using 2 - 2 . 4 × 105 mLEs, the HEs were retrieved. The ML procedure allowed to reproduce the structure of the mixed spaces in great detail.

A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application

NASA Astrophysics Data System (ADS)

He, Ling-Yun; Qian, Wen-Bin

2012-07-01

A correct or precise estimation of the Hurst exponent is one of the fundamentally important problems in the financial economics literature. There are three widely used tools to estimate the Hurst exponent, the canonical rescaled range (R/S), the variance rescaled statistic (V/S) and the Modified rescaled range (Modified R/S). To clarify their performance, we compare them by Monte Carlo simulations; we generate many time-series of a fractal Brownian motion, of a Weierstrass-Mandelbrot cosine fractal function and of a fractionally integrated process, whose theoretical Hurst exponents are known, to compare the Hurst exponents estimated by the three methods. To better understand their pragmatic performance, we further apply all of these methods empirically in real-world applications. Our results imply it is not appropriate to conclude simply which method is better as V/S performs better when the analyzed market is anti-persistent while R/S seems to be a reliable tool used in persistent market.

Higher-Order Hurst Signatures: Dynamical Information in Time Series

NASA Astrophysics Data System (ADS)

Ferenbaugh, Willis

2005-10-01

Understanding and comparing time series from different systems requires characteristic measures of the dynamics embedded in the series. The Hurst exponent is a second-order dynamical measure of a time series which grew up within the blossoming fractal world of Mandelbrot. This characteristic measure is directly related to the behavior of the autocorrelation, the power-spectrum, and other second-order things. And as with these other measures, the Hurst exponent captures and quantifies some but not all of the intrinsic nature of a series. The more elusive characteristics live in the phase spectrum and the higher-order spectra. This research is a continuing quest to (more) fully characterize the dynamical information in time series produced by plasma experiments or models. The goal is to supplement the series information which can be represented by a Hurst exponent, and we would like to develop supplemental techniques in analogy with Hurst's original R/S analysis. These techniques should be another way to plumb the higher-order dynamics.

An accurate algorithm to calculate the Hurst exponent of self-similar processes

NASA Astrophysics Data System (ADS)

Fernández-Martínez, M.; Sánchez-Granero, M. A.; Trinidad Segovia, J. E.; Román-Sánchez, I. M.

2014-06-01

In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.

Change of Multifractal Thermal Characteristics in the Western Philippine Sea Upper Layer During Internal Wave-Soliton Propagation

DTIC Science & Technology

2007-01-01

where H is the scaling exponent , or called the Hurst exponent . In 1941, Kolmogorov suggested that the velocity increment in high-Reynolds number...turbulent flows should scale with the mean (time-averaged) energy dissipation and the separation length scale. The Hurst exponent H is equal to 1/3. For...the internal solitons change the power exponent of the power spectra drastically especially in the low wave number domain; break down the power law

Fast and unbiased estimator of the time-dependent Hurst exponent.

PubMed

Pianese, Augusto; Bianchi, Sergio; Palazzo, Anna Maria

2018-03-01

We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement.

Fast and unbiased estimator of the time-dependent Hurst exponent

NASA Astrophysics Data System (ADS)

Pianese, Augusto; Bianchi, Sergio; Palazzo, Anna Maria

2018-03-01

We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement.

Enterprise Risk Management: The Way Ahead for DRDC within the DND Enterprise

DTIC Science & Technology

2010-03-01

Taleb Distributions, the Hurst Exponent (to deal with long time events), Life Extinction Events, Zero-Infinity Dilemmas (which characterize the...Time dependent Hurst exponent in financial time series”, Physica A 344 (2004) 267-271 35. Yoav Ben-Shlomo and Diana Koh, “A Life Course Approach to

The Statistical Differences Between the Gridded Temperature Datasets, and its Implications for Stochastic Modelling

NASA Astrophysics Data System (ADS)

Fredriksen, H. B.; Løvsletten, O.; Rypdal, M.; Rypdal, K.

2014-12-01

Several research groups around the world collect instrumental temperature data and combine them in different ways to obtain global gridded temperature fields. The three most well known datasets are HadCRUT4 produced by the Climatic Research Unit and the Met Office Hadley Centre in UK, one produced by NASA GISS, and one produced by NOAA. Recently Berkeley Earth has also developed a gridded dataset. All these four will be compared in our analysis. The statistical properties we will focus on are the standard deviation and the Hurst exponent. These two parameters are sufficient to describe the temperatures as long-range memory stochastic processes; the standard deviation describes the general fluctuation level, while the Hurst exponent relates the strength of the long-term variability to the strength of the short-term variability. A higher Hurst exponent means that the slow variations are stronger compared to the fast, and that the autocovariance function will have a stronger tail. Hence the Hurst exponent gives us information about the persistence or memory of the process. We make use of these data to show that data averaged over a larger area exhibit higher Hurst exponents and lower variance than data averaged over a smaller area, which provides information about the relationship between temporal and spatial correlations of the temperature fluctuations. Interpolation in space has some similarities with averaging over space, although interpolation is more weighted towards the measurement locations. We demonstrate that the degree of spatial interpolation used can explain some differences observed between the variances and memory exponents computed from the various datasets.

First Passage Time Analysis on Climate Indices

DTIC Science & Technology

2008-01-01

13) 12 with 0 1H< < . Here H is the Hurst exponent . For H = 1/2, the random process is the ordinary...14) with 0α ~1/2. Since the Hurst exponent of an ordinary Brownian motion is H = 1/2, the empirically observed...ρ = 10, 20, and 30 for SOI. From this figure it is seen that the tail exponent , ρα , is rather insensitive to the value of ρ . In particular one

Optimal Combining Data for Improving Ocean Modeling

DTIC Science & Technology

2008-09-30

hyperbolic or elliptic) and on the Hurst exponent characterizing the dynamics type (local or non-local). 3. Fusion data for estimating RD. Theoretical...1) RD vs time and different values of Hurst exponent h = 0.1 (black), h = 1 (red), h = 2 (blue) γ = 0.1,Ω = 0, 2) Same for γ = 0.1,Ω = 2 ). 3...accurate estimating the upper ocean velocity field and mixing characteristics such as relative dispersion and finite size Lyapunov exponent , (2

Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone

NASA Astrophysics Data System (ADS)

Anagnostidis, P.; Varsakelis, C.; Emmanouilides, C. J.

2016-04-01

In this paper, the impact of the 2008 financial crisis on the weak-form efficiency of twelve Eurozone stock markets is investigated empirically. Efficiency is tested via the Generalized Hurst Exponent method, while dynamic Hurst exponents are estimated by means of the rolling window technique. To account for biases associated with the finite sample size and the leptokurtosis of the financial data, the statistical significance of the Hurst exponent estimates is assessed through a series of Monte-Carlo simulations drawn from the class of α-stable distributions. According to our results, the 2008 crisis has adversely affected stock price efficiency in most of the Eurozone capital markets, leading to the emergence of significant mean-reverting patterns in stock price movements.

Group-Wise Herding Behavior in Financial Markets: An Agent-Based Modeling Approach

PubMed Central

Kim, Minsung; Kim, Minki

2014-01-01

In this paper, we shed light on the dynamic characteristics of rational group behaviors and the relationship between monetary policy and economic units in the financial market by using an agent-based model (ABM), the Hurst exponent, and the Shannon entropy. First, an agent-based model is used to analyze the characteristics of the group behaviors at different levels of irrationality. Second, the Hurst exponent is applied to analyze the characteristics of the trend-following irrationality group. Third, the Shannon entropy is used to analyze the randomness and unpredictability of group behavior. We show that in a system that focuses on macro-monetary policy, steep fluctuations occur, meaning that the medium-level irrationality group has the highest Hurst exponent and Shannon entropy among all of the groups. However, in a system that focuses on micro-monetary policy, all group behaviors follow a stable trend, and the medium irrationality group thus remains stable, too. Likewise, in a system that focuses on both micro- and macro-monetary policies, all groups tend to be stable. Consequently, we find that group behavior varies across economic units at each irrationality level for micro- and macro-monetary policy in the financial market. Together, these findings offer key insights into monetary policy. PMID:24714635

Group-wise herding behavior in financial markets: an agent-based modeling approach.

PubMed

Kim, Minsung; Kim, Minki

2014-01-01

In this paper, we shed light on the dynamic characteristics of rational group behaviors and the relationship between monetary policy and economic units in the financial market by using an agent-based model (ABM), the Hurst exponent, and the Shannon entropy. First, an agent-based model is used to analyze the characteristics of the group behaviors at different levels of irrationality. Second, the Hurst exponent is applied to analyze the characteristics of the trend-following irrationality group. Third, the Shannon entropy is used to analyze the randomness and unpredictability of group behavior. We show that in a system that focuses on macro-monetary policy, steep fluctuations occur, meaning that the medium-level irrationality group has the highest Hurst exponent and Shannon entropy among all of the groups. However, in a system that focuses on micro-monetary policy, all group behaviors follow a stable trend, and the medium irrationality group thus remains stable, too. Likewise, in a system that focuses on both micro- and macro-monetary policies, all groups tend to be stable. Consequently, we find that group behavior varies across economic units at each irrationality level for micro- and macro-monetary policy in the financial market. Together, these findings offer key insights into monetary policy.

Statistical analysis of financial returns for a multiagent order book model of asset trading

NASA Astrophysics Data System (ADS)

Preis, Tobias; Golke, Sebastian; Paul, Wolfgang; Schneider, Johannes J.

2007-07-01

We recently introduced a realistic order book model [T. Preis , Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.

The use of copula functions for modeling the risk of investment in shares traded on the Warsaw Stock Exchange

NASA Astrophysics Data System (ADS)

Domino, Krzysztof; Błachowicz, Tomasz

2014-11-01

In our work copula functions and the Hurst exponent calculated using the local Detrended Fluctuation Analysis (DFA) were used to investigate the risk of investment made in shares traded on the Warsaw Stock Exchange. The combination of copula functions and the Hurst exponent calculated using local DFA is a new approach. For copula function analysis bivariate variables composed of shares prices of the PEKAO bank (a big bank with high capitalization) and other banks (PKOBP, BZ WBK, MBANK and HANDLOWY in decreasing capitalization order) and companies from other branches (KGHM-mining industry, PKNORLEN-petrol industry as well as ASSECO-software industry) were used. Hurst exponents were calculated for daily shares prices and used to predict high drops of those prices. It appeared to be a valuable indicator in the copula selection procedure, since Hurst exponent’s low values were pointing on heavily tailed copulas e.g. the Clayton one.

Long-range correlations and charge transport properties of DNA sequences

NASA Astrophysics Data System (ADS)

Liu, Xiao-liang; Ren, Yi; Xie, Qiong-tao; Deng, Chao-sheng; Xu, Hui

2010-04-01

By using Hurst's analysis and transfer approach, the rescaled range functions and Hurst exponents of human chromosome 22 and enterobacteria phage lambda DNA sequences are investigated and the transmission coefficients, Landauer resistances and Lyapunov coefficients of finite segments based on above genomic DNA sequences are calculated. In a comparison with quasiperiodic and random artificial DNA sequences, we find that λ-DNA exhibits anticorrelation behavior characterized by a Hurst exponent 0.5

a Comparison of Three Hurst Exponent Approaches to Predict Nascent Bubbles in S&P500 Stocks

NASA Astrophysics Data System (ADS)

Fernández-Martínez, M.; Sánchez-Granero, M. A.; Muñoz Torrecillas, M. J.; McKelvey, Bill

Since the pioneer contributions due to Vandewalle and Ausloos, the Hurst exponent has been applied by econophysicists as a useful indicator to deal with investment strategies when such a value is above or below 0.5, the Hurst exponent of a Brownian motion. In this paper, we hypothesize that the self-similarity exponent of financial time series provides a reliable indicator for herding behavior (HB) in the following sense: if there is HB, then the higher the price, the more the people will buy. This will generate persistence in the stocks which we shall measure by their self-similarity exponents. Along this work, we shall explore whether there is some connections between the self-similarity exponent of a stock (as a HB indicator) and the stock’s future performance under the assumption that the HB will last for some time. With this aim, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which performs best to identify the transition from random efficient market behavior to HB and hence, to detect the beginning of a bubble. Generalized Hurst Exponent, Detrended Fluctuation Analysis, and GM2 algorithms have been tested. Traditionally, researchers have focused on identifying the beginning of a crash. We study the beginning of the transition from efficient market behavior to a market bubble, instead. Our empirical results support that the higher (respectively the lower) the self-similarity index, the higher (respectively the lower) the mean of the price change, and hence, the better (respectively the worse) the performance of the corresponding stock. This would imply, as a consequence, that the transition process from random efficient market to HB has started. For experimentation purposes, S&P500 stock Index constituted our main data source.

Measuring the self-similarity exponent in Lévy stable processes of financial time series

NASA Astrophysics Data System (ADS)

Fernández-Martínez, M.; Sánchez-Granero, M. A.; Trinidad Segovia, J. E.

2013-11-01

Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions. In this paper, we prove empirically by Monte Carlo simulation that GM algorithms are able to calculate accurately the self-similarity index in Lévy stable motions and find empirical evidence that they are more precise than the absolute value exponent (denoted by AVE onwards) and the multifractal detrended fluctuation analysis (MF-DFA) algorithms, especially with a short length time series. We also compare them with the generalized Hurst exponent (GHE) algorithm and conclude that both GM2 and GHE algorithms are the most accurate to study financial series. In addition to that, we provide empirical evidence, based on the accuracy of GM algorithms to estimate the self-similarity index in Lévy motions, that the evolution of the stocks of some international market indices, such as U.S. Small Cap and Nasdaq100, cannot be modelized by means of a Brownian motion.

Influence of granulometry in the Hurst exponent of air liquid interfaces formed during capillary rising in a granular media

NASA Astrophysics Data System (ADS)

Gontijo, Guilherme L.; Souza, Flávia B.; Braga, Rafael M. L.; Silva, Pedro H. E.; Correia, Maury D.; Atman, A. P. F.

2017-06-01

We report results concerning the fractal dimension of a air/fluid interface formed during the capillary rising of a fluid into a dense granular media. The system consists in a modified Hele-Shaw cell filled with grains at different granulometries and confined in a narrow gap between the glass plates. The system is then placed onto a water reservoir, and the liquid penetrates the medium due to capillary forces. We measure the Hurst exponent of the liquid/air interface with help of image processing, and follow the temporal evolution of the profiles. We observe that the Hurst exponent can be related with the granulometry, but the range of values are odd to the predicted values from models or theory.

Some stylized facts of the Bitcoin market

NASA Astrophysics Data System (ADS)

Bariviera, Aurelio F.; Basgall, María José; Hasperué, Waldo; Naiouf, Marcelo

2017-10-01

In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.

Changes in the Hurst exponent of heartbeat intervals during physical activity

NASA Astrophysics Data System (ADS)

Martinis, M.; Knežević, A.; Krstačić, G.; Vargović, E.

2004-07-01

The fractal scaling properties of the heartbeat time series are studied in different controlled ergometric regimes using both the improved Hurst rescaled range (R/S) analysis and the detrended fluctuation analysis (DFA). The long-time “memory effect” quantified by the value of the Hurst exponent H>0.5 is found to increase during progressive physical activity in healthy subjects, in contrast to those having stable angina pectoris, where it decreases. The results are also supported by the detrended fluctuation analysis. We argue that this finding may be used as a useful new diagnostic parameter for short heartbeat time series.

Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

NASA Astrophysics Data System (ADS)

Setty, V. A.; Sharma, A. S.

2015-02-01

The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t) , such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.

Temporal and spatial variations of seismicity scaling behavior in Southern México

NASA Astrophysics Data System (ADS)

Alvarez-Ramirez, J.; Echeverria, J. C.; Ortiz-Cruz, A.; Hernandez, E.

2012-03-01

R/S analysis is used in this work to investigate the fractal correlations in terms of the Hurst exponent for the 1998-2011 seismicity data in Southern Mexico. This region is the most seismically active area in Mexico, where epicenters for severe earthquakes (e.g., September 19, 1985, Mw = 8.1) causing extensive damage in highly populated areas have been located. By only considering the seismic events that meet the Gutenberg-Ritcher law completeness requirement ( b = 0.97, MGR = 3.6), we found time clustering for scales of about 100 and 135 events. In both cases, a cyclic behavior with dominant spectral components at about one cycle per year is revealed. It is argued that such a one-year cycle could be related to tidal effects in the Pacific coast. Interestingly, it is also found that high-magnitude events ( Mw ≥ 6.0) are more likely to occur under increased interevent correlations with Hurst exponent values H > 0.65. This suggests that major earthquakes can occur when the tectonic stress accumulates in preferential directions. In contrast, the high-magnitude seismic risk is reduced when stresses are uniformly distributed in the tectonic shell. Such cointegration between correlations (i.e., Hurst exponent) and macroseismicity is confirmed for spatial variations of the Hurst exponent. In this way, we found that, using the Hurst exponent standpoint, the former presumed Michoacan and the Guerrero seismic gaps are the riskiest seismic zones. To test this empirical finding, two Southern Mexico local regions with large earthquakes were considered. These are the Atoyac de Alvarez, Guerrero ( Mw = 6.3), and Union Hidalgo, Oaxaca ( Mw = 6.6), events. In addition, we used the Loma Prieta, California, earthquake (October 17, 1989, Mw = 6.9) to show that the high-magnitude earthquakes in the San Andreas Fault region can also be linked to the increments of determinism (quantified in terms of the Hurst exponent) displayed by the stochastic dynamics of the interevent period time series. The results revealed that the analysis of seismic activity by means of R/S analysis could provide further insights in the advent of major earthquakes.

Decomposing intraday dependence in currency markets: evidence from the AUD/USD spot market

NASA Astrophysics Data System (ADS)

Batten, Jonathan A.; Ellis, Craig A.; Hogan, Warren P.

2005-07-01

The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a time-varying range, or standard deviation, or both of these simultaneously, values for the range, standard deviation and local Hurst exponent are recorded and analyzed separately. To illustrate this approach, a high-frequency data set of the spot Australian dollar/US dollar provides evidence of the returns distribution across the 24-hour trading ‘day’, with time-varying dependence and volatility clearly aligning with the opening and closing of markets. This variation is attributed to the effects of liquidity and the price-discovery actions of dealers.

On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points

NASA Astrophysics Data System (ADS)

Tarnopolski, Mariusz

2016-11-01

The long range dependence of the fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst exponent H. Considering the realizations of these three processes as time series, they might be described by their statistical features, such as half of the ratio of the mean square successive difference to the variance, A, and the number of turning points, T. This paper investigates the relationships between A and H, and between T and H. It is found numerically that the formulae A(H) = aebH in case of fBm, and A(H) = a + bHc for fGn and DfGn, describe well the A(H) relationship. When T(H) is considered, no simple formula is found, and it is empirically found that among polynomials, the fourth and second order description applies best. The most relevant finding is that when plotted in the space of (A , T) , the three process types form separate branches. Hence, it is examined whether A and T may serve as Hurst exponent indicators. Some real world data (stock market indices, sunspot numbers, chaotic time series) are analyzed for this purpose, and it is found that the H's estimated using the H(A) relations (expressed as inverted A(H) functions) are consistent with the H's extracted with the well known wavelet approach. This allows to efficiently estimate the Hurst exponent based on fast and easy to compute A and T, given that the process type: fBm, fGn or DfGn, is correctly classified beforehand. Finally, it is suggested that the A(H) relation for fGn and DfGn might be an exact (shifted) 3 / 2 power-law.

A case study on Discrete Wavelet Transform based Hurst exponent for epilepsy detection.

PubMed

Madan, Saiby; Srivastava, Kajri; Sharmila, A; Mahalakshmi, P

2018-01-01

Epileptic seizures are manifestations of epilepsy. Careful analysis of EEG records can provide valuable insight and improved understanding of the mechanism causing epileptic disorders. The detection of epileptic form discharges in EEG is an important component in the diagnosis of epilepsy. As EEG signals are non-stationary, the conventional frequency and time domain analysis does not provide better accuracy. So, in this work an attempt has been made to provide an overview of the determination of epilepsy by implementation of Hurst exponent (HE)-based discrete wavelet transform techniques for feature extraction from EEG data sets obtained during ictal and pre ictal stages of affected person and finally classifying EEG signals using SVM and KNN Classifiers. The The highest accuracy of 99% is obtained using SVM.

Fractal rigidity in migraine

NASA Astrophysics Data System (ADS)

Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz; West, Bruce J.

2004-04-01

We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.

Multi-scaling modelling in financial markets

NASA Astrophysics Data System (ADS)

Liu, Ruipeng; Aste, Tomaso; Di Matteo, T.

2007-12-01

In the recent years, a new wave of interest spurred the involvement of complexity in finance which might provide a guideline to understand the mechanism of financial markets, and researchers with different backgrounds have made increasing contributions introducing new techniques and methodologies. In this paper, Markov-switching multifractal models (MSM) are briefly reviewed and the multi-scaling properties of different financial data are analyzed by computing the scaling exponents by means of the generalized Hurst exponent H(q). In particular we have considered H(q) for price data, absolute returns and squared returns of different empirical financial time series. We have computed H(q) for the simulated data based on the MSM models with Binomial and Lognormal distributions of the volatility components. The results demonstrate the capacity of the multifractal (MF) models to capture the stylized facts in finance, and the ability of the generalized Hurst exponents approach to detect the scaling feature of financial time series.

The use of the Hurst exponent to investigate the global maximum of the Warsaw Stock Exchange WIG20 index

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2012-01-01

The WIG20 index-the index of the 20 biggest companies traded on the Warsaw Stock Exchange-reached the global maximum on 29th October 2007. I have used the local DFA (Detrended Functional Analysis) to obtain the Hurst exponent (diffusion exponent) and investigate the signature of anti-correlation of share price evolution around the maximum. The analysis was applied to the share price evolution for variable DFA parameters. For many values of parameters, the evidence of anti-correlation near the WIG20 maximum was pointed out.

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2011-01-01

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.

The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient

NASA Astrophysics Data System (ADS)

Cajueiro, Daniel O.; Tabak, Benjamin M.

2004-05-01

This paper is concerned with the assertion found in the financial literature that emerging markets are becoming more efficient over time. To verify whether this assertion is true or not, we propose the calculation of the Hurst exponent over time using a time window with 4 years of data. The data used here comprises the bulk of emerging markets for Latin America and Asia. Our empirical results show that this assertion seems to be true for most countries, but it does not hold for countries such as Brazil, The Philippines and Thailand. Moreover, in order to check whether or not these results depend on the short term memory and the volatility of returns common in such financial asset return data, we filter the data by an AR-GARCH procedure and present the Hurst exponents for this filtered data.

Comparative study of nonlinear properties of EEG signals of normal persons and epileptic patients

PubMed Central

2009-01-01

Background Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak et al. [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusion In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation. PMID:19619290

Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Yuan, Ying; Zhuang, Xin-tian; Jin, Xiu

2009-06-01

Analyzing the Shanghai stock price index daily returns using MF-DFA method, it is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and non-linear temporal correlations. Based on that, a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the generalized Hurst exponents h(q). Therefore, two measures, Δh and σ, based on generalized Hurst exponents were proposed to compare financial risks before and after Price Limits and Reform of Non-tradable Shares. The empirical results verify the validity of the measures, and this has led to a better understanding of complex stock markets.

Multifractal features in stock and foreign exchange markets

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Yoon, Seong-Min

2004-03-01

We investigate the tick dynamical behavior of three assets(the yen-dollar exchange rate, the won-dollar exchange rate, and the KOSPI) using the rescaled range analysis in stock and foreign exchange markets. The multifractal Hurst exponents with long-run memory effects can be obtained from assets, and we discuss whether it exists the crossover or not for the Hurst exponents at charateristic time scales. Particularly, we find that the probability distribution of prices is approached to a Lorentz distribution, different from fat-tailed properties.

Speckle patterns produced by an optical vortex and its application to surface roughness measurements.

PubMed

Passos, M H M; Lemos, M R; Almeida, S R; Balthazar, W F; da Silva, L; Huguenin, J A O

2017-01-10

In this work, we report on the analysis of speckle patterns produced by illuminating different rough surfaces with an optical vortex, a first-order (l=1) Laguerre-Gaussian beam. The generated speckle patterns were observed in the normal direction exploring four different planes: the diffraction plane, image plane, focal plane, and exact Fourier transform plane. The digital speckle patterns were analyzed using the Hurst exponent of digital images, an interesting tool used to study surface roughness. We show a proof of principle that the Hurst exponent of a digital speckle pattern is more sensitive with respect to the surface roughness when the speckle pattern is produced by an optical vortex and observed at a focal plane. We also show that Hurst exponents are not so sensitive with respect to the topological charge l. These results open news possibilities of investigation into speckle metrology once we have several techniques that use speckle patterns for different applications.

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

NASA Astrophysics Data System (ADS)

Cristescu, Constantin P.; Stan, Cristina; Scarlat, Eugen I.; Minea, Teofil; Cristescu, Cristina M.

2012-04-01

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.

An early prediction of 25th solar cycle using Hurst exponent

NASA Astrophysics Data System (ADS)

Singh, A. K.; Bhargawa, Asheesh

2017-11-01

The analysis of long memory processes in solar activity, space weather and other geophysical phenomena has been a major issue even after the availability of enough data. We have examined the data of various solar parameters like sunspot numbers, 10.7 cm radio flux, solar magnetic field, proton flux and Alfven Mach number observed for the year 1976-2016. We have done the statistical test for persistence of solar activity based on the value of Hurst exponent (H) which is one of the most classical applied methods known as rescaled range analysis. We have discussed the efficiency of this methodology as well as prediction content for next solar cycle based on long term memory. In the present study, Hurst exponent analysis has been used to investigate the persistence of above mentioned (five) solar activity parameters and a simplex projection analysis has been used to predict the ascension time and the maximum number of counts for 25th solar cycle. For available dataset of the year 1976-2016, we have calculated H = 0.86 and 0.82 for sunspot number and 10.7 cm radio flux respectively. Further we have calculated maximum number of counts for sunspot numbers and F10.7 cm index as 102.8± 24.6 and 137.25± 8.9 respectively. Using the simplex projection analysis, we have forecasted that the solar cycle 25th would start in the year 2021 (January) and would last up to the year 2031 (September) with its maxima in June 2024.

Visibility graph approach to exchange rate series

NASA Astrophysics Data System (ADS)

Yang, Yue; Wang, Jianbo; Yang, Huijie; Mang, Jingshi

2009-10-01

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.

How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Reboredo, Juan C.; Rivera-Castro, Miguel A.; Miranda, José G. V.; García-Rubio, Raquel

2013-04-01

In this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak-form efficiency, i.e., how long it takes for prices to adjust to a fractional Brownian motion with a Hurst exponent of 0.5. The Hurst exponent is estimated for different time horizons using detrended fluctuation analysis-a method suitable for non-stationary series with trends-in order to identify at which time scale the Hurst exponent is consistent with the efficient market hypothesis. Using high-frequency share price, exchange rate and stock data, we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min; thereafter, price dynamics was consistent with a geometric Brownian motion. The intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency, which would enable investors to exploit price deviations from fundamental values. This result is consistent with intraday volume, volatility and transaction time duration patterns.

Some comments on Hurst exponent and the long memory processes on capital markets

NASA Astrophysics Data System (ADS)

Sánchez Granero, M. A.; Trinidad Segovia, J. E.; García Pérez, J.

2008-09-01

The analysis of long memory processes in capital markets has been one of the topics in finance, since the existence of the market memory could implicate the rejection of an efficient market hypothesis. The study of these processes in finance is realized through Hurst exponent and the most classical method applied is R/S analysis. In this paper we will discuss the efficiency of this methodology as well as some of its more important modifications to detect the long memory. We also propose the application of a classical geometrical method with short modifications and we compare both approaches.

Modeling the Neurodynamics of Submarine Piloting and Navigation Teams

DTIC Science & Technology

2014-05-07

phenomena. The Hurst exponent , H, which is commonly used in a number of scientific fields, provides an estimate of correlation overtime scales...times series for a SPAN performance and CWT representation. The CWT is superimposed by scaling exponent trend near a time of stress. Scaling... exponents at the outset correspond to corrective or anticorrelated behavior. Scaling exponents increase throughout as the team manages the incident and

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

NASA Astrophysics Data System (ADS)

Gao, Feng-Yin; Kang, Yan-Mei; Chen, Xi; Chen, Guanrong

2018-05-01

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H ∈(1 /2 ,1 ) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H ∈(1 /2 ,1 ) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

Multifractality in plasma edge electrostatic turbulence

NASA Astrophysics Data System (ADS)

Neto, C. Rodrigues; Guimarães-Filho, Z. O.; Caldas, I. L.; Nascimento, I. C.; Kuznetsov, Yu. K.

2008-08-01

Plasma edge turbulence in Tokamak Chauffage Alfvén Brésilien (TCABR) [R. M. O. Galvão et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences.

Persistence Probability Analyzed on the Taiwan STOCK Market

NASA Astrophysics Data System (ADS)

Chen, I.-Chun; Chen, Hung-Jung; Tseng, Hsen-Che

We report a numerical study of the Taiwan stock market, in which we used three data sources: the daily Taiwan stock exchange index (TAIEX) from January 1983 to May 2006, the daily OTC index from January 1995 to May 2006, and the one-min intraday data from February 2000 to December 2003. Our study is based on numerical estimates of persistence exponent θp, Hurst exponent H2, and fluctuation exponent h2. We also discuss the results concerning persistence probability P(t), qth-order price-price correlation function Gq(t), and qth-order normalized fluctuation function fq(t) among these indices.

Patching C2n Time Series Data Holes using Principal Component Analysis

DTIC Science & Technology

2007-01-01

characteristic local scale exponent , regardless of dilation of the length examined. THE HURST PARAMETER There are a slew of methods13 available to...fractal dimension D0, which characterises the roughness of the data, and the Hurst parameter, H , which is a measure of the long range dependence (LRD...estimate H . For simplicity, we have opted to use the well known Hurst –Mandelbrot R/S technique, which is also the most elementary. The fitting curve

Investigation of the complexity of streamflow fluctuations in a large heterogeneous lake catchment in China

NASA Astrophysics Data System (ADS)

Ye, Xuchun; Xu, Chong-Yu; Li, Xianghu; Zhang, Qi

2018-05-01

The occurrence of flood and drought frequency is highly correlated with the temporal fluctuations of streamflow series; understanding of these fluctuations is essential for the improved modeling and statistical prediction of extreme changes in river basins. In this study, the complexity of daily streamflow fluctuations was investigated by using multifractal detrended fluctuation analysis (MF-DFA) in a large heterogeneous lake basin, the Poyang Lake basin in China, and the potential impacts of human activities were also explored. Major results indicate that the multifractality of streamflow fluctuations shows significant regional characteristics. In the study catchment, all the daily streamflow series present a strong long-range correlation with Hurst exponents bigger than 0.8. The q-order Hurst exponent h( q) of all the hydrostations can be characterized well by only two parameters: a (0.354 ≤ a ≤ 0.384) and b (0.627 ≤ b ≤ 0.677), with no pronounced differences. Singularity spectrum analysis pointed out that small fluctuations play a dominant role in all daily streamflow series. Our research also revealed that both the correlation properties and the broad probability density function (PDF) of hydrological series can be responsible for the multifractality of streamflow series that depends on watershed areas. In addition, we emphasized the relationship between watershed area and the estimated multifractal parameters, such as the Hurst exponent and fitted parameters a and b from the q-order Hurst exponent h( q). However, the relationship between the width of the singularity spectrum (Δ α) and watershed area is not clear. Further investigation revealed that increasing forest coverage and reservoir storage can effectively enhance the persistence of daily streamflow, decrease the hydrological complexity of large fluctuations, and increase the small fluctuations.

Stress Corrosion Cracking Study of Aluminum Alloys Using Electrochemical Noise Analysis

NASA Astrophysics Data System (ADS)

Rathod, R. C.; Sapate, S. G.; Raman, R.; Rathod, W. S.

2013-12-01

Stress corrosion cracking studies of aluminum alloys AA2219, AA8090, and AA5456 in heat-treated and non heat-treated condition were carried out using electrochemical noise technique with various applied stresses. Electrochemical noise time series data (corrosion potential vs. time) was obtained for the stressed tensile specimens in 3.5% NaCl aqueous solution at room temperature (27 °C). The values of drop in corrosion potential, total corrosion potential, mean corrosion potential, and hydrogen overpotential were evaluated from corrosion potential versus time series data. The electrochemical noise time series data was further analyzed with rescaled range ( R/ S) analysis proposed by Hurst to obtain the Hurst exponent. According to the results, higher values of the Hurst exponents with increased applied stresses showed more susceptibility to stress corrosion cracking as confirmed in case of alloy AA 2219 and AA8090.

Dynamical analyses of the time series for three foreign exchange rates

NASA Astrophysics Data System (ADS)

Kim, Sehyun; Kim, Soo Yong; Jung, Jae-Won; Kim, Kyungsik

2012-05-01

In this study, we investigate the multifractal properties of three foreign exchange rates (USD-KRW, USD-JPY, and EUR-USD) that are quoted with different economic scales. We estimate and analyze both the generalized Hurst exponent and the autocorrelation function in three foreign exchange rates. The USD-KRW is shown to have the strongest of the Hurst exponents when compared with the other two foreign exchange rates. In particular, the autocorrelation function of the USD-KRW has the largest memory behavior among three foreign exchange rates. It also exhibits a long-memory property in the first quarter, more than those in the other quarters.

Nonlinear Complexity Analysis of Brain fMRI Signals in Schizophrenia

PubMed Central

Sokunbi, Moses O.; Gradin, Victoria B.; Waiter, Gordon D.; Cameron, George G.; Ahearn, Trevor S.; Murray, Alison D.; Steele, Douglas J.; Staff, Roger T.

2014-01-01

We investigated the differences in brain fMRI signal complexity in patients with schizophrenia while performing the Cyberball social exclusion task, using measures of Sample entropy and Hurst exponent (H). 13 patients meeting diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM IV) criteria for schizophrenia and 16 healthy controls underwent fMRI scanning at 1.5 T. The fMRI data of both groups of participants were pre-processed, the entropy characterized and the Hurst exponent extracted. Whole brain entropy and H maps of the groups were generated and analysed. The results after adjusting for age and sex differences together show that patients with schizophrenia exhibited higher complexity than healthy controls, at mean whole brain and regional levels. Also, both Sample entropy and Hurst exponent agree that patients with schizophrenia have more complex fMRI signals than healthy controls. These results suggest that schizophrenia is associated with more complex signal patterns when compared to healthy controls, supporting the increase in complexity hypothesis, where system complexity increases with age or disease, and also consistent with the notion that schizophrenia is characterised by a dysregulation of the nonlinear dynamics of underlying neuronal systems. PMID:24824731

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

NASA Astrophysics Data System (ADS)

Pal, Mayukha; Madhusudana Rao, P.; Manimaran, P.

2014-12-01

We apply the recently developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation behavior and fractal nature between two non-stationary time series. We analyze the daily return price of gold, West Texas Intermediate and Brent crude oil, foreign exchange rate data, over a period of 18 years. The cross correlation has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, the existence of multifractal cross-correlation between all of these time series is found. We also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior. It was observed for five bivariate series that the cross-correlation exponents are less than the calculated average generalized Hurst exponents (GHE) for q<0 and greater than GHE when q>0 and for one bivariate series the cross-correlation exponent is greater than GHE for all q values.

Dispersion and Attenuation Due to Scattering from Heterogeneities of the Frame Bulk Modulus of a Poroelastic Medium

DTIC Science & Technology

2010-02-19

attenuation is a function of the Hurst exponent which characterizes the fractal het- erogeneity. Muller and Gurevich15,16 used statistical smoothing of...modified Bessel function of the third kind, Γ denotes the gamma function, and ν is the Hurst coefficient which is assumed to be 0 < ν ≤ 1. The three...The Hurst coefficient, ν, is ν = 0.1 (long-dashed line), ν = 0.5 (short-dashed line), and ν = 0.9 (long-short dashed line). In (a) the sound speed

Influence of government controls over the currency exchange rate in the evolution of Hurst's exponent: An autonomous agent-based model

NASA Astrophysics Data System (ADS)

Chávez Muñoz, Pablo; Fernandes da Silva, Marcus; Vivas Miranda, José; Claro, Francisco; Gomez Diniz, Raimundo

2007-12-01

We have studied the performance of the Hurst's index associated with the currency exchange rate in Brazil and Chile. It is shown that this index maps the degree of government control in the exchange rate. A model of supply and demand based in an autonomous agent is proposed, that simulates a virtual market of sale and purchase, where buyer or seller are forced to negotiate through an intermediary. According to this model, the average of the price of daily transactions correspond to the theoretical balance proposed by the law of supply and demand. The influence of an added tendency factor is also analyzed.

Extracting sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Jiang, Shan; Wang, Fang; Shen, Luming; Liao, Guiping; Wang, Lin

2017-03-01

Spectrum technology has been widely used in crop non-destructive testing diagnosis for crop information acquisition. Since spectrum covers a wide range of bands, it is of critical importance to extract the sensitive bands. In this paper, we propose a methodology to extract the sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis. Our obtained sensitive bands are relatively robust in the range of 534 nm-574 nm. Further, by using the multifractal parameter (Hurst exponent) of the extracted sensitive bands, we propose a prediction model to forecast the Soil and plant analyzer development values ((SPAD), often used as a parameter to indicate the chlorophyll content) and an identification model to distinguish the different planting patterns. Three vegetation indices (VIs) based on previous work are used for comparison. Three evaluation indicators, namely, the root mean square error, the correlation coefficient, and the relative error employed in the SPAD values prediction model all demonstrate that our Hurst exponent has the best performance. Four rapeseed compound planting factors, namely, seeding method, planting density, fertilizer type, and weed control method are considered in the identification model. The Youden indices calculated by the random decision forest method and the K-nearest neighbor method show that our Hurst exponent is superior to other three Vis, and their combination for the factor of seeding method. In addition, there is no significant difference among the five features for other three planting factors. This interesting finding suggests that the transplanting and the direct seeding would make a big difference in the growth of rapeseed.

Generalized Hurst exponent approach to efficiency in MENA markets

NASA Astrophysics Data System (ADS)

Sensoy, A.

2013-10-01

We study the time-varying efficiency of 15 Middle East and North African (MENA) stock markets by generalized Hurst exponent analysis of daily data with a rolling window technique. The study covers a time period of six years from January 2007 to December 2012. The results reveal that all MENA stock markets exhibit different degrees of long-range dependence varying over time and that the Arab Spring has had a negative effect on market efficiency in the region. The least inefficient market is found to be Turkey, followed by Israel, while the most inefficient markets are Iran, Tunisia, and UAE. Turkey and Israel show characteristics of developed financial markets. Reasons and implications are discussed.

Fractality Evidence and Long-Range Dependence on Capital Markets: a Hurst Exponent Evaluation

NASA Astrophysics Data System (ADS)

Oprean, Camelia; Tănăsescu, Cristina

2014-07-01

Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.

Modelling the time behaviour of a self-organized seismic region: a cellular automaton with memory

NASA Astrophysics Data System (ADS)

Cisternas, A.; Rivera, L.; Munoz, D.

2003-04-01

The range of a cumulative sequence of earthquake moments in a seismic region varies according to Hurst's law, namely a power law in the length of the time window. The range allows for an estimation of Mmax in a seismic zone. In the case of an independent process, the Hurst exponent H is 0.5. Memory implies 0.5

Complex Analysis of Combat in Afghanistan

DTIC Science & Technology

2014-12-01

analysis we have β−ffE ~)( where β= 2H - 1 = 1 - γ, with H being the Hurst exponent , related to the correlation exponent γ. Usually, real-world data are...statistical nature. In every instance we found strong power law correlations in the data, and were able to extract accurate scaling exponents . On the... exponents , α. The case αɘ.5 corresponds to long-term anti-correlations, meaning that large values are most likely to be followed by small values and

Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data

NASA Astrophysics Data System (ADS)

von Wegner, Frederic; Laufs, Helmut; Tagliazucchi, Enzo

2018-02-01

Long-range memory in time series is often quantified by the Hurst exponent H , a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H >0.5 ) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H >0.5 , whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.

Effect of Trader Composition on Stock Market

NASA Astrophysics Data System (ADS)

Wang, Mo-Gei; Wang, Xing-Yuan; Liu, Zhen-Zhen

2011-05-01

In this study, we build a double auction market model, which contains two types of agent traders, i.e., the noise traders and fundamentalists, to investigate the effect of the trader composition on the stock market. It is found that, the non-trivial Hurst exponent and the fat-tailed distribution of transaction prices can be observed at any ratio of the noise traders. Analyses on the price variation properties, including the Hurst exponent and the price variation region, show that these properties are stable when the ratio is moderate. However, the non-price variation properties, including the trading volume and the profitability of the two kinds of agents, do not keep stable untrivially in any interval of the ratio of noise traders.

Multiscale multifractal detrended-fluctuation analysis of two-dimensional surfaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Fan, Qingju; Stanley, H. Eugene

2016-04-01

Two-dimensional (2D) multifractal detrended fluctuation analysis (MF-DFA) has been used to study monofractality and multifractality on 2D surfaces, but when it is used to calculate the generalized Hurst exponent in a fixed time scale, the presence of crossovers can bias the outcome. To solve this problem, multiscale multifractal analysis (MMA) was recent employed in a one-dimensional case. MMA produces a Hurst surface h (q ,s ) that provides a spectrum of local scaling exponents at different scale ranges such that the positions of the crossovers can be located. We apply this MMA method to a 2D surface and identify factors that influence the results. We generate several synthesized surfaces and find that crossovers are consistently present, which means that their fractal properties differ at different scales. We apply MMA to the surfaces, and the results allow us to observe these differences and accurately estimate the generalized Hurst exponents. We then study eight natural texture images and two real-world images and find (i) that the moving window length (WL) and the slide length (SL) are the key parameters in the MMA method, that the WL more strongly influences the Hurst surface than the SL, and that the combination of WL =4 and SL =4 is optimal for a 2D image; (ii) that the robustness of h (2 ,s ) to four common noises is high at large scales but variable at small scales; and (iii) that the long-term correlations in the images weaken as the intensity of Gaussian noise and salt and pepper noise is increased. Our findings greatly improve the performance of the MMA method on 2D surfaces.

Optical Measurements in Non-Equilibrium Plasmas and Flows

DTIC Science & Technology

2009-09-01

collision model, the exponent x is equal to 0.5, from simple kinetic theory. For most realistic inter-molecular potentials, the exponent x is in the range...Chemical Physics, Vol. 89, p. 5568 (1988). 9. Rosasco, G.J., Lempert, W., Hurst , W.S., and Fein, A., in “Spectral Line Shapes, Vol 2, Walter de Gruyter

Fractal and Chaos Analysis for Dynamics of Radon Exhalation from Uranium Mill Tailings

NASA Astrophysics Data System (ADS)

Li, Yongmei; Tan, Wanyu; Tan, Kaixuan; Liu, Zehua; Xie, Yanshi

2016-08-01

Tailings from mining and milling of uranium ores potentially are large volumes of low-level radioactive materials. A typical environmental problem associated with uranium tailings is radon exhalation, which can significantly pose risks to environment and human health. In order to reduce these risks, it is essential to study the dynamical nature and underlying mechanism of radon exhalation from uranium mill tailings. This motivates the conduction of this study, which is based on the fractal and chaotic methods (e.g. calculating the Hurst exponent, Lyapunov exponent and correlation dimension) and laboratory experiments of the radon exhalation rates. The experimental results show that the radon exhalation rate from uranium mill tailings is highly oscillated. In addition, the nonlinear analyses of the time series of radon exhalation rate demonstrate the following points: (1) the value of Hurst exponent much larger than 0.5 indicates non-random behavior of the radon time series; (2) the positive Lyapunov exponent and non-integer correlation dimension of the time series imply that the radon exhalation from uranium tailings is a chaotic dynamical process; (3) the required minimum number of variables should be five to describe the time evolution of radon exhalation. Therefore, it can be concluded that the internal factors, including heterogeneous distribution of radium, and randomness of radium decay, as well as the fractal characteristics of the tailings, can result in the chaotic evolution of radon exhalation from the tailings.

Identifying major depressive disorder using Hurst exponent of resting-state brain networks.

PubMed

Wei, Maobin; Qin, Jiaolong; Yan, Rui; Li, Haoran; Yao, Zhijian; Lu, Qing

2013-12-30

Resting-state functional magnetic resonance imaging (fMRI) studies of major depressive disorder (MDD) have revealed abnormalities of functional connectivity within or among the resting-state networks. They provide valuable insight into the pathological mechanisms of depression. However, few reports were involved in the "long-term memory" of fMRI signals. This study was to investigate the "long-term memory" of resting-state networks by calculating their Hurst exponents for identifying depressed patients from healthy controls. Resting-state networks were extracted from fMRI data of 20 MDD and 20 matched healthy control subjects. The Hurst exponent of each network was estimated by Range Scale analysis for further discriminant analysis. 95% of depressed patients and 85% of healthy controls were correctly classified by Support Vector Machine with an accuracy of 90%. The right fronto-parietal and default mode network constructed a deficit network (lower memory and more irregularity in MDD), while the left fronto-parietal, ventromedial prefrontal and salience network belonged to an excess network (longer memory in MDD), suggesting these dysfunctional networks may be related to a portion of the complex of emotional and cognitive disturbances. The abnormal "long-term memory" of resting-state networks associated with depression may provide a new possibility towards the exploration of the pathophysiological mechanisms of MDD. © 2013 Elsevier Ireland Ltd. All rights reserved.

Anomalous scaling of stochastic processes and the Moses effect

NASA Astrophysics Data System (ADS)

Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Anomalous scaling of stochastic processes and the Moses effect.

PubMed

Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Statistical analysis of Geopotential Height (GH) timeseries based on Tsallis non-extensive statistical mechanics

NASA Astrophysics Data System (ADS)

Karakatsanis, L. P.; Iliopoulos, A. C.; Pavlos, E. G.; Pavlos, G. P.

2018-02-01

In this paper, we perform statistical analysis of time series deriving from Earth's climate. The time series are concerned with Geopotential Height (GH) and correspond to temporal and spatial components of the global distribution of month average values, during the period (1948-2012). The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis' q-triplet, namely {qstat, qsens, qrel}, the reconstructed phase space and the estimation of correlation dimension and the Hurst exponent of rescaled range analysis (R/S). The deviation of Tsallis q-triplet from unity indicates non-Gaussian (Tsallis q-Gaussian) non-extensive character with heavy tails probability density functions (PDFs), multifractal behavior and long range dependences for all timeseries considered. Also noticeable differences of the q-triplet estimation found in the timeseries at distinct local or temporal regions. Moreover, in the reconstructive phase space revealed a lower-dimensional fractal set in the GH dynamical phase space (strong self-organization) and the estimation of Hurst exponent indicated multifractality, non-Gaussianity and persistence. The analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth's climate.

A signal processing based analysis and prediction of seizure onset in patients with epilepsy

PubMed Central

Namazi, Hamidreza; Kulish, Vladimir V.

2016-01-01

One of the main areas of behavioural neuroscience is forecasting the human behaviour. Epilepsy is a central nervous system disorder in which nerve cell activity in the brain becomes disrupted, causing seizures or periods of unusual behaviour, sensations and sometimes loss of consciousness. An estimated 5% of the world population has epileptic seizure but there is not any method to cure it. More than 30% of people with epilepsy cannot control seizure. Epileptic seizure prediction, refers to forecasting the occurrence of epileptic seizures, is one of the most important but challenging problems in biomedical sciences, across the world. In this research we propose a new methodology which is based on studying the EEG signals using two measures, the Hurst exponent and fractal dimension. In order to validate the proposed method, it is applied to epileptic EEG signals of patients by computing the Hurst exponent and fractal dimension, and then the results are validated versus the reference data. The results of these analyses show that we are able to forecast the onset of a seizure on average of 25.76 seconds before the time of occurrence. PMID:26586477

Effect of angle of deposition on the Fractal properties of ZnO thin film surface

NASA Astrophysics Data System (ADS)

Yadav, R. P.; Agarwal, D. C.; Kumar, Manvendra; Rajput, Parasmani; Tomar, D. S.; Pandey, S. N.; Priya, P. K.; Mittal, A. K.

2017-09-01

Zinc oxide (ZnO) thin films were prepared by atom beam sputtering at various deposition angles in the range of 20-75°. The deposited thin films were examined by glancing angle X-ray diffraction and atomic force microscopy (AFM). Scaling law analysis was performed on AFM images to show that the thin film surfaces are self-affine. Fractal dimension of each of the 256 vertical sections along the fast scan direction of a discretized surface, obtained from the AFM height data, was estimated using the Higuchi's algorithm. Hurst exponent was computed from the fractal dimension. The grain sizes, as determined by applying self-correlation function on AFM micrographs, varied with the deposition angle in the same manner as the Hurst exponent.

Focused-based multifractal analysis of the wake in a wind turbine array utilizing proper orthogonal decomposition

NASA Astrophysics Data System (ADS)

Kadum, Hawwa; Ali, Naseem; Cal, Raúl

2016-11-01

Hot-wire anemometry measurements have been performed on a 3 x 3 wind turbine array to study the multifractality of the turbulent kinetic energy dissipations. A multifractal spectrum and Hurst exponents are determined at nine locations downstream of the hub height, and bottom and top tips. Higher multifractality is found at 0.5D and 1D downstream of the bottom tip and hub height. The second order of the Hurst exponent and combination factor show an ability to predict the flow state in terms of its development. Snapshot proper orthogonal decomposition is used to identify the coherent and incoherent structures and to reconstruct the stochastic velocity using a specific number of the POD eigenfunctions. The accumulation of the turbulent kinetic energy in top tip location exhibits fast convergence compared to the bottom tip and hub height locations. The dissipation of the large and small scales are determined using the reconstructed stochastic velocities. The higher multifractality is shown in the dissipation of the large scale compared to small-scale dissipation showing consistency with the behavior of the original signals.

Application of Fractal theory for crash rate prediction: Insights from random parameters and latent class tobit models.

PubMed

Chand, Sai; Dixit, Vinayak V

2018-03-01

The repercussions from congestion and accidents on major highways can have significant negative impacts on the economy and environment. It is a primary objective of transport authorities to minimize the likelihood of these phenomena taking place, to improve safety and overall network performance. In this study, we use the Hurst Exponent metric from Fractal Theory, as a congestion indicator for crash-rate modeling. We analyze one month of traffic speed data at several monitor sites along the M4 motorway in Sydney, Australia and assess congestion patterns with the Hurst Exponent of speed (H speed ). Random Parameters and Latent Class Tobit models were estimated, to examine the effect of congestion on historical crash rates, while accounting for unobserved heterogeneity. Using a latent class modeling approach, the motorway sections were probabilistically classified into two segments, based on the presence of entry and exit ramps. This will allow transportation agencies to implement appropriate safety/traffic countermeasures when addressing accident hotspots or inadequately managed sections of motorway. Copyright © 2017 Elsevier Ltd. All rights reserved.

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series

NASA Astrophysics Data System (ADS)

Ausloos, M.

2012-09-01

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined: two written texts by one author (Lewis Carroll) are considered, together with one translation into an artificial language (i.e., Esperanto) are mapped into time series. Their corresponding shuffled versions are used for obtaining a baseline. Two different one-dimensional time series are used here: one based on word lengths (LTS), the other on word frequencies (FTS). It is shown that the generalized Hurst exponent h(q) and the derived f(α) curves of the original and translated texts show marked differences. The original texts are far from giving a parabolic f(α) function, in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time-asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS f(α) curves are more opened than the LTS ones.

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series.

PubMed

Ausloos, M

2012-09-01

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined: two written texts by one author (Lewis Carroll) are considered, together with one translation into an artificial language (i.e., Esperanto) are mapped into time series. Their corresponding shuffled versions are used for obtaining a baseline. Two different one-dimensional time series are used here: one based on word lengths (LTS), the other on word frequencies (FTS). It is shown that the generalized Hurst exponent h(q) and the derived f(α) curves of the original and translated texts show marked differences. The original texts are far from giving a parabolic f(α) function, in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time-asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS f(α) curves are more opened than the LTS ones.

The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2017-02-01

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.

Anti-correlation and multifractal features of Spain electricity spot market

NASA Astrophysics Data System (ADS)

Norouzzadeh, P.; Dullaert, W.; Rahmani, B.

2007-07-01

We use multifractal detrended fluctuation analysis (MF-DFA) to numerically investigate correlation, persistence, multifractal properties and scaling behavior of the hourly spot prices for the Spain electricity exchange-Compania O Peradora del Mercado de Electricidad (OMEL). Through multifractal analysis, fluctuations behavior, the scaling exponents and generalized Hurst exponents are studied. Moreover, contribution of fat-tailed probability distributions and nonlinear temporal correlations to multifractality is studied.

R/S analysis of reaction time in Neuron Type Test for human activity in civil aviation

NASA Astrophysics Data System (ADS)

Zhang, Hong-Yan; Kang, Ming-Cui; Li, Jing-Qiang; Liu, Hai-Tao

2017-03-01

Human factors become the most serious problem leading to accidents of civil aviation, which stimulates the design and analysis of Neuron Type Test (NTT) system to explore the intrinsic properties and patterns behind the behaviors of professionals and students in civil aviation. In the experiment, normal practitioners' reaction time sequences, collected from NTT, exhibit log-normal distribution approximately. We apply the χ2 test to compute the goodness-of-fit by transforming the time sequence with Box-Cox transformation to cluster practitioners. The long-term correlation of different individual practitioner's time sequence is represented by the Hurst exponent via Rescaled Range Analysis, also named by Range/Standard deviation (R/S) Analysis. The different Hurst exponent suggests the existence of different collective behavior and different intrinsic patterns of human factors in civil aviation.

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

NASA Astrophysics Data System (ADS)

Buonocore, R. J.; Aste, T.; Di Matteo, T.

2017-04-01

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

Nonlinear Dynamics Used to Classify Effects of Mild Traumatic Brain Injury

DTIC Science & Technology

2012-01-11

evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both Shannon and Renyi entropy...fluctuation analysis to evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both...often called the Hurst parameter [32]. When the scaling law described by Eq. (2) holds, the September 2011 I Volume 6 I Issue 9 I e24446 -Q.384

The role of Hurst exponent on cold field electron emission from conducting materials: from electric field distribution to Fowler-Nordheim plots

PubMed Central

de Assis, T. A.

2015-01-01

This work considers the effects of the Hurst exponent (H) on the local electric field distribution and the slope of the Fowler-Nordheim (FN) plot when considering the cold field electron emission properties of rough Large-Area Conducting Field Emitter Surfaces (LACFESs). A LACFES is represented by a self-affine Weierstrass-Mandelbrot function in a given spatial direction. For 0.1 ≤ H < 0.5, the local electric field distribution exhibits two clear exponential regimes. Moreover, a scaling between the macroscopic current density () and the characteristic kernel current density (), , with an H-dependent exponent , has been found. This feature, which is less pronounced (but not absent) in the range where more smooth surfaces have been found (), is a consequence of the dependency between the area efficiency of emission of a LACFES and the macroscopic electric field, which is often neglected in the interpretation of cold field electron emission experiments. Considering the recent developments in orthodox field emission theory, we show that the exponent must be considered when calculating the slope characterization parameter (SCP) and thus provides a relevant method of more precisely extracting the characteristic field enhancement factor from the slope of the FN plot. PMID:26035290

The scale-dependent market trend: Empirical evidences using the lagged DFA method

NASA Astrophysics Data System (ADS)

Li, Daye; Kou, Zhun; Sun, Qiankun

2015-09-01

In this paper we make an empirical research and test the efficiency of 44 important market indexes in multiple scales. A modified method based on the lagged detrended fluctuation analysis is utilized to maximize the information of long-term correlations from the non-zero lags and keep the margin of errors small when measuring the local Hurst exponent. Our empirical result illustrates that a common pattern can be found in the majority of the measured market indexes which tend to be persistent (with the local Hurst exponent > 0.5) in the small time scale, whereas it displays significant anti-persistent characteristics in large time scales. Moreover, not only the stock markets but also the foreign exchange markets share this pattern. Considering that the exchange markets are only weakly synchronized with the economic cycles, it can be concluded that the economic cycles can cause anti-persistence in the large time scale but there are also other factors at work. The empirical result supports the view that financial markets are multi-fractal and it indicates that deviations from efficiency and the type of model to describe the trend of market price are dependent on the forecasting horizon.

A Novel Signal Modeling Approach for Classification of Seizure and Seizure-Free EEG Signals.

PubMed

Gupta, Anubha; Singh, Pushpendra; Karlekar, Mandar

2018-05-01

This paper presents a signal modeling-based new methodology of automatic seizure detection in EEG signals. The proposed method consists of three stages. First, a multirate filterbank structure is proposed that is constructed using the basis vectors of discrete cosine transform. The proposed filterbank decomposes EEG signals into its respective brain rhythms: delta, theta, alpha, beta, and gamma. Second, these brain rhythms are statistically modeled with the class of self-similar Gaussian random processes, namely, fractional Brownian motion and fractional Gaussian noises. The statistics of these processes are modeled using a single parameter called the Hurst exponent. In the last stage, the value of Hurst exponent and autoregressive moving average parameters are used as features to design a binary support vector machine classifier to classify pre-ictal, inter-ictal (epileptic with seizure free interval), and ictal (seizure) EEG segments. The performance of the classifier is assessed via extensive analysis on two widely used data set and is observed to provide good accuracy on both the data set. Thus, this paper proposes a novel signal model for EEG data that best captures the attributes of these signals and hence, allows to boost the classification accuracy of seizure and seizure-free epochs.

Memory persistency and nonlinearity in daily mean dew point across India

NASA Astrophysics Data System (ADS)

Ray, Rajdeep; Khondekar, Mofazzal Hossain; Ghosh, Koushik; Bhattacharjee, Anup Kumar

2016-04-01

Enterprising endeavour has been taken in this work to realize and estimate the persistence in memory of the daily mean dew point time series obtained from seven different weather stations viz. Kolkata, Chennai (Madras), New Delhi, Mumbai (Bombay), Bhopal, Agartala and Ahmedabad representing different geographical zones in India. Hurst exponent values reveal an anti-persistent behaviour of these dew point series. To affirm the Hurst exponent values, five different scaling methods have been used and the corresponding results are compared to synthesize a finer and reliable conclusion out of it. The present analysis also bespeaks that the variation in daily mean dew point is governed by a non-stationary process with stationary increments. The delay vector variance (DVV) method has been exploited to investigate nonlinearity, and the present calculation confirms the presence of deterministic nonlinear profile in the daily mean dew point time series of the seven stations.

Long-term persistence of solar activity

NASA Technical Reports Server (NTRS)

Ruzmaikin, Alexander; Feynman, Joan; Robinson, Paul

1994-01-01

We examine the question of whether or not the non-periodic variations in solar activity are caused by a white-noise, random process. The Hurst exponent, which characterizes the persistence of a time series, is evaluated for the series of C-14 data for the time interval from about 6000 BC to 1950 AD. We find a constant Hurst exponent, suggesting that solar activity in the frequency range from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate, H approximately 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process and that it is the same type of process over a wide range of time interval lengths.

Relation between the Surface Friction of Plates and their Statistical Microgeometry

DTIC Science & Technology

1980-01-01

3-6 and 𔃽-7. Calibration-- are taken for each of the Uicr~r unit exponent values and best fit li;nes by least squares fitted through each"n set of...parameter, [ = 1.de (2-43) (Clauser 1954, 1956). Data from near equilibrium flows (Coles & Hurst 1968) was plotted along with some typical non-equilibrium...too bad a fit even for the non equilibrium flows. Coles and Hurst (1968) recommended that the fit of the law of the wake to velocity profiles should be

Price-volume multifractal analysis of the Moroccan stock market

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane

2017-11-01

In this paper, we analyzed price-volume multifractal cross-correlations of Moroccan Stock Exchange. We chose the period from January 1st 2000 to January 20th 2017 to investigate the multifractal behavior of price change and volume change series. Then, we used multifractal detrended cross-correlations analysis method (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) to analyze the series. We computed bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross-correlations. Furthermore, we used detrended cross-correlations coefficient (DCCA) and cross-correlation test (Q(m)) to analyze cross-correlation quantitatively and qualitatively. By analyzing results, we found existence of price-volume multifractal cross-correlations. The spectrum width has a strong multifractal cross-correlation. We remarked that volume change series is anti-persistent when we analyzed the generalized Hurst exponent for all moments q. The cross-correlation test showed the presence of a significant cross-correlation. However, DCCA coefficient had a small positive value, which means that the level of correlation is not very significant. Finally, we analyzed sources of multifractality and their degree of contribution in the series.

Cross-correlations between agricultural commodity futures markets in the US and China

NASA Astrophysics Data System (ADS)

Li, Zhihui; Lu, Xinsheng

2012-08-01

This paper examines the cross-correlation properties of agricultural futures markets between the US and China using a cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). The results show that the cross-correlations between the two geographically distant markets for four pairs of important agricultural commodities futures are significantly multifractal. By introducing the concept of a “crossover”, we find that the multifractality of cross-correlations between the two markets is not long lasting. The cross-correlations in the short term are more strongly multifractal, but they are weakly so in the long term. Moreover, cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term while cross-correlations of all kinds of fluctuations for soy bean and soy meal futures are persistent and for corn and wheat futures are anti-persistent in the long term. We also find that cross-correlation exponents are less than the averaged generalized Hurst exponent when q<0 and more than the averaged generalized Hurst exponent when q>0 in the short term, while in the long term they are almost the same.

Quantum Mechanical Studies of Molecular Hyperpolarizabilities.

DTIC Science & Technology

1980-04-30

exponent , reflects the screening of an electron in a given orbital by the interior electrons in the atom or molecule. In practice, when studying...Basis sets have evolved over the years in molecular quantum mechanics until sets of orbital exponents for the different atoms composing the molecule have...and R. P. Hurst , J. Chem. Phys. 46, 2356 (1967); S. P. LickmannI and J. W. Moskowitz, J. Chem. Phys. 54, 3622 7T971). 26. T. H. Dunning, J. Chem. Phys

Cost Benefit Assessment of Candidate Decision Aids for Naval Air ASW.

DTIC Science & Technology

1981-09-01

and I respectively), the value of the term where they appear has an increasingly pronounced effect. The exponents were included simply to limit the...effect of these terms to the cases when the limits are very nearly reached. The difference in exponents reflects giving more weight to T than to S. The...MD 20670 Dr. G. Hurst University of Pennsylvania Dr. Amos Freedy Wharton School Perceptronics, Inc. Philadelphia, PA 19174 6271 Variel Avenue

Approximate Probabilistic Methods for Survivability/Vulnerability Analysis of Strategic Structures.

DTIC Science & Technology

1978-07-15

weapon yield, in kilotons; K = energy coupling factor; C = coefficient determined from linear regression; a, b = exponents determined from linear...hn(l + .582 00 = 0.54 In the case of the applied pressure, according to Perret and Bass (1975), the variabilities in the exponents a and b of Eq. 32...ATTN: WESSF, L. Ingram ATTN: ATC-T ATTN: Library ATTN: F. Brown BMD Systems Command ATTN: J. Strange Deoartment of the Army ATTN: BMDSC-H, N. Hurst

WESCOM. A Fortran Code for Evaluation of Nuclear Weapon Effects on Satellite Communications. Volume 2. Code Structure

DTIC Science & Technology

1981-01-31

quantities for h i ;.;h-:t It i 1 ndc hurst s 1BMI.I Determines t ime-independent fireball quantities for low-altitude bursts 10 Table 1...of reference Oval of Cassini (km) LAFBP - vortex longitudinal radius (km) LAFBP - vortex transverse radius (km) Power law exponent Inner scale...Maximum slant range of ionization from transmitter (km) Power law exponent Frequency (Hz) Striation velocity flag Propagation path index Radius

Hurst exponent used as a tool to differentiate between magmatic and fluid-induced processes as reflected in crystal geochemistry

NASA Astrophysics Data System (ADS)

Domonik, A.; Słaby, E.; Śmigielski, M.

2012-04-01

A self-similarity parameter, the Hurst exponent (H) (called also roughness exponent) has been used to show the long-range dependence of element behaviour during the processes. The H value ranges between 0 and 1; a value of 0.5 indicates a random distribution indistinguishable from noise. For values greater or less than 0.5, the system shows non-linear dynamics. H < 0.5 represents anti-persistent (more chaotic) behaviour, whereas H > 0.5 corresponds to increasing persistence (less chaotic). Such persistence is characterized as an effect of a long-term memory, and thus by a large degree of positive correlation. In theory, the preceding data constantly affect the next in the whole temporal series. Applied to chaotic dynamics, the system shows a subtle sensitivity to initial conditions. The process can show some degree of chaos, due to local variations, but generally, the trend preserves its persistent character through time. If the exponent value is low, the process shows frequent and sudden reversals e.g. the trends of such a process show mutual negative correlation of the succeding values in the data series. Thus, the system can be described as having a high degree of deterministic chaos. Alkali feldspar megacrysts grown from mixed magmas and recrystallized due to interaction with fluids have been selected for the study (Słaby et al., 2011). Hurst exponent variability has been calculated within some primary-magmatic and secondary-recrystallized crystal domains for some elements redistributed by crystal fluid interaction. Based on the Hurst exponent value two different processes can easily be recognized. In the core of the megacrysts the element distribution can be ascribed to magmatic growth. By contrast, the marginal zones can relate to inferred late crystal-fluid interactions. Both processes are deterministic, not random. The spatial distribution of elements in the crystal margins is irregular, with high-H values identifying the process as persistent. The trace element distributions in feldspar cores are almost homogeneous and only relatively small and irregular variations in trace element contents makes their growth morphology slightly patchy. Despite homogenization the fractal statistics reveal that trace elements were incorporated chaotically into the growing crystal. The anti-persistent chaotic behaviour of elements during magmatic growth of the feldspars progressively changes into persistent behaviour within domains, where re-crystallization reaction took place. Elements demonstrate variable dynamics of this exchange corresponding to increasing persistency. This dynamics is different for individual elements compared to analogical, observed for crystallization process proceeding from mixed magmas. Consequently, it appears that fractal statistics clearly discriminate between two different processes, with contrasted element behaviour during these processes. One process is magma crystallization and it is recorded in the core of the megacrysts; the second is recorded in the crystal rims and along cleavages and cracks, such that it can be related to a post-crystallization process linked to fluid percolation. Słaby, E., Martin, H., Hamada, M., Śmigielski, M., Domonik, A., Götze, J., Hoefs, J., Hałas, S., Simon, K., Devidal, J-L., Moyen, J-F., Jayananda, M. (2011) Evidence in Archaean alkali-feldspar megacrysts for high-temperature interaction with mantle fluids. Journal of Petrology (on line). doi:10.1093/petrology/egr056

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the ``Chaos Game Representation'' (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene- coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent ``sub-periods'' in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration. This work examines the model's behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system ``information dynamics'' correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed.

Plasma Wave Turbulence and Particle Heating Caused by Electron Beams, Radiation and Pinches.

DTIC Science & Technology

1982-05-01

Eq. (1) gives the quasi- longitudinal disier si i type-Ill solar radio hursts . ’i for the radar-modified relation for an oblique Langni i.-.ave...Detailed cot’" irisons are miade v. oh (other i-ditsol models of-strong" Langmuir turbulence associated with type Ill hurst -s 1. INTRODUCTION Zakharov...1,1;, Ail ft oscillites abtout :in averaige v~uims that tiv,’ri expon - (ti v h. (1’-25, andn (c) s- 6. 412!t1. ev~w, , enti:,t in time’. lioi, ,-t

Hurst exponent of very long birth time series in XX century Romania. Social and religious aspects

NASA Astrophysics Data System (ADS)

Rotundo, G.; Ausloos, M.; Herteliu, C.; Ileanu, B.

2015-07-01

The Hurst exponent of very long birth time series in Romania has been extracted from official daily records, i.e. over 97 years between 1905 and 2001 included. The series result from distinguishing between families located in urban (U) or rural (R) areas, and belonging (Ox) or not (NOx) to the orthodox religion. Four time series combining both criteria, (U,R) and (Ox, NOx), are also examined. A statistical information is given on these sub-populations measuring their XX-th century state as a snapshot. However, the main goal is to investigate whether the "daily" production of babies is purely noisy or is fluctuating according to some non trivial fractional Brownian motion, - in the four types of populations, characterized by either their habitat or their religious attitude, yet living within the same political regime. One of the goals was also to find whether combined criteria implied a different behavior. Moreover, we wish to observe whether some seasonal periodicity exists. The detrended fluctuation analysis technique is used for finding the fractal correlation dimension of such (9) signals. It has been first necessary, due to two periodic tendencies, to define the range regime in which the Hurst exponent is meaningfully defined. It results that the birth of babies in all cases is a very strongly persistent signal. It is found that the signal fractal correlation dimension is weaker (i) for NOx than for Ox, and (ii) or U with respect to R. Moreover, it is observed that the combination of U or R with NOx or OX enhances the UNOx, UOx, and ROx fluctuations, but smoothens the RNOx signal, thereby suggesting a stronger conditioning on religiosity rituals or rules.

The scaling behavior of hand motions reveals self-organization during an executive function task

NASA Astrophysics Data System (ADS)

Anastas, Jason R.; Stephen, Damian G.; Dixon, James A.

2011-05-01

Recent approaches to cognition explain cognitive phenomena in terms of interaction-dominant dynamics. In the current experiment, we extend this approach to executive function, a construct used to describe flexible, goal-oriented behavior. Participants were asked to perform a widely used executive function task, card sorting, under two conditions. In one condition, participants were given a rule with which to sort the cards. In the other condition, participants had to induce the rule from experimenter feedback. The motion of each participant’s hand was tracked during the sorting task. Detrended fluctuation analysis was performed on the inter-point time series using a windowing strategy to capture changes over each trial. For participants in the induction condition, the Hurst exponent sharply increased and then decreased. The Hurst exponents for the explicit condition did not show this pattern. Our results suggest that executive function may be understood in terms of changes in stability that arise from interaction-dominant dynamics.

Multifractal detrended fluctuation analysis to characterize phase couplings in seahorse (Hippocampus kuda) feeding clicks.

PubMed

Haris, K; Chakraborty, Bishwajit; Menezes, A; Sreepada, R A; Fernandes, W A

2014-10-01

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α) calculated in the procedure followed were analyzed to comprehend the underlying nonlinearities in the seahorse clicks. The analyses carried out reveal long-range power-law correlation properties in the data, substantiating the multifractal behavior. The resulting h(q) spectrum exhibits a distinct characteristic pattern in relation to the seahorse sex and size, and reveals a spectral blind spot in the data that was not possible to detect by conventional spectral analyses. The corresponding multifractal spectrum related width parameter Δh(q) is well clustered, defining the individual seahorse clicks. The highest degree of multifractality is evident in the 18 cm male seahorse, signifying greater heterogeneity. A further comparison between the seahorse body size and weight (wet) with respect to the width parameter Δh(q) and the second-order Hurst exponent h(q=2) underscores the versatility of MFDFA as a robust statistical tool to analyze bioacoustic observations.

How microfracture roughness can be used to distinguish between exhumed cracks and in-situ flow paths in shales

NASA Astrophysics Data System (ADS)

Pluymakers, Anne; Kobchenko, Maya; Renard, François

2017-01-01

Flow through fractures in shales is of importance to many geoengineering purposes. Shales are not only caprocks to hydrocarbon reservoirs and nuclear waste or CO2 storage sites, but also potential source and reservoir rocks for hydrocarbons. The presence of microfractures in shales controls their permeability and transport properties. Using X-ray micro-tomography and white light interferometry we scanned borehole samples obtained from 4 km depth in the Pomeranian shales in Poland. These samples contain open exhumation/drying cracks as well as intact vein-rock interfaces plus one striated slip surface. At micron resolution and above tensile drying cracks exhibit a power-law roughness with a scaling exponent, called the Hurst exponent H, of 0.3. At sub-micron resolution we capture the properties of the clay interface only, with H = 0.6. In contrast, the in-situ formed veins and slip surface exhibit H = 0.4-0.5, which is deemed representative for in-situ fractures. These results are discussed in relation to the shale microstructure and linear elastic fracture mechanics theory. The data imply that the Hurst roughness exponent can be used as a microstructural criterion to distinguish between exhumation and in-situ fractures, providing a step forward towards the characterization of potential flow paths at depth in shales.

A Brainnetome Atlas Based Mild Cognitive Impairment Identification Using Hurst Exponent

PubMed Central

Long, Zhuqing; Jing, Bin; Guo, Ru; Li, Bo; Cui, Feiyi; Wang, Tingting; Chen, Hongwen

2018-01-01

Mild cognitive impairment (MCI), which generally represents the transition state between normal aging and the early changes related to Alzheimer’s disease (AD), has drawn increasing attention from neuroscientists due that efficient AD treatments need early initiation ahead of irreversible brain tissue damage. Thus effective MCI identification methods are desperately needed, which may be of great importance for the clinical intervention of AD. In this article, the range scaled analysis, which could effectively detect the temporal complexity of a time series, was utilized to calculate the Hurst exponent (HE) of functional magnetic resonance imaging (fMRI) data at a voxel level from 64 MCI patients and 60 healthy controls (HCs). Then the average HE values of each region of interest (ROI) in brainnetome atlas were extracted and compared between MCI and HC. At last, the abnormal average HE values were adopted as the classification features for a proposed support vector machine (SVM) based identification algorithm, and the classification performance was estimated with leave-one-out cross-validation (LOOCV). Our results indicated 83.1% accuracy, 82.8% sensitivity and 83.3% specificity, and an area under curve of 0.88, suggesting that the HE index could serve as an effective feature for the MCI identification. Furthermore, the abnormal HE brain regions in MCI were predominately involved in left middle frontal gyrus, right hippocampus, bilateral parahippocampal gyrus, bilateral amygdala, left cingulate gyrus, left insular gyrus, left fusiform gyrus, left superior parietal gyrus, left orbital gyrus and left basal ganglia. PMID:29692721

Characterization of the Hydrocarbon Potential and Non-Potential Zones Using Wavelet-Based Fractal Analysis

NASA Astrophysics Data System (ADS)

Mukherjee, Bappa; Roy, P. N. S.

The identification of prospective and dry zone is of major importance from well log data. Truthfulness in the identification of potential zone is a very crucial issue in hydrocarbon exploration. In this line, the problem has received considerable attention and many conventional techniques have been proposed. The purpose of this study is to recognize the hydrocarbon and non-hydrocarbon bearing portion within a reservoir by using the non-conventional technique. The wavelet based fractal analysis (WBFA) has been applied on the wire-line log data in order to obtain the pre-defined hydrocarbon (HC) and non-hydrocarbon (NHC) zones by their self-affine signal nature is demonstrated in this paper. The feasibility of the proposed technique is tested with the help of most commonly used logs, like self-potential, gamma ray, resistivity and porosity log responses. These logs are obtained from the industry to make out several HC and NHC zones of all wells in the study region belonging to the upper Assam basin. The results obtained in this study for a particular log response, where in the case of HC bearing zones, it is found that they are mainly situated in a variety of sandstones lithology which leads to the higher Hurst exponent. Further, the NHC zones found to be analogous to lithology with higher shale content having lower Hurst exponent. The above proposed technique can overcome the chance of miss interpretation in conventional reservoir characterization.

Mathematics of Failures in Complex Systems: Characterization and Mitigation of Service Failures in Complex Dynamic Systems

DTIC Science & Technology

2007-06-30

fractal dimensions and Lyapunov exponents . Fractal dimensions characterize geometri- cal complexity of dynamics (e.g., spatial distribution of points along...ant classi3ers (e.g., Lyapunov exponents , and fractal dimensions). The 3rst three steps show how chaotic systems may be separated from stochastic...correlated random walk in which a ¼ 2H, where H is the Hurst exponen interval 0pHp1 with the case H ¼ 0:5 corresponding to a simple rando This model has been

Damage Models for Delamination and Transverse Fracture.

DTIC Science & Technology

1987-08-01

is metals mas be Aritten in this form (Leek ic and lls.\\ en tm ’r [ hus . except for consideration of hurst 19-f4 .I In analop. as th elasicits t her... exponent % . that theisirrir- must sols e siniultaneousls for f, g and 11 using the J, (but not past %alues) determines, the irrst:irtar ie dlinienionless...in this last case does r’hc’r pirrmeersl so that a J, is not necessaril% the nonlinearit% exponent appear in the equatioin for I’llp. I hc. results

Identifying current and remitted major depressive disorder with the Hurst exponent: a comparative study on two automated anatomical labeling atlases

PubMed Central

Yan, Huagang; Dong, Jianxin; Mo, Xiao; Li, Dan; Liu, Chunhong; Li, Haiyun

2017-01-01

Major depressive disorder (MDD) is a leading world-wide psychiatric disorder with high recurrence rate, therefore, it is desirable to identify current MDD (cMDD) and remitted MDD (rMDD) for their appropriate therapeutic interventions. In the study, 19 cMDD, 19 rMDD and 19 well-matched healthy controls (HC) were enrolled and scanned with the resting-state functional magnetic resonance imaging (rs-fMRI). The Hurst exponent (HE) of rs-fMRI in AAL-90 and AAL-1024 atlases were calculated and compared between groups. Then, a radial basis function (RBF) based support vector machine was proposed to identify every pair of the cMDD, rMDD and HC groups using the abnormal HE features, and a leave-one-out cross-validation was used to evaluate the classification performance. Applying the proposed method with AAL-1024 and AAL-90 atlas respectively, 87% and 84% subjects were correctly identified between cMDD and HC, 84% and 71% between rMDD and HC, and 89% and 74% between cMDD and rMDD. Our results indicated that the HE was an effective feature to distinguish cMDD and rMDD from HC, and the recognition performances with AAL-1024 parcellation were better than that with the conventional AAL-90 parcellation. PMID:29163844

A non linear analysis of human gait time series based on multifractal analysis and cross correlations

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.

2005-01-01

We analyzed databases with gait time series of adults and persons with Parkinson, Huntington and amyotrophic lateral sclerosis (ALS) diseases. We obtained the staircase graphs of accumulated events that can be bounded by a straight line whose slope can be used to distinguish between gait time series from healthy and ill persons. The global Hurst exponent of these series do not show tendencies, we intend that this is because some gait time series have monofractal behavior and others have multifractal behavior so they cannot be characterized with a single Hurst exponent. We calculated the multifractal spectra, obtained the spectra width and found that the spectra of the healthy young persons are almost monofractal. The spectra of ill persons are wider than the spectra of healthy persons. In opposition to the interbeat time series where the pathology implies loss of multifractality, in the gait time series the multifractal behavior emerges with the pathology. Data were collected from healthy and ill subjects as they walked in a roughly circular path and they have sensors in both feet, so we have one time series for the left foot and other for the right foot. First, we analyzed these time series separately, and then we compared both results, with direct comparison and with a cross correlation analysis. We tried to find differences in both time series that can be used as indicators of equilibrium problems.

Simulation of Gas-Surface Dynamical Interactions

DTIC Science & Technology

2007-07-01

the interacting particle on the surface. Trapping probabilities often scale as Ei cosn θi with n < 2. An exponent of n = 0 corresponds to total energy...1996). [85] A. E. Wiskerke, F. H. Geuzebroek, A. W. Kleyn, and B. E. Hayden, Surf. Sci. 272, 256 (1992). [86] J. E. Hurst , L. Wharton, K. C. Janda

Rectified brownian transport in corrugated channels: Fractional brownian motion and Lévy flights.

PubMed

Ai, Bao-quan; Shao, Zhi-gang; Zhong, Wei-rong

2012-11-07

We study fractional brownian motion and Lévy flights in periodic corrugated channels without any external driving forces. From numerical simulations, we find that both fractional gaussian noise and Lévy-stable noise in asymmetric corrugated channels can break thermodynamical equilibrium and induce directed transport. The rectified mechanisms for fractional brownian motion and Lévy flights are different. The former is caused by non-uniform spectral distribution (low or high frequencies) of fractional gaussian noise, while the latter is due to the nonthermal character (occasional long jumps) of the Lévy-stable noise. For fractional brownian motion, average velocity increases with the Hurst exponent for the persistent case, while for the antipersistent case there exists an optimal value of Hurst exponent at which average velocity takes its maximal value. For Lévy flights, the group velocity decreases monotonically as the Lévy index increases. In addition, for both cases, the optimized periodicity and radius at the bottleneck can facilitate the directed transport. Our results could be implemented in constrained structures with narrow channels and pores where the particles undergo anomalous diffusion.

The Hurst exponent in energy futures prices

NASA Astrophysics Data System (ADS)

Serletis, Apostolos; Rosenberg, Aryeh Adam

2007-07-01

This paper extends the work in Elder and Serletis [Long memory in energy futures prices, Rev. Financial Econ., forthcoming, 2007] and Serletis et al. [Detrended fluctuation analysis of the US stock market, Int. J. Bifurcation Chaos, forthcoming, 2007] by re-examining the empirical evidence for random walk type behavior in energy futures prices. In doing so, it uses daily data on energy futures traded on the New York Mercantile Exchange, over the period from July 2, 1990 to November 1, 2006, and a statistical physics approach-the ‘detrending moving average’ technique-providing a reliable framework for testing the information efficiency in financial markets as shown by Alessio et al. [Second-order moving average and scaling of stochastic time series, Eur. Phys. J. B 27 (2002) 197-200] and Carbone et al. [Time-dependent hurst exponent in financial time series. Physica A 344 (2004) 267-271; Analysis of clusters formed by the moving average of a long-range correlated time series. Phys. Rev. E 69 (2004) 026105]. The results show that energy futures returns display long memory and that the particular form of long memory is anti-persistence.

Generalized Hurst exponent estimates differentiate EEG signals of healthy and epileptic patients

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2018-01-01

The aim of our current study is to check whether multifractal patterns of the electroencephalographic (EEG) signals of normal and epileptic patients are statistically similar or different. In this regard, the generalized Hurst exponent (GHE) method is used for robust estimation of the multifractals in each type of EEG signals, and three powerful statistical tests are performed to check existence of differences between estimated GHEs from healthy control subjects and epileptic patients. The obtained results show that multifractals exist in both types of EEG signals. Particularly, it was found that the degree of fractal is more pronounced in short variations of normal EEG signals than in short variations of EEG signals with seizure free intervals. In contrary, it is more pronounced in long variations of EEG signals with seizure free intervals than in normal EEG signals. Importantly, both parametric and nonparametric statistical tests show strong evidence that estimated GHEs of normal EEG signals are statistically and significantly different from those with seizure free intervals. Therefore, GHEs can be efficiently used to distinguish between healthy and patients suffering from epilepsy.

Measuring efficiency of international crude oil markets: A multifractality approach

NASA Astrophysics Data System (ADS)

Niere, H. M.

2015-01-01

The three major international crude oil markets are treated as complex systems and their multifractal properties are explored. The study covers daily prices of Brent crude, OPEC reference basket and West Texas Intermediate (WTI) crude from January 2, 2003 to January 2, 2014. A multifractal detrended fluctuation analysis (MFDFA) is employed to extract the generalized Hurst exponents in each of the time series. The generalized Hurst exponent is used to measure the degree of multifractality which in turn is used to quantify the efficiency of the three international crude oil markets. To identify whether the source of multifractality is long-range correlations or broad fat-tail distributions, shuffled data and surrogated data corresponding to each of the time series are generated. Shuffled data are obtained by randomizing the order of the price returns data. This will destroy any long-range correlation of the time series. Surrogated data is produced using the Fourier-Detrended Fluctuation Analysis (F-DFA). This is done by randomizing the phases of the price returns data in Fourier space. This will normalize the distribution of the time series. The study found that for the three crude oil markets, there is a strong dependence of the generalized Hurst exponents with respect to the order of fluctuations. This shows that the daily price time series of the markets under study have signs of multifractality. Using the degree of multifractality as a measure of efficiency, the results show that WTI is the most efficient while OPEC is the least efficient market. This implies that OPEC has the highest likelihood to be manipulated among the three markets. This reflects the fact that Brent and WTI is a very competitive market hence, it has a higher level of complexity compared against OPEC, which has a large monopoly power. Comparing with shuffled data and surrogated data, the findings suggest that for all the three crude oil markets, the multifractality is mainly due to long-range correlations.

Soil porosity correlation and its influence in percolation dynamics

NASA Astrophysics Data System (ADS)

Rodriguez, Alfredo; Capa-Morocho, Mirian; Ruis-Ramos, Margarita; Tarquis, Ana M.

2016-04-01

The prediction of percolation in natural soils is relevant for modeling root growth and optimizing infiltration of water and nutrients. Also, it would improve our understanding on how pollutants as pesticides, and virus and bacteria (Darnault et al., 2003) reach significant depths without being filtered out by the soil matrix (Beven and Germann, 2013). Random walk algorithms have been used successfully to date to characterize the dynamical characteristics of disordered media. This approach has been used here to describe how soil at different bulk densities and with different threshold values applied to the 3D gray images influences the structure of the pore network and their implications on particle flow and distribution (Ruiz-Ramos et al., 2009). In order to do so first we applied several threshold values to each image analyzed and characterized them through Hurst exponents, then we computed random walks algorithms to calculate distances reached by the particles and speed of those particles. At the same time, 3D structures with a Hurst exponent of ca 0.5 and with different porosities were constructed and the same random walks simulations were replicated over these generated structures. We have found a relationship between Hurst exponents and the speed distribution of the particles reaching percolation of the total soil depth. REFERENCES Darnault, C.J. G., P. Garnier, Y.J. Kim, K.L. Oveson, T.S. Steenhuis, J.Y. Parlange, M. Jenkins, W.C. Ghiorse, and P. Baveye (2003), Preferential transport of Cryptosporidium parvum oocysts in variably saturated subsurface environments, Water Environ. Res., 75, 113-120. Beven, Keith and Germann, Peter. 2013. Macropores and water flow in soils revisited. Water Resources Research, 49(6), 3071-3092. DOI: 10.1002/wrcr.20156. Ruiz-Ramos, M., D. del Valle, D. Grinev, and A.M. Tarquis. 2009. Soil hydraulic behaviour at different bulk densities. Geophysical Research Abstracts, 11, EGU2009-6234.

Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2015-11-20

Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of H test these analytical predictions and show excellent agreement, even for large ϵ.

Irregular-regular-irregular mixed mode oscillations in a glow discharge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Sabuj, E-mail: sabuj.ghosh@saha.ac.in; Shaw, Pankaj Kumar, E-mail: pankaj.shaw@saha.ac.in; Saha, Debajyoti, E-mail: debajyoti.saha@saha.ac.in

2015-05-15

Floating potential fluctuations of a glow discharge plasma are found to exhibit different kinds of mixed mode oscillations. Power spectrum analysis reveals that with change in the nature of the mixed mode oscillation (MMO), there occurs a transfer of power between the different harmonics and subharmonics. The variation in the chaoticity of different types of mmo was observed with the study of Lyapunov exponents. Estimates of correlation dimension and the Hurst exponent suggest that these MMOs are of low dimensional nature with an anti persistent character. Numerical modeling also reflects the experimentally found transitions between the different MMOs.

Assessing inefficiency in euro bilateral exchange rates

NASA Astrophysics Data System (ADS)

Tabak, Benjamin M.; Cajueiro, Daniel O.

2006-07-01

This paper assesses inefficiency for 10 euro bilateral exchange rates. We study the dynamics of these time series by estimating Tsallis q entropic index and Hurst exponents using the local Whittle estimator. Empirical results suggest that US, Canadian and Singapore dollar are amongst the most efficient currencies, while Japanese yen and Swedish krona are amongst the most inefficient.

Winner Takes All: Competing Viruses or Ideas on Fair-Play Networks

DTIC Science & Technology

2012-01-01

ratio (up to some exponents ). Also, clearly, the maximal ratios are attained at one of the last two fixed points. 4.3 Special Case: Barbell Graph A...Huberman. The dynamics of viral marketing. In EC, 2006. [24] J. Leskovec, M. McGlohon, C. Faloutsos, N. Glance, and M. Hurst . Cascading behavior in large

Implications of China’s Growing Demand for Oil: A Case Study in Venezuela

DTIC Science & Technology

2007-12-01

Mearsheimer is a leading exponent of the perspective that a rising China poses a danger. He contends that a rising power is always interested in...Soft power. 57 Mike Hurst , “A Giant Awakens - $48 bn to kick-start a new era --- Beijing 2008,” The Daily Telegraph (Australia), Extended Metro

Profit Maximization Models for Exponential Decay Processes.

DTIC Science & Technology

1980-08-01

assumptions could easily be analyzed in similar fashion. References [1] Bensoussan, A., Hurst , E.G. and Nislund, B., Management Applications of Modern...TVIPe OF r 04PORNT A i M0 CiH O .V9RAE PROFIT MAXIMIZATION .ODELS FOR EXPONENT IAL Technical Report DECAY PROCESSES August 1990 ~~~I. PtA’OR~idNG ONqG

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

Development of multiscale complexity and multifractality of fetal heart rate variability.

PubMed

Gierałtowski, Jan; Hoyer, Dirk; Tetschke, Florian; Nowack, Samuel; Schneider, Uwe; Zebrowski, Jan

2013-11-01

During fetal development a complex system grows and coordination over multiple time scales is formed towards an integrated behavior of the organism. Since essential cardiovascular and associated coordination is mediated by the autonomic nervous system (ANS) and the ANS activity is reflected in recordable heart rate patterns, multiscale heart rate analysis is a tool predestined for the diagnosis of prenatal maturation. The analyses over multiple time scales requires sufficiently long data sets while the recordings of fetal heart rate as well as the behavioral states studied are themselves short. Care must be taken that the analysis methods used are appropriate for short data lengths. We investigated multiscale entropy and multifractal scaling exponents from 30 minute recordings of 27 normal fetuses, aged between 23 and 38 weeks of gestational age (WGA) during the quiet state. In multiscale entropy, we found complexity lower than that of non-correlated white noise over all 20 coarse graining time scales investigated. Significant maturation age related complexity increase was strongest expressed at scale 2, both using sample entropy and generalized mutual information as complexity estimates. Multiscale multifractal analysis (MMA) in which the Hurst surface h(q,s) is calculated, where q is the multifractal parameter and s is the scale, was applied to the fetal heart rate data. MMA is a method derived from detrended fluctuation analysis (DFA). We modified the base algorithm of MMA to be applicable for short time series analysis using overlapping data windows and a reduction of the scale range. We looked for such q and s for which the Hurst exponent h(q,s) is most correlated with gestational age. We used this value of the Hurst exponent to predict the gestational age based only on fetal heart rate variability properties. Comparison with the true age of the fetus gave satisfying results (error 2.17±3.29 weeks; p<0.001; R(2)=0.52). In addition, we found that the normally used DFA scale range is non-optimal for fetal age evaluation. We conclude that 30 min recordings are appropriate and sufficient for assessing fetal age by multiscale entropy and multiscale multifractal analysis. The predominant prognostic role of scale 2 heart beats for MSE and scale 39 heart beats (at q=-0.7) for MMA cannot be explored neither by single scale complexity measures nor by standard detrended fluctuation analysis. Copyright © 2013 Elsevier B.V. All rights reserved.

Endogenous and exogenous dynamics in the fluctuations of capital fluxes. An empirical analysis of the Chinese stock market

NASA Astrophysics Data System (ADS)

Jiang, Z.-Q.; Guo, L.; Zhou, W.-X.

2007-06-01

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σexo / σendo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent Hi increase in logarithmic form with the time scale Δt and the mean traded value per minute , respectively. We find that the scaling exponent αendo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.

Statistical analysis of strait time index and a simple model for trend and trend reversal

NASA Astrophysics Data System (ADS)

Chen, Kan; Jayaprakash, C.

2003-06-01

We analyze the daily closing prices of the Strait Time Index (STI) as well as the individual stocks traded in Singapore's stock market from 1988 to 2001. We find that the Hurst exponent is approximately 0.6 for both the STI and individual stocks, while the normal correlation functions show the random walk exponent of 0.5. We also investigate the conditional average of the price change in an interval of length T given the price change in the previous interval. We find strong correlations for price changes larger than a threshold value proportional to T; this indicates that there is no uniform crossover to Gaussian behavior. A simple model based on short-time trend and trend reversal is constructed. We show that the model exhibits statistical properties and market swings similar to those of the real market.

Quantitative spectral light scattering polarimetry for monitoring fractal growth pattern of Bacillus thuringiensis bacterial colonies

NASA Astrophysics Data System (ADS)

Banerjee, Paromita; Soni, Jalpa; Ghosh, Nirmalya; Sengupta, Tapas K.

2013-02-01

It is of considerable current interest to develop various methods which help to understand and quantify the cellular association in growing bacterial colonies and is also important in terms of detection and identification of a bacterial species. A novel approach is used here to probe the morphological structural changes occurring during the growth of the bacterial colony of Bacillus thuringiensis under different environmental conditions (in normal nutrient agar, in presence of glucose - acting as additional nutrient and additional 3mM arsenate as additional toxic material). This approach combines the quantitative Mueller matrix polarimetry to extract intrinsic polarization properties and inverse analysis of the polarization preserving part of the light scattering spectra to determine the fractal parameter H (Hurst exponent) using Born approximation. Interesting differences are observed in the intrinsic polarization parameters and also in the Hurst exponent, which is a measurement of the fractality of a pattern formed by bacteria while growing as a colony. These findings are further confirmed with optical microscopic studies of the same sample and the results indicate a very strong and distinct dependence on the environmental conditions during growth, which can be exploited to quantify different bacterial species and their growth patterns.

Long-Range Correlations in Sentence Series from A Story of the Stone

PubMed Central

Yang, Tianguang; Gu, Changgui; Yang, Huijie

2016-01-01

A sentence is the natural unit of language. Patterns embedded in series of sentences can be used to model the formation and evolution of languages, and to solve practical problems such as evaluating linguistic ability. In this paper, we apply de-trended fluctuation analysis to detect long-range correlations embedded in sentence series from A Story of the Stone, one of the greatest masterpieces of Chinese literature. We identified a weak long-range correlation, with a Hurst exponent of 0.575±0.002 up to a scale of 104. We used the structural stability to confirm the behavior of the long-range correlation, and found that different parts of the series had almost identical Hurst exponents. We found that noisy records can lead to false results and conclusions, even if the noise covers a limited proportion of the total records (e.g., less than 1%). Thus, the structural stability test is an essential procedure for confirming the existence of long-range correlations, which has been widely neglected in previous studies. Furthermore, a combination of de-trended fluctuation analysis and diffusion entropy analysis demonstrated that the sentence series was generated by a fractional Brownian motion. PMID:27648941

Long-Range Correlations in Sentence Series from A Story of the Stone.

PubMed

Yang, Tianguang; Gu, Changgui; Yang, Huijie

2016-01-01

A sentence is the natural unit of language. Patterns embedded in series of sentences can be used to model the formation and evolution of languages, and to solve practical problems such as evaluating linguistic ability. In this paper, we apply de-trended fluctuation analysis to detect long-range correlations embedded in sentence series from A Story of the Stone, one of the greatest masterpieces of Chinese literature. We identified a weak long-range correlation, with a Hurst exponent of 0.575±0.002 up to a scale of 104. We used the structural stability to confirm the behavior of the long-range correlation, and found that different parts of the series had almost identical Hurst exponents. We found that noisy records can lead to false results and conclusions, even if the noise covers a limited proportion of the total records (e.g., less than 1%). Thus, the structural stability test is an essential procedure for confirming the existence of long-range correlations, which has been widely neglected in previous studies. Furthermore, a combination of de-trended fluctuation analysis and diffusion entropy analysis demonstrated that the sentence series was generated by a fractional Brownian motion.

Rescaled range analysis of streamflow records in the São Francisco River Basin, Brazil

NASA Astrophysics Data System (ADS)

Araujo, Marcelo Vitor Oliveira; Celeste, Alcigeimes B.

2018-01-01

Hydrological time series are sometimes found to have a distinctive behavior known as long-term persistence, in which subsequent values depend on each other even under very large time scales. This implies multiyear consecutive droughts or floods. Typical models used to generate synthetic hydrological scenarios, widely used in the planning and management of water resources, fail to preserve this kind of persistence in the generated data and therefore may have a major impact on projects whose design lives span for long periods of time. This study deals with the evaluation of long-term persistence in streamflow records by means of the rescaled range analysis proposed by British engineer Harold E. Hurst, who first observed the phenomenon in the mid-twentieth century. In this paper, Hurst's procedure is enhanced by a strategy based on statistical hypothesis testing. The case study comprises the six main hydroelectric power plants located in the São Francisco River Basin, part of the Brazilian National Grid. Historical time series of inflows to the major reservoirs of the system are investigated and 5/6 sites show significant persistence, with values for the so-called Hurst exponent near or greater than 0.7, i.e., around 40% above the value 0.5 that represents a white noise process, suggesting that decision makers should take long-term persistence into consideration when conducting water resources planning and management studies in the region.

Relating the large-scale structure of time series and visibility networks.

PubMed

Rodríguez, Miguel A

2017-06-01

The structure of time series is usually characterized by means of correlations. A new proposal based on visibility networks has been considered recently. Visibility networks are complex networks mapped from surfaces or time series using visibility properties. The structures of time series and visibility networks are closely related, as shown by means of fractional time series in recent works. In these works, a simple relationship between the Hurst exponent H of fractional time series and the exponent of the distribution of edges γ of the corresponding visibility network, which exhibits a power law, is shown. To check and generalize these results, in this paper we delve into this idea of connected structures by defining both structures more properly. In addition to the exponents used before, H and γ, which take into account local properties, we consider two more exponents that, as we will show, characterize global properties. These are the exponent α for time series, which gives the scaling of the variance with the size as var∼T^{2α}, and the exponent κ of their corresponding network, which gives the scaling of the averaged maximum of the number of edges, 〈k_{M}〉∼N^{κ}. With this representation, a more precise connection between the structures of general time series and their associated visibility network is achieved. Similarities and differences are more clearly established, and new scaling forms of complex networks appear in agreement with their respective classes of time series.

On the probability distribution of stock returns in the Mike-Farmer model

NASA Astrophysics Data System (ADS)

Gu, G.-F.; Zhou, W.-X.

2009-02-01

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important stylized facts. There are three key ingredients in the Mike-Farmer (MF) model: the long memory of order signs characterized by the Hurst index Hs, the distribution of relative order prices x in reference to the same best price described by a Student distribution (or Tsallis’ q-Gaussian), and the dynamics of order cancelation. They showed that different values of the Hurst index Hs and the freedom degree αx of the Student distribution can always produce power-law tails in the return distribution fr(r) with different tail exponent αr. In this paper, we study the origin of the power-law tails of the return distribution fr(r) in the MF model, based on extensive simulations with different combinations of the left part L(x) for x < 0 and the right part R(x) for x > 0 of fx(x). We find that power-law tails appear only when L(x) has a power-law tail, no matter R(x) has a power-law tail or not. In addition, we find that the distributions of returns in the MF model at different timescales can be well modeled by the Student distributions, whose tail exponents are close to the well-known cubic law and increase with the timescale.

Essays in financial economics and econometrics

NASA Astrophysics Data System (ADS)

La Spada, Gabriele

Chapter 1 (my job market paper) asks the following question: Do asset managers reach for yield because of competitive pressures in a low rate environment? I propose a tournament model of money market funds (MMFs) to study this issue. I show that funds with different costs of default respond differently to changes in interest rates, and that it is important to distinguish the role of risk-free rates from that of risk premia. An increase in the risk premium leads funds with lower default costs to increase risk-taking, while funds with higher default costs reduce risk-taking. Without changes in the premium, low risk-free rates reduce risk-taking. My empirical analysis shows that these predictions are consistent with the risk-taking of MMFs during the 2006--2008 period. Chapter 2, co-authored with Fabrizio Lillo and published in Studies in Nonlinear Dynamics and Econometrics (2014), studies the effect of round-off error (or discretization) on stationary Gaussian long-memory process. For large lags, the autocovariance is rescaled by a factor smaller than one, and we compute this factor exactly. Hence, the discretized process has the same Hurst exponent as the underlying one. We show that in presence of round-off error, two common estimators of the Hurst exponent, the local Whittle (LW) estimator and the detrended fluctuation analysis (DFA), are severely negatively biased in finite samples. We derive conditions for consistency and asymptotic normality of the LW estimator applied to discretized processes and compute the asymptotic properties of the DFA for generic long-memory processes that encompass discretized processes. Chapter 3, co-authored with Fabrizio Lillo, studies the effect of round-off error on integrated Gaussian processes with possibly correlated increments. We derive the variance and kurtosis of the realized increment process in the limit of both "small" and "large" round-off errors, and its autocovariance for large lags. We propose novel estimators for the variance and lag-one autocorrelation of the underlying, unobserved increment process. We also show that for fractionally integrated processes, the realized increments have the same Hurst exponent as the underlying ones, but the LW estimator applied to the realized series is severely negatively biased in medium-sized samples.

THE DEPENDENCE OF PRESTELLAR CORE MASS DISTRIBUTIONS ON THE STRUCTURE OF THE PARENTAL CLOUD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parravano, Antonio; Sanchez, Nestor; Alfaro, Emilio J.

2012-08-01

The mass distribution of prestellar cores is obtained for clouds with arbitrary internal mass distributions using a selection criterion based on the thermal and turbulent Jeans mass and applied hierarchically from small to large scales. We have checked this methodology by comparing our results for a log-normal density probability distribution function with the theoretical core mass function (CMF) derived by Hennebelle and Chabrier, namely a power law at large scales and a log-normal cutoff at low scales, but our method can be applied to any mass distributions representing a star-forming cloud. This methodology enables us to connect the parental cloudmore » structure with the mass distribution of the cores and their spatial distribution, providing an efficient tool for investigating the physical properties of the molecular clouds that give rise to the prestellar core distributions observed. Simulated fractional Brownian motion (fBm) clouds with the Hurst exponent close to the value H = 1/3 give the best agreement with the theoretical CMF derived by Hennebelle and Chabrier and Chabrier's system initial mass function. Likewise, the spatial distribution of the cores derived from our methodology shows a surface density of companions compatible with those observed in Trapezium and Ophiucus star-forming regions. This method also allows us to analyze the properties of the mass distribution of cores for different realizations. We found that the variations in the number of cores formed in different realizations of fBm clouds (with the same Hurst exponent) are much larger than the expected root N statistical fluctuations, increasing with H.« less

Long-range persistence in the global mean surface temperature and the global warming "time bomb"

NASA Astrophysics Data System (ADS)

Rypdal, M.; Rypdal, K.

2012-04-01

Detrended Fluctuation Analysis (DFA) and Maximum Likelihood Estimations (MLE) based on instrumental data over the last 160 years indicate that there is Long-Range Persistence (LRP) in Global Mean Surface Temperature (GMST) on time scales of months to decades. The persistence is much higher in sea surface temperature than in land temperatures. Power spectral analysis of multi-model, multi-ensemble runs of global climate models indicate further that this persistence may extend to centennial and maybe even millennial time-scales. We also support these conclusions by wavelet variogram analysis, DFA, and MLE of Northern hemisphere mean surface temperature reconstructions over the last two millennia. These analyses indicate that the GMST is a strongly persistent noise with Hurst exponent H>0.9 on time scales from decades up to at least 500 years. We show that such LRP can be very important for long-term climate prediction and for the establishment of a "time bomb" in the climate system due to a growing energy imbalance caused by the slow relaxation to radiative equilibrium under rising anthropogenic forcing. We do this by the construction of a multi-parameter dynamic-stochastic model for the GMST response to deterministic and stochastic forcing, where LRP is represented by a power-law response function. Reconstructed data for total forcing and GMST over the last millennium are used with this model to estimate trend coefficients and Hurst exponent for the GMST on multi-century time scale by means of MLE. Ensembles of solutions generated from the stochastic model also allow us to estimate confidence intervals for these estimates.

The Dependence of Prestellar Core Mass Distributions on the Structure of the Parental Cloud

NASA Astrophysics Data System (ADS)

Parravano, Antonio; Sánchez, Néstor; Alfaro, Emilio J.

2012-08-01

The mass distribution of prestellar cores is obtained for clouds with arbitrary internal mass distributions using a selection criterion based on the thermal and turbulent Jeans mass and applied hierarchically from small to large scales. We have checked this methodology by comparing our results for a log-normal density probability distribution function with the theoretical core mass function (CMF) derived by Hennebelle & Chabrier, namely a power law at large scales and a log-normal cutoff at low scales, but our method can be applied to any mass distributions representing a star-forming cloud. This methodology enables us to connect the parental cloud structure with the mass distribution of the cores and their spatial distribution, providing an efficient tool for investigating the physical properties of the molecular clouds that give rise to the prestellar core distributions observed. Simulated fractional Brownian motion (fBm) clouds with the Hurst exponent close to the value H = 1/3 give the best agreement with the theoretical CMF derived by Hennebelle & Chabrier and Chabrier's system initial mass function. Likewise, the spatial distribution of the cores derived from our methodology shows a surface density of companions compatible with those observed in Trapezium and Ophiucus star-forming regions. This method also allows us to analyze the properties of the mass distribution of cores for different realizations. We found that the variations in the number of cores formed in different realizations of fBm clouds (with the same Hurst exponent) are much larger than the expected root {\\cal N} statistical fluctuations, increasing with H.

Pricing geometric Asian rainbow options under fractional Brownian motion

NASA Astrophysics Data System (ADS)

Wang, Lu; Zhang, Rong; Yang, Lin; Su, Yang; Ma, Feng

2018-03-01

In this paper, we explore the pricing of the assets of Asian rainbow options under the condition that the assets have self-similar and long-range dependence characteristics. Based on the principle of no arbitrage, stochastic differential equation, and partial differential equation, we obtain the pricing formula for two-asset rainbow options under fractional Brownian motion. Next, our Monte Carlo simulation experiments show that the derived pricing formula is accurate and effective. Finally, our sensitivity analysis of the influence of important parameters, such as the risk-free rate, Hurst exponent, and correlation coefficient, on the prices of Asian rainbow options further illustrate the rationality of our pricing model.

Aids for the Study of Electromagnetic Blackout

DTIC Science & Technology

1975-02-25

to gamma rays, 1-MT burst at 20 km 5-32 5-23B One-way absorption due to gamma rays. o-MT hurst at ’O km 5-32 5-23C One-way absorption due to ga’ma...0 2- F ( n)z I I L -I 0. 0.2L.~ INTEGRAL VALUES OF EXPONENT n Figure 6-13. Multiplying factors for refraction and range errors in a spherically

Physics of fashion fluctuations

NASA Astrophysics Data System (ADS)

Donangelo, R.; Hansen, A.; Sneppen, K.; Souza, S. R.

2000-12-01

We consider a market where many agents trade different types of products with each other. We model development of collective modes in this market, and quantify these by fluctuations that scale with time with a Hurst exponent of about 0.7. We demonstrate that individual products in the model occasionally become globally accepted means of exchange, and simultaneously become very actively traded. Thus collective features similar to money spontaneously emerge, without any a priori reason.

Hurst exponent: A Brownian approach to characterize the nonlinear behavior of red blood cells deformability

NASA Astrophysics Data System (ADS)

Mancilla Canales, M. A.; Leguto, A. J.; Riquelme, B. D.; León, P. Ponce de; Bortolato, S. A.; Korol, A. M.

2017-12-01

Ektacytometry techniques quantifies red blood cells (RBCs) deformability by measuring the elongation of suspended RBCs subjected to shear stress. Raw shear stress elongation plots are difficult to understand, thus most research papers apply data reduction methods characterizing the relationship between curve fitting. Our approach works with the naturally generated photometrically recorded time series of the diffraction pattern of several million of RBCs subjected to shear stress, and applies nonlinear quantifiers to study the fluctuations of these elongations. The development of new quantitative methods is crucial for restricting the subjectivity in the study of the cells behavior, mainly if they are capable of analyze at the same time biological and mechanical aspects of the cells in flowing conditions and compare their dynamics. A patented optical system called Erythrocyte Rheometer was used to evaluate viscoelastic properties of erythrocytes by Ektacytometry. To analyze cell dynamics we used the technique of Time Delay Coordinates, False Nearest Neighbors, the forecasting procedure proposed by Sugihara and May, and Hurst exponent. The results have expressive meaning on comparing healthy samples with parasite treated samples, suggesting that apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize biological and mechanical aspects of cells at the same time in flowing conditions.

Experimental study of crack initiation and propagation in high- and gigacycle fatigue in titanium alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bannikov, Mikhail, E-mail: mbannikov@icmm.ru, E-mail: oborin@icmm.ru, E-mail: naimark@icmm.ru; Oborin, Vladimir, E-mail: mbannikov@icmm.ru, E-mail: oborin@icmm.ru, E-mail: naimark@icmm.ru; Naimark, Oleg, E-mail: mbannikov@icmm.ru, E-mail: oborin@icmm.ru, E-mail: naimark@icmm.ru

Fatigue (high- and gigacycle) crack initiation and its propagation in titanium alloys with coarse and fine grain structure are studied by fractography analysis of fracture surface. Fractured specimens were analyzed by interferometer microscope and SEM to improve methods of monitoring of damage accumulation during fatigue test and to verify the models for fatigue crack kinetics. Fatigue strength was estimated for high cycle fatigue regime using the Luong method [1] by “in-situ” infrared scanning of the sample surface for the step-wise loading history for different grain size metals. Fine grain alloys demonstrated higher fatigue resistance for both high cycle fatigue andmore » gigacycle fatigue regimes. Fracture surface analysis for plane and cylindrical samples was carried out using optical and electronic microscopy method. High resolution profilometry (interferometer-profiler New View 5010) data of fracture surface roughness allowed us to estimate scale invariance (the Hurst exponent) and to establish the existence of two characteristic areas of damage localization (different values of the Hurst exponent). Area 1 with diameter ∼300 μm has the pronounced roughness and is associated with damage localization hotspot. Area 2 shows less amplitude roughness, occupies the rest fracture surface and considered as the trace of the fatigue crack path corresponding to the Paris kinetics.« less

Tissue multifractality and hidden Markov model based integrated framework for optimum precancer detection

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Sabyasachi; Das, Nandan K.; Kurmi, Indrajit; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.

2017-10-01

We report the application of a hidden Markov model (HMM) on multifractal tissue optical properties derived via the Born approximation-based inverse light scattering method for effective discrimination of precancerous human cervical tissue sites from the normal ones. Two global fractal parameters, generalized Hurst exponent and the corresponding singularity spectrum width, computed by multifractal detrended fluctuation analysis (MFDFA), are used here as potential biomarkers. We develop a methodology that makes use of these multifractal parameters by integrating with different statistical classifiers like the HMM and support vector machine (SVM). It is shown that the MFDFA-HMM integrated model achieves significantly better discrimination between normal and different grades of cancer as compared to the MFDFA-SVM integrated model.

Temporal correlations in the Vicsek model with vectorial noise

NASA Astrophysics Data System (ADS)

Gulich, Damián; Baglietto, Gabriel; Rozenfeld, Alejandro F.

2018-07-01

We study the temporal correlations in the evolution of the order parameter ϕ(t) for the Vicsek model with vectorial noise by estimating its Hurst exponent H with detrended fluctuation analysis (DFA). We present results on this parameter as a function of noise amplitude η introduced in simulations. We also compare with well known order-disorder phase transition for that same noise range. We find that - regardless of detrending degree - H spikes at the known coexistence noise for phase transition, and that this is due to nonstationarities introduced by the transit of the system between two well defined states with lower exponents. We statistically support this claim by successfully synthesizing equivalent cases derived from a transformed fractional Brownian motion (TfBm).

The Effect of the Underlying Distribution in Hurst Exponent Estimation

PubMed Central

Sánchez, Miguel Ángel; Trinidad, Juan E.; García, José; Fernández, Manuel

2015-01-01

In this paper, a heavy-tailed distribution approach is considered in order to explore the behavior of actual financial time series. We show that this kind of distribution allows to properly fit the empirical distribution of the stocks from S&P500 index. In addition to that, we explain in detail why the underlying distribution of the random process under study should be taken into account before using its self-similarity exponent as a reliable tool to state whether that financial series displays long-range dependence or not. Finally, we show that, under this model, no stocks from S&P500 index show persistent memory, whereas some of them do present anti-persistent memory and most of them present no memory at all. PMID:26020942

Anisotropy of anomalous diffusion improves the accuracy of differentiating low- and high-grade cerebral gliomas.

PubMed

Xu, Boyan; Su, Lu; Wang, Zhenxiong; Fan, Yang; Gong, Gaolang; Zhu, Wenzhen; Gao, Peiyi; Gao, Jia-Hong

2018-04-17

Anomalous diffusion model has been introduced and shown to be beneficial in clinical applications. However, only the directionally averaged values of anomalous diffusion parameters were investigated, and the anisotropy of anomalous diffusion remains unexplored. The aim of this study was to demonstrate the feasibility of using anisotropy of anomalous diffusion for differentiating low- and high-grade cerebral gliomas. Diffusion MRI images were acquired from brain tumor patients and analyzed using the fractional motion (FM) model. Twenty-two patients with histopathologically confirmed gliomas were selected. An anisotropy metric for the FM-related parameters, including the Noah exponent (α) and the Hurst exponent (H), was introduced and their values were statistically compared between the low- and high-grade gliomas. Additionally, multivariate logistic regression analysis was performed to assess the combination of the anisotropy metric and the directionally averaged value for each parameter. The diagnostic performances for grading gliomas were evaluated using a receiver operating characteristic (ROC) analysis. The Hurst exponent H was more anisotropic in high-grade than in low-grade gliomas (P = 0.015), while no significant difference was observed for the anisotropy of α. The ROC analysis revealed that larger areas under the ROC curves were produced for the combination of α (1) and the combination of H (0.813) compared with the directionally averaged α (0.979) and H (0.594), indicating an improved performance for tumor differentiation. The anisotropy of anomalous diffusion can provide distinctive information and benefit the differentiation of low- and high-grade gliomas. The utility of anisotropic anomalous diffusion may have an improved effect for investigating pathological changes in tissues. Copyright © 2018 Elsevier Inc. All rights reserved.

Complex network approach to fractional time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manshour, Pouya

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacencymore » matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.« less

Generalized Weierstrass-Mandelbrot Function Model for Actual Stocks Markets Indexes with Nonlinear Characteristics

NASA Astrophysics Data System (ADS)

Zhang, L.; Yu, C.; Sun, J. Q.

2015-03-01

It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.

Optimizing Complexity Measures for fMRI Data: Algorithm, Artifact, and Sensitivity

PubMed Central

Rubin, Denis; Fekete, Tomer; Mujica-Parodi, Lilianne R.

2013-01-01

Introduction Complexity in the brain has been well-documented at both neuronal and hemodynamic scales, with increasing evidence supporting its use in sensitively differentiating between mental states and disorders. However, application of complexity measures to fMRI time-series, which are short, sparse, and have low signal/noise, requires careful modality-specific optimization. Methods Here we use both simulated and real data to address two fundamental issues: choice of algorithm and degree/type of signal processing. Methods were evaluated with regard to resilience to acquisition artifacts common to fMRI as well as detection sensitivity. Detection sensitivity was quantified in terms of grey-white matter contrast and overlap with activation. We additionally investigated the variation of complexity with activation and emotional content, optimal task length, and the degree to which results scaled with scanner using the same paradigm with two 3T magnets made by different manufacturers. Methods for evaluating complexity were: power spectrum, structure function, wavelet decomposition, second derivative, rescaled range, Higuchi’s estimate of fractal dimension, aggregated variance, and detrended fluctuation analysis. To permit direct comparison across methods, all results were normalized to Hurst exponents. Results Power-spectrum, Higuchi’s fractal dimension, and generalized Hurst exponent based estimates were most successful by all criteria; the poorest-performing measures were wavelet, detrended fluctuation analysis, aggregated variance, and rescaled range. Conclusions Functional MRI data have artifacts that interact with complexity calculations in nontrivially distinct ways compared to other physiological data (such as EKG, EEG) for which these measures are typically used. Our results clearly demonstrate that decisions regarding choice of algorithm, signal processing, time-series length, and scanner have a significant impact on the reliability and sensitivity of complexity estimates. PMID:23700424

Multi-fractality in aeroelastic response as a precursor to flutter

NASA Astrophysics Data System (ADS)

Venkatramani, J.; Nair, Vineeth; Sujith, R. I.; Gupta, Sayan; Sarkar, Sunetra

2017-01-01

Wind tunnel tests on a NACA 0012 airfoil have been carried out to study the transition in aeroelastic response from an initial state characterised by low-amplitude aperiodic fluctuations to aeroelastic flutter when the system exhibits limit cycle oscillations. An analysis of the aeroelastic measurements reveals multi-fractal characteristics in the pre-flutter regime. This has not been studied in the literature. As the flow velocity approaches the flutter velocity from below, a gradual loss in multi-fractality is observed. Measures based on the generalised Hurst exponents are developed and are shown to have the potential to warn against impending aeroelastic flutter. The results of this study could be useful for health monitoring of aeroelastic structures.

Multifractal analysis of time series generated by discrete Ito equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Detection of long term persistence in time series of the Neuquen River (Argentina)

NASA Astrophysics Data System (ADS)

Seoane, Rafael; Paz González, Antonio

2014-05-01

In the Patagonian region (Argentina), previous hydrometeorological studies that have been developed using general circulation models show variations in annual mean flows. Future climate scenarios obtained from high-resolution models indicate decreases in total annual precipitation, and these scenarios are more important in the Neuquén river basin (23000 km2). The aim of this study was the estimation of long term persistence in the Neuquén River basin (Argentina). The detection of variations in the long range dependence term and long memory of time series was evaluated with the Hurst exponent. We applied rescaled adjusted range analysis (R/S) to time series of River discharges measured from 1903 to 2011 and this time series was divided into two subperiods: the first was from 1903 to 1970 and the second from 1970 to 2011. Results show a small increase in persistence for the second period. Our results are consistent with those obtained by Koch and Markovic (2007), who observed and estimated an increase of the H exponent for the period 1960-2000 in the Elbe River (Germany). References Hurst, H. (1951).Long term storage capacities of reservoirs". Trans. Am. Soc. Civil Engrs., 116:776-808. Koch and Markovic (2007). Evidences for Climate Change in Germany over the 20th Century from the Stochastic Analysis of hydro-meteorological Time Series, MODSIM07, International Congress on Modelling and Simulation, Christchurch, New Zealand.

Proneness to social anxiety modulates neural complexity in the absence of exposure: A resting state fMRI study using Hurst exponent.

PubMed

Gentili, Claudio; Vanello, Nicola; Cristea, Ioana; David, Daniel; Ricciardi, Emiliano; Pietrini, Pietro

2015-05-30

To test the hypothesis that brain activity is modulated by trait social anxiety, we measured the Hurst Exponent (HE), an index of complexity in time series, in healthy individuals at rest in the absence of any social trigger. Functional magnetic resonance imaging (fMRI) time series were recorded in 36 subjects at rest. All volunteers were healthy without any psychiatric, medical or neurological disorder. Subjects completed the Liebowitz Social Anxiety Scale (LSAS) and the Brief Fear of Negative Evaluation (BFNE) to assess social anxiety and thoughts in social contexts. We also obtained the fractional Amplitude of Low Frequency Fluctuations (fALFF) of the BOLD signal as an independent control measure for HE data. BFNE scores correlated positively with HE in the posterior cingulate/precuneus, while LSAS scores correlated positively with HE in the precuneus, in the inferior parietal sulci and in the parahippocamus. Results from fALFF were highly consistent with those obtained using LSAS and BFNE to predict HE. Overall our data indicate that spontaneous brain activity is influenced by the degree of social anxiety, on a continuum and in the absence of social stimuli. These findings suggest that social anxiety is a trait characteristic that shapes brain activity and predisposes to different reactions in social contexts. Copyright © 2015. Published by Elsevier Ireland Ltd.

Multiscaling behavior of atomic-scale friction

NASA Astrophysics Data System (ADS)

Jannesar, M.; Jamali, T.; Sadeghi, A.; Movahed, S. M. S.; Fesler, G.; Meyer, E.; Khoshnevisan, B.; Jafari, G. R.

2017-06-01

The scaling behavior of friction between rough surfaces is a well-known phenomenon. It might be asked whether such a scaling feature also exists for friction at an atomic scale despite the absence of roughness on atomically flat surfaces. Indeed, other types of fluctuations, e.g., thermal and instrumental fluctuations, become appreciable at this length scale and can lead to scaling behavior of the measured atomic-scale friction. We investigate this using the lateral force exerted on the tip of an atomic force microscope (AFM) when the tip is dragged over the clean NaCl (001) surface in ultra-high vacuum at room temperature. Here the focus is on the fluctuations of the lateral force profile rather than its saw-tooth trend; we first eliminate the trend using the singular value decomposition technique and then explore the scaling behavior of the detrended data, which contains only fluctuations, using the multifractal detrended fluctuation analysis. The results demonstrate a scaling behavior for the friction data ranging from 0.2 to 2 nm with the Hurst exponent H =0.61 ±0.02 at a 1 σ confidence interval. Moreover, the dependence of the generalized Hurst exponent, h (q ) , on the index variable q confirms the multifractal or multiscaling behavior of the nanofriction data. These results prove that fluctuation of nanofriction empirical data has a multifractal behavior which deviates from white noise.

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.

Perturbative expansion for the maximum of fractional Brownian motion.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2016-07-01

Brownian motion is the only random process which is Gaussian, scale invariant, and Markovian. Dropping the Markovian property, i.e., allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent H. For H=1/2, Brownian motion is recovered. We develop a perturbative approach to treat the nonlocality in time in an expansion in ɛ=H-1/2. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: the maximum m of the process and the time t_{max} at which this maximum is reached, as well as their joint distribution. We test our analytical predictions with extensive numerical simulations for different values of H. They show excellent agreement, even for H far from 1/2.

Multifractal property of Chinese stock market in the CSI 800 index based on MF-DFA approach

NASA Astrophysics Data System (ADS)

Zhu, Huijian; Zhang, Weiguo

2018-01-01

CSI 800 index consists of CSI 500 index and CSI 300 index, aiming to reflect the performance of stocks with large, mid and small size of China A share market. In this paper we analyze the multifractal structure of Chinese stock market in the CSI 800 index based on the multifractal detrended fluctuation analysis (MF-DFA) method. We find that the fluctuation of the closing logarithmic returns have multifractal properties, the shape and width of multifractal spectrum are depended on the weighing order q. More interestingly, we observe a bigger market crash in June-August 2015 than the one in 2008 based on the local Hurst exponents. The result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis.

Applications of physical methods in high-frequency futures markets

NASA Astrophysics Data System (ADS)

Bartolozzi, M.; Mellen, C.; Chan, F.; Oliver, D.; Di Matteo, T.; Aste, T.

2007-12-01

In the present work we demonstrate the application of different physical methods to high-frequency or tick-bytick financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price time series taken from a range of futures indices. Additionally, we show that in a limit order book the relaxation times of an imbalanced book state with more demand or supply can be described by stretched exponential laws analogous to those seen in many physical systems.

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

PubMed Central

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

2016-01-01

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

DOE PAGES

Chen, Shuying; Yu, Liping; Ren, Jingli; ...

2016-07-20

Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, andmore » there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

PubMed

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

2016-07-20

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

Non-stationary dynamics in the bouncing ball: A wavelet perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

Evaluation of scaling invariance embedded in short time series.

PubMed

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

Evaluation of Scaling Invariance Embedded in Short Time Series

PubMed Central

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length . Calculations with specified Hurst exponent values of show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias () and sharp confidential interval (standard deviation ). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records. PMID:25549356

Statistical persistence of air pollutants (O3,SO2,NO2 and PM10) in Mexico City

NASA Astrophysics Data System (ADS)

Meraz, M.; Rodriguez, E.; Femat, R.; Echeverria, J. C.; Alvarez-Ramirez, J.

2015-06-01

The rescaled range (R / S) analysis was used for analyzing the statistical persistence of air pollutants in Mexico City. The air-pollution time series consisted of hourly observations of ozone, nitrogen dioxide, sulfur dioxide and particulate matter obtained at the Mexico City downtown monitoring station during 1999-2014. The results showed that long-range persistence is not a uniform property over a wide range of time scales, from days to months. In fact, although the air pollutant concentrations exhibit an average persistent behavior, environmental (e.g., daily and yearly) and socio-economic (e.g., daily and weekly) cycles are reflected in the dependence of the persistence strength as quantified in terms of the Hurst exponent. It was also found that the Hurst exponent exhibits time variations, with the ozone and nitrate oxide concentrations presenting some regularity, such as annual cycles. The persistence dynamics of the pollutant concentrations increased during the rainy season and decreased during the dry season. The time and scale dependences of the persistence properties provide some insights in the mechanisms involved in the internal dynamics of the Mexico City atmosphere for accumulating and dissipating dangerous air pollutants. While in the short-term individual pollutants dynamics seems to be governed by specific mechanisms, in the long-term (for monthly and higher scales) meteorological and seasonal mechanisms involved in atmospheric recirculation seem to dominate the dynamics of all air pollutant concentrations.

Long-range properties and data validity for hydrogeological time series: The case of the Paglia river

NASA Astrophysics Data System (ADS)

Ausloos, Marcel; Cerqueti, Roy; Lupi, Claudio

2017-03-01

This paper explores a large collection of about 377,000 observations, spanning more than 20 years with a frequency of 30 min, of the streamflow of the Paglia river, in central Italy. We analyze the long-term persistence properties of the series by computing the Hurst exponent, not only in its original form but also under an evolutionary point of view by analyzing the Hurst exponents over a rolling windows basis. The methodological tool adopted for the persistence is the detrended fluctuation analysis (DFA), which is classically known as suitable for our purpose. As an ancillary exploration, we implement a control on the data validity by assessing if the data exhibit the regularity stated by Benford's law. Results are interesting under different viewpoints. First, we show that the Paglia river streamflow exhibits periodicities which broadly suggest the existence of some common behavior with El Niño and the North Atlantic Oscillations: this specifically points to a (not necessarily direct) effect of these oceanic phenomena on the hydrogeological equilibria of very far geographical zones: however, such an hypothesis needs further analyses to be validated. Second, the series of streamflows shows an antipersistent behavior. Third, data are not consistent with Benford's law: this suggests that the measurement criteria should be opportunely revised. Fourth, the streamflow distribution is well approximated by a discrete generalized Beta distribution: this is well in accordance with the measured streamflows being the outcome of a complex system.

Fractal analyses reveal independent complexity and predictability of gait

PubMed Central

Dierick, Frédéric; Nivard, Anne-Laure

2017-01-01

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures. PMID:29182659

The performance-variability paradox, financial decision making, and the curious case of negative Hurst exponents.

PubMed

Guastello, Stephen J; Reiter, Katherine; Shircel, Anton; Timm, Paul; Malon, Matthew; Fabisch, Megan

2014-07-01

This study examined the relationship between performance variability and actual performance of financial decision makers who were working under experimental conditions of increasing workload and fatigue. The rescaled range statistic, also known as the Hurst exponent (H) was used as an index of variability. Although H is defined as having a range between 0 and 1, 45% of the 172 time series generated by undergraduates were negative. Participants in the study chose the optimum investment out of sets of 3 to 5 options that were presented a series of 350 displays. The sets of options varied in both the complexity of the options and number of options under simultaneous consideration. One experimental condition required participants to make their choices within 15 sec, and the other condition required them to choose within 7.5 sec. Results showed that (a) negative H was possible and not a result of psychometric error; (b) negative H was associated with negative autocorrelations in a time series. (c) H was the best predictor of performance of the variables studied; (d) three other significant predictors were scores on an anagrams test and ratings of physical demands and performance demands; (e) persistence as evidenced by the autocorrelations was associated with ratings of greater time pressure. It was concluded, furthermore, that persistence and overall performance were correlated, that 'healthy' variability only exists within a limited range, and other individual differences related to ability and resistance to stress or fatigue are also involved in the prediction of performance.

Evidence of Long Range Dependence and Self-similarity in Urban Traffic Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thakur, Gautam S; Helmy, Ahmed; Hui, Pan

2015-01-01

Transportation simulation technologies should accurately model traffic demand, distribution, and assignment parame- ters for urban environment simulation. These three param- eters significantly impact transportation engineering bench- mark process, are also critical in realizing realistic traffic modeling situations. In this paper, we model and charac- terize traffic density distribution of thousands of locations around the world. The traffic densities are generated from millions of images collected over several years and processed using computer vision techniques. The resulting traffic den- sity distribution time series are then analyzed. It is found using the goodness-of-fit test that the traffic density dis- tributions follows heavy-tailmore » models such as Log-gamma, Log-logistic, and Weibull in over 90% of analyzed locations. Moreover, a heavy-tail gives rise to long-range dependence and self-similarity, which we studied by estimating the Hurst exponent (H). Our analysis based on seven different Hurst estimators strongly indicate that the traffic distribution pat- terns are stochastically self-similar (0.5 H 1.0). We believe this is an important finding that will influence the design and development of the next generation traffic simu- lation techniques and also aid in accurately modeling traffic engineering of urban systems. In addition, it shall provide a much needed input for the development of smart cities.« less

How long will the traffic flow time series keep efficacious to forecast the future?

NASA Astrophysics Data System (ADS)

Yuan, PengCheng; Lin, XuXun

2017-02-01

This paper investigate how long will the historical traffic flow time series keep efficacious to forecast the future. In this frame, we collect the traffic flow time series data with different granularity at first. Then, using the modified rescaled range analysis method, we analyze the long memory property of the traffic flow time series by computing the Hurst exponent. We calculate the long-term memory cycle and test its significance. We also compare it with the maximum Lyapunov exponent method result. Our results show that both of the freeway traffic flow time series and the ground way traffic flow time series demonstrate positively correlated trend (have long-term memory property), both of their memory cycle are about 30 h. We think this study is useful for the short-term or long-term traffic flow prediction and management.

Multifractal detrended cross-correlation analysis in the MENA area

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane; Benbachir, Saâd

2013-12-01

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.

The influence of statistical properties of Fourier coefficients on random Gaussian surfaces.

PubMed

de Castro, C P; Luković, M; Andrade, R F S; Herrmann, H J

2017-05-16

Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.

Multifractals in Western Major STOCK Markets Historical Volatilities in Times of Financial Crisis

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

In this paper, the generalized Hurst exponent is used to investigate multifractal properties of historical volatility (CHV) in stock market price and return series before, during and after 2008 financial crisis. Empirical results from NASDAQ, S&P500, TSE, CAC40, DAX, and FTSE stock market data show that there is strong evidence of multifractal patterns in HV of both price and return series. In addition, financial crisis deeply affected the behavior and degree of multifractality in volatility of Western financial markets at price and return levels.

Cross-correlations between West Texas Intermediate crude oil and the stock markets of the BRIC

NASA Astrophysics Data System (ADS)

Ma, Feng; Wei, Yu; Huang, Dengshi; Zhao, Lin

2013-11-01

In this paper, we investigate the cross-correlation properties between West Texas Intermediate crude oil and the stock markets of the BRIC. We use not only the qualitative analysis of the cross-correlation test, but also take the quantitative analysis of the MF-DXA, confirming the cross-correlation relationship between West Texas Intermediate crude oil and the stock markets of the BRIC (Brazil, Russia, India and China) respectively, which have strongly multifractal features, and the cross-correlations are more strongly multifractal in the short term than in the long term. Furthermore, based on the multifractal spectrum, we also find the multifractality strength between the crude oil WTI and Chinese stock market is stronger than the multifractality strength of other pairs. Based on the Iraq war (Mar 20, 2003) and the Financial crisis in 2008, we divide sample period into four segments to research the degree of the multifractal (ΔH) and the market efficiency (and the risk). Finally, we employ the technique of the rolling window to calculate the time-varying EI (efficiency index) and dependent on the EI, we can easily observe the change of stock markets. Furthermore, we explore the relationship between bivariate cross-correlation exponents (Hxy(q)) and the generalized Hurst exponents.

An analysis of stock market efficiency: Developed vs Islamic stock markets using MF-DFA

NASA Astrophysics Data System (ADS)

Rizvi, Syed Aun R.; Dewandaru, Ginanjar; Bacha, Obiyathulla I.; Masih, Mansur

An efficient market has been theoretically proven to be a key component for effective and efficient resource allocation in an economy. This paper incorporates econophysics with Efficient Market Hypothesis to undertake a comparative analysis of Islamic and developed countries’ markets by extending the understanding of their multifractal nature. By applying the Multifractal Detrended Fluctuation Analysis (MFDFA) we calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for 22 broad market indices. The findings provide a deeper understanding of the markets in Islamic countries, where they have traces of highly efficient performance particularly in crisis periods. A key finding is the empirical evidence of the impact of the ‘stage of market development’ on the efficiency of the market. If Islamic countries aim to improve the efficiency of resource allocation, an important area to address is to focus, among others, on enhancing the stage of market development.

Fractal measures of video-recorded trajectories can classify motor subtypes in Parkinson's Disease

NASA Astrophysics Data System (ADS)

Figueiredo, Thiago C.; Vivas, Jamile; Peña, Norberto; Miranda, José G. V.

2016-11-01

Parkinson's Disease is one of the most prevalent neurodegenerative diseases in the world and affects millions of individuals worldwide. The clinical criteria for classification of motor subtypes in Parkinson's Disease are subjective and may be misleading when symptoms are not clearly identifiable. A video recording protocol was used to measure hand tremor of 14 individuals with Parkinson's Disease and 7 healthy subjects. A method for motor subtype classification was proposed based on the spectral distribution of the movement and compared with the existing clinical criteria. Box-counting dimension and Hurst Exponent calculated from the trajectories were used as the relevant measures for the statistical tests. The classification based on the power-spectrum is shown to be well suited to separate patients with and without tremor from healthy subjects and could provide clinicians with a tool to aid in the diagnosis of patients in an early stage of the disease.

Are pound and euro the same currency?

NASA Astrophysics Data System (ADS)

Matsushita, Raul; Gleria, Iram; Figueiredo, Annibal; da Silva, Sergio

2007-08-01

Based on long-range dependence, some analysts claim that the exchange rate time series of the pound sterling and of an artificially extended euro have been locked together for years despite daily changes [M. Ausloos, K. Ivanova, Physica A 286 (2000) 353; K. Ivanova, M. Ausloos, False EUR exchange rates vs DKK, CHF, JPY and USD. What is a strong currency? in: H. Takayasu (Ed.), Empirical Sciences in Financial Fluctuations: The Advent of Econophysics, Springer-Verlag, Berlin, 2002, pp. 62 76]. They conclude that pound and euro are in practice the same currency. We assess the long-range dependence over time through Hurst exponents of pound dollar and extended euro dollar exchange rates employing three alternative techniques, namely rescaled range analysis, detrended fluctuation analysis, and detrended moving average. We find the result above (which is based on detrended fluctuation analysis) not to be robust to the changing techniques and parameterizing.

Appraisal of long term groundwater quality of peninsular India using water quality index and fractal dimension

NASA Astrophysics Data System (ADS)

Rawat, Kishan Singh; Singh, Sudhir Kumar; Jacintha, T. German Amali; Nemčić-Jurec, Jasna; Tripathi, Vinod Kumar

2017-12-01

A review has been made to understand the hydrogeochemical behaviour of groundwater through statistical analysis of long term water quality data (year 2005-2013). Water Quality Index ( WQI), descriptive statistics, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. WQI results showed that majority of samples fall in moderate category during 2005-2013, but monitoring site four falls under severe category (water unfit for domestic use). Brownian time series behaviour (a true random walk nature) exists between calcium (Ca^{2+}) and electric conductivity (EC); magnesium (Mg^{2+}) with EC; sodium (Na+) with EC; sulphate (SO4^{2-}) with EC; total dissolved solids (TDS) with chloride (Cl-) during pre- (2005-2013) and post- (2006-2013) monsoon season. These parameters have a closer value of Hurst exponent ( H) with Brownian time series behaviour condition (H=0.5). The result of times series analysis of water quality data shows a persistent behaviour (a positive autocorrelation) that has played a role between Cl- and Mg^{2+}, Cl- and Ca^{2+}, TDS and Na+, TDS and SO4^{2-}, TDS and Ca^{2+} in pre- and post-monsoon time series because of the higher value of H (>1). Whereas an anti-persistent behaviour (or negative autocorrelation) was found between Cl- and EC, TDS and EC during pre- and post-monsoon due to low value of H. The work outline shows that the groundwater of few areas needs treatment before direct consumption, and it also needs to be protected from contamination.

Hurst Exponent Analysis of Resting-State fMRI Signal Complexity across the Adult Lifespan

PubMed Central

Dong, Jianxin; Jing, Bin; Ma, Xiangyu; Liu, Han; Mo, Xiao; Li, Haiyun

2018-01-01

Exploring functional information among various brain regions across time enables understanding of healthy aging process and holds great promise for age-related brain disease diagnosis. This paper proposed a method to explore fractal complexity of the resting-state functional magnetic resonance imaging (rs-fMRI) signal in the human brain across the adult lifespan using Hurst exponent (HE). We took advantage of the examined rs-fMRI data from 116 adults 19 to 85 years of age (44.3 ± 19.4 years, 49 females) from NKI/Rockland sample. Region-wise and voxel-wise analyses were performed to investigate the effects of age, gender, and their interaction on complexity. In region-wise analysis, we found that the healthy aging is accompanied by a loss of complexity in frontal and parietal lobe and increased complexity in insula, limbic, and temporal lobe. Meanwhile, differences in HE between genders were found to be significant in parietal lobe (p = 0.04, corrected). However, there was no interaction between gender and age. In voxel-wise analysis, the significant complexity decrease with aging was found in frontal and parietal lobe, and complexity increase was found in insula, limbic lobe, occipital lobe, and temporal lobe with aging. Meanwhile, differences in HE between genders were found to be significant in frontal, parietal, and limbic lobe. Furthermore, we found age and sex interaction in right parahippocampal gyrus (p = 0.04, corrected). Our findings reveal HE variations of the rs-fMRI signal across the human adult lifespan and show that HE may serve as a new parameter to assess healthy aging process. PMID:29456489

A shift to randomness of brain oscillations in people with autism.

PubMed

Lai, Meng-Chuan; Lombardo, Michael V; Chakrabarti, Bhismadev; Sadek, Susan A; Pasco, Greg; Wheelwright, Sally J; Bullmore, Edward T; Baron-Cohen, Simon; Suckling, John

2010-12-15

Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions. Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism. Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex. Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions. Copyright © 2010 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

On fractality and chaos in Moroccan family business stock returns and volatility

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-05-01

The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

Long-range dependence in earthquake-moment release and implications for earthquake occurrence probability.

PubMed

Barani, Simone; Mascandola, Claudia; Riccomagno, Eva; Spallarossa, Daniele; Albarello, Dario; Ferretti, Gabriele; Scafidi, Davide; Augliera, Paolo; Massa, Marco

2018-03-28

Since the beginning of the 1980s, when Mandelbrot observed that earthquakes occur on 'fractal' self-similar sets, many studies have investigated the dynamical mechanisms that lead to self-similarities in the earthquake process. Interpreting seismicity as a self-similar process is undoubtedly convenient to bypass the physical complexities related to the actual process. Self-similar processes are indeed invariant under suitable scaling of space and time. In this study, we show that long-range dependence is an inherent feature of the seismic process, and is universal. Examination of series of cumulative seismic moment both in Italy and worldwide through Hurst's rescaled range analysis shows that seismicity is a memory process with a Hurst exponent H ≈ 0.87. We observe that H is substantially space- and time-invariant, except in cases of catalog incompleteness. This has implications for earthquake forecasting. Hence, we have developed a probability model for earthquake occurrence that allows for long-range dependence in the seismic process. Unlike the Poisson model, dependent events are allowed. This model can be easily transferred to other disciplines that deal with self-similar processes.

Multifractality of sectoral price indices: Hurst signature analysis of Cantillon effects in disequilibrium factor markets

NASA Astrophysics Data System (ADS)

Mulligan, Robert F.

2014-06-01

This paper presents Hurst exponent signatures from time series of aggregate price indices for the US over the 1975-2011 time period. Though all highly aggregated, these indices include both broad measures of consumer and producer prices. The constellation of prices evolves as a complex system throughout processes of production and distribution, culminating in the final delivery of output to consumers. Massive feedback characterizes this system, where the demand for consumable output determines the demand for the inputs used to produce it, and supply scarcities for the necessary inputs in turn determine the supply of the final product. Prices in both factor and output markets are jointly determined by interdependent supply and demand conditions. Fractal examination of the interplay among market prices would be of interest regardless, but added interest arises from the consideration of how these markets respond to external shocks over the business cycle, particularly monetary expansion. Because the initial impact of monetary injection is localized in specific sectors, the way the impact on prices diffuses throughout the economy is of special interest.

Fractional Ornstein-Uhlenbeck for index prices of FTSE Bursa Malaysia KLCI

NASA Astrophysics Data System (ADS)

Chen, Kho Chia; Bahar, Arifah; Ting, Chee-Ming

2014-07-01

This paper studies the Ornstein-Uhlenbeck model that incorporates long memory stochastic volatility which is known as fractional Ornstein-Uhlenbeck model. The determination of the existence of long range dependence of the index prices of FTSE Bursa Malaysia KLCI is measured by the Hurst exponent. The empirical distribution of unobserved volatility is estimated using the particle filtering method. The performance between fractional Ornstein -Uhlenbeck and standard Ornstein -Uhlenbeck process had been compared. The mean square errors of the fractional Ornstein-Uhlenbeck model indicated that the model describes index prices better than the standard Ornstein-Uhlenbeck process.

Microstructural investigation of a locally mirror-like surface collected at 4 km depth in a Pomeranian shale sample

NASA Astrophysics Data System (ADS)

Pluymakers, Anne; Renard, Francois

2016-04-01

The presence of shiny sliding surfaces, or mirror surfaces, is sometimes thought to have been caused by slip at seismic velocities. Many fault mirrors reported so far are described to occur in carbonate-rich rocks. Here we present microstructural data on a mirror-like slip surface in the Pomeranian shale, recovered from approximately 4 km depth. The accommodated sliding of this fault is probably small, not more than one or two centimeter. The Pomeranian shale is a dark-grey to black shale, composed of 40-60% illite plus mica, 1-10% organic matter, 10% chlorite, and 10 % carbonates plus minor amounts of K-feldspar, plagioclase and kaolinite. In this sample, the surface is optically smooth with striations and some patches that reflect light. Observations using a Hitachi TM3000 (table-top) SEM show that the striations are omnipresent, though more prominent in the carbonate patches (determined using EDS analysis). The smooth surface is locally covered by granular material with a grain size up to 10 μm. This is shown to consist of a mixture of elements and thus likely locally derived fault gouge. The clay-rich parts of the smooth surface are equidimensional grains, with sub-micron grain sizes, whereas in the unperturbed part of the shale core the individual clay platelets are easy to distinguish, with lengths up to 10 μm. The striated calcite-rich patches appear as single grains with sizes up to several millimeters, though they occasionally are smeared out in a direction parallel to the striations. We have analyzed surface roughness at magnifications of 2.5x to 100x using a standard White Light Interferometer, parallel and perpendicular to slip. At low magnifications, 2.5x and 5x, Hurst exponents were anomalously low, around 0.1 to 0.2, interpreted to be related to a lack of sufficient resolution to pick up the striations. At higher magnification the Hurst exponent is 0.34 to 0.43 parallel to the striation, and 0.44 to 0.61 perpendicular to the striation. This relatively low Hurst exponent suggests that this surface has not experienced high strains, even though it locally exhibits mirror-like properties. As such, this data supports the notion that the formation of shiny surfaces is related to grain size reduction, but does not necessarily indicate major slip events. Additionally, the more strongly visible striation in the carbonate-rich parts indicates that some mineralogies are more prone to the formation of striations than others. A full interpretation of this sample is of course complicated by its small size, but these data suggest that when examining fault mirrors and the presence of striations spatial difference in mineralogy need to be taken into account.

Multiscale multifractal DCCA and complexity behaviors of return intervals for Potts price model

NASA Astrophysics Data System (ADS)

Wang, Jie; Wang, Jun; Stanley, H. Eugene

2018-02-01

To investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events, we use a Potts dynamic system to construct a random financial time series model of the attitudes of market traders. We use multiscale multifractal detrended cross-correlation analysis (MM-DCCA) and Lempel-Ziv complexity (LZC) perform numerical research of the return intervals for two significant China's stock market indices and for the proposed model. The new MM-DCCA method is based on the Hurst surface and provides more interpretable cross-correlations of the dynamic mechanism between different return interval series. We scale the LZC method with different exponents to illustrate the complexity of return intervals in different scales. Empirical studies indicate that the proposed return intervals from the Potts system and the real stock market indices hold similar statistical properties.

Fault diagnosis of rolling bearings based on multifractal detrended fluctuation analysis and Mahalanobis distance criterion

NASA Astrophysics Data System (ADS)

Lin, Jinshan; Chen, Qian

2013-07-01

Vibration data of faulty rolling bearings are usually nonstationary and nonlinear, and contain fairly weak fault features. As a result, feature extraction of rolling bearing fault data is always an intractable problem and has attracted considerable attention for a long time. This paper introduces multifractal detrended fluctuation analysis (MF-DFA) to analyze bearing vibration data and proposes a novel method for fault diagnosis of rolling bearings based on MF-DFA and Mahalanobis distance criterion (MDC). MF-DFA, an extension of monofractal DFA, is a powerful tool for uncovering the nonlinear dynamical characteristics buried in nonstationary time series and can capture minor changes of complex system conditions. To begin with, by MF-DFA, multifractality of bearing fault data was quantified with the generalized Hurst exponent, the scaling exponent and the multifractal spectrum. Consequently, controlled by essentially different dynamical mechanisms, the multifractality of four heterogeneous bearing fault data is significantly different; by contrast, controlled by slightly different dynamical mechanisms, the multifractality of homogeneous bearing fault data with different fault diameters is significantly or slightly different depending on different types of bearing faults. Therefore, the multifractal spectrum, as a set of parameters describing multifractality of time series, can be employed to characterize different types and severity of bearing faults. Subsequently, five characteristic parameters sensitive to changes of bearing fault conditions were extracted from the multifractal spectrum and utilized to construct fault features of bearing fault data. Moreover, Hilbert transform based envelope analysis, empirical mode decomposition (EMD) and wavelet transform (WT) were utilized to study the same bearing fault data. Also, the kurtosis and the peak levels of the EMD or the WT component corresponding to the bearing tones in the frequency domain were carefully checked and used as the bearing fault features. Next, MDC was used to classify the bearing fault features extracted by EMD, WT and MF-DFA in the time domain and assess the abilities of the three methods to extract fault features from bearing fault data. The results show that MF-DFA seems to outperform each of envelope analysis, statistical parameters, EMD and WT in feature extraction of bearing fault data and then the proposed method in this paper delivers satisfactory performances in distinguishing different types and severity of bearing faults. Furthermore, to further ascertain the nature causing the multifractality of bearing vibration data, the generalized Hurst exponents of the original bearing vibration data were compared with those of the shuffled and the surrogated data. Consequently, the long-range correlations for small and large fluctuations of data seem to be chiefly responsible for the multifractality of bearing vibration data.

EYE MOVEMENT RECORDING AND NONLINEAR DYNAMICS ANALYSIS – THE CASE OF SACCADES#

PubMed Central

Aştefănoaei, Corina; Pretegiani, Elena; Optican, L.M.; Creangă, Dorina; Rufa, Alessandra

2015-01-01

Evidence of a chaotic behavioral trend in eye movement dynamics was examined in the case of a saccadic temporal series collected from a healthy human subject. Saccades are highvelocity eye movements of very short duration, their recording being relatively accessible, so that the resulting data series could be studied computationally for understanding the neural processing in a motor system. The aim of this study was to assess the complexity degree in the eye movement dynamics. To do this we analyzed the saccadic temporal series recorded with an infrared camera eye tracker from a healthy human subject in a special experimental arrangement which provides continuous records of eye position, both saccades (eye shifting movements) and fixations (focusing over regions of interest, with rapid, small fluctuations). The semi-quantitative approach used in this paper in studying the eye functioning from the viewpoint of non-linear dynamics was accomplished by some computational tests (power spectrum, portrait in the state space and its fractal dimension, Hurst exponent and largest Lyapunov exponent) derived from chaos theory. A high complexity dynamical trend was found. Lyapunov largest exponent test suggested bi-stability of cellular membrane resting potential during saccadic experiment. PMID:25698889

Underlying mathematics in diversification of human olfactory receptors in different loci.

PubMed

Hassan, Sk Sarif; Choudhury, Pabitra Pal; Goswami, Arunava

2013-12-01

As per conservative estimate, approximately 51-105 Olfactory Receptors (ORs) loci are present in human genome occurring in clusters. These clusters are apparently unevenly spread as mosaics over 21 pairs of human chromosomes. Olfactory Receptor (OR) gene families which are thought to have expanded for the need to provide recognition capability for a huge number of pure and complex odorants, form the largest known multigene family in the human genome. Recent studies have shown that 388 full length and 414 OR pseudo-genes are present in these OR genomic clusters. In this paper, the authors report a classification method for all human ORs based on their sequential quantitative information like presence of poly strings of nucleotides bases, long range correlation and so on. An L-System generated sequence has been taken as an input into a star-model of specific subfamily members and resultant sequence has been mapped to a specific OR based on the classification scheme using fractal parameters like Hurst exponent and fractal dimensions.

Entropy of balance - some recent results

PubMed Central

2010-01-01

Background Entropy when applied to biological signals is expected to reflect the state of the biological system. However the physiological interpretation of the entropy is not always straightforward. When should high entropy be interpreted as a healthy sign, and when as marker of deteriorating health? We address this question for the particular case of human standing balance and the Center of Pressure data. Methods We have measured and analyzed balance data of 136 participants (young, n = 45; elderly, n = 91) comprising in all 1085 trials, and calculated the Sample Entropy (SampEn) for medio-lateral (M/L) and anterior-posterior (A/P) Center of Pressure (COP) together with the Hurst self-similariy (ss) exponent α using Detrended Fluctuation Analysis (DFA). The COP was measured with a force plate in eight 30 seconds trials with eyes closed, eyes open, foam, self-perturbation and nudge conditions. Results 1) There is a significant difference in SampEn for the A/P-direction between the elderly and the younger groups Old > young. 2) For the elderly we have in general A/P > M/L. 3) For the younger group there was no significant A/P-M/L difference with the exception for the nudge trials where we had the reverse situation, A/P < M/L. 4) For the elderly we have, Eyes Closed > Eyes Open. 5) In case of the Hurst ss-exponent we have for the elderly, M/L > A/P. Conclusions These results seem to be require some modifications of the more or less established attention-constraint interpretation of entropy. This holds that higher entropy correlates with a more automatic and a less constrained mode of balance control, and that a higher entropy reflects, in this sense, a more efficient balancing. PMID:20670457

Nanoscale Roughness of Natural Fault Surfaces Controlled by Scale-Dependent Yield Strength

NASA Astrophysics Data System (ADS)

Thom, C. A.; Brodsky, E. E.; Carpick, R. W.; Pharr, G. M.; Oliver, W. C.; Goldsby, D. L.

2017-09-01

Many natural fault surfaces exhibit remarkably similar scale-dependent roughness, which may reflect the scale-dependent yield strength of rocks. Using atomic force microscopy (AFM), we show that a sample of the Corona Heights Fault exhibits isotropic surface roughness well-described by a power law, with a Hurst exponent of 0.75 +/- 0.05 at all wavelengths from 60 nm to 10 μm. The roughness data and a recently proposed theoretical framework predict that yield strength varies with length scale as λ-0.25+/-0.05. Nanoindentation tests on the Corona Heights sample and another fault sample whose topography was previously measured with AFM (the Yair Fault) reveal a scale-dependent yield stress with power-law exponents of -0.12 +/- 0.06 and -0.18 +/- 0.08, respectively. These values are within one to two standard deviations of the predicted value, and provide experimental evidence that fault roughness is controlled by intrinsic material properties, which produces a characteristic surface geometry.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burkholder, Michael B.; Litster, Shawn, E-mail: litster@andrew.cmu.edu

In this study, we analyze the stability of two-phase flow regimes and their transitions using chaotic and fractal statistics, and we report new measurements of dynamic two-phase pressure drop hysteresis that is related to flow regime stability and channel water content. Two-phase flow dynamics are relevant to a variety of real-world systems, and quantifying transient two-phase flow phenomena is important for efficient design. We recorded two-phase (air and water) pressure drops and flow images in a microchannel under both steady and transient conditions. Using Lyapunov exponents and Hurst exponents to characterize the steady-state pressure fluctuations, we develop a new, measurablemore » regime identification criteria based on the dynamic stability of the two-phase pressure signal. We also applied a new experimental technique by continuously cycling the air flow rate to study dynamic hysteresis in two-phase pressure drops, which is separate from steady-state hysteresis and can be used to understand two-phase flow development time scales. Using recorded images of the two-phase flow, we show that the capacitive dynamic hysteresis is related to channel water content and flow regime stability. The mixed-wettability microchannel and in-channel water introduction used in this study simulate a polymer electrolyte fuel cell cathode air flow channel.« less

Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price

NASA Astrophysics Data System (ADS)

Zhuang, Xiaoyang; Wei, Yu; Ma, Feng

2015-07-01

In this paper, the multifractality and efficiency degrees of ten important Chinese sectoral indices are evaluated using the methods of MF-DFA and generalized Hurst exponents. The study also scrutinizes the dynamics of the efficiency of Chinese sectoral stock market by the rolling window approach. The overall empirical findings revealed that all the sectoral indices of Chinese stock market exist different degrees of multifractality. The results of different efficiency measures have agreed on that the 300 Materials index is the least efficient index. However, they have a slight diffidence on the most efficient one. The 300 Information Technology, 300 Telecommunication Services and 300 Health Care indices are comparatively efficient. We also investigate the cross-correlations between the ten sectoral indices and WTI crude oil price based on Multifractal Detrended Cross-correlation Analysis. At last, some relevant discussions and implications of the empirical results are presented.

Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2015-11-01

The purpose of this study is to investigate long-range dependence in trend and short variation of stock market price and return series before, during, and after 2008 financial crisis. Variational mode decomposition (VMD), a newly introduced technique for signal processing, is adopted to decompose stock market data into a finite set of modes so as to obtain long term trends and short term movements of stock market data. Then, the detrended fluctuation analysis (DFA) and range scale (R/S) analysis are used to estimate Hurst exponent in each variational mode obtained from VMD. For both price and return series, the empirical results from twelve international stock markets show evidence that long term trends are persistent, whilst short term variations are anti-persistent before, during, and after 2008 financial crisis.

A random walk model to evaluate autism

NASA Astrophysics Data System (ADS)

Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.

2018-02-01

A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.

Assessing Spontaneous Combustion Instability with Recurrence Quantification Analysis

NASA Technical Reports Server (NTRS)

Eberhart, Chad J.; Casiano, Matthew J.

2016-01-01

Spontaneous instabilities can pose a significant challenge to verification of combustion stability, and characterizing its onset is an important avenue of improvement for stability assessments of liquid propellant rocket engines. Recurrence Quantification Analysis (RQA) is used here to explore nonlinear combustion dynamics that might give insight into instability. Multiple types of patterns representative of different dynamical states are identified within fluctuating chamber pressure data, and markers for impending instability are found. A class of metrics which describe these patterns is also calculated. RQA metrics are compared with and interpreted against another metric from nonlinear time series analysis, the Hurst exponent, to help better distinguish between stable and unstable operation.

Long-range correlations in an online betting exchange for a football tournament

NASA Astrophysics Data System (ADS)

Hardiman, Stephen J.; Richmond, Peter; Hutzler, Stefan

2010-10-01

We analyze the changes in the market odds of football matches in an online betting exchange, Betfair.com. We identify the statistical differences between the returns that occur when the game play is under way, which we argue are driven by match events, and the returns that occur during half-time, which we ascribe to a trader-driven noise. Furthermore, using detrended fluctuation analysis we identify anti-persistence (Hurst exponent H<0.5) in odds returns and long memory (H>0.5) in the volatilities, which we attribute to the trader-driven noise. The time series of trading volume are found to be short-memory processes.

Self-organized criticality in a cold plasma

NASA Astrophysics Data System (ADS)

Alex, Prince; Carreras, Benjamin Andres; Arumugam, Saravanan; Sinha, Suraj Kumar

2017-12-01

We present direct evidence for the existence of self-organized critical behavior in cold plasma. A multiple anodic double layer structure generated in a double discharge plasma setup shows critical behavior for the anode bias above a threshold value. Analysis of the floating potential fluctuations reveals the existence of long-range time correlations and power law behavior in the tail of the probability distribution function of the fluctuations. The measured Hurst exponent and the power law tail in the rank function are strong indication of the self-organized critical behavior of the system and hence provide a condition under which complexities arise in cold plasma.

Characteristic time scales in the American dollar-Mexican peso exchange currency market

NASA Astrophysics Data System (ADS)

Alvarez-Ramirez, Jose

2002-06-01

Daily fluctuations of the American dollar-Mexican peso exchange currency market are studied using multifractal analysis methods. It is found evidence of multiaffinity of daily fluctuations in the sense that the qth-order (roughness) Hurst exponent Hq varies with changes in q. It is also found that there exist several characteristic time scales ranging from week to year. Accordingly, the market exhibits persistence in the sense that instabilities introduced by market events acting around the characteristic time scales (mainly, quarter and year) would propagate through the future market activity. Some implications of our results on the regulation of the dollar-mexpeso market activity are discussed.

Quantification of scaling exponents and dynamical complexity of microwave refractivity in a tropical climate

NASA Astrophysics Data System (ADS)

Fuwape, Ibiyinka A.; Ogunjo, Samuel T.

2016-12-01

Radio refractivity index is used to quantify the effect of atmospheric parameters in communication systems. Scaling and dynamical complexities of radio refractivity across different climatic zones of Nigeria have been studied. Scaling property of the radio refractivity across Nigeria was estimated from the Hurst Exponent obtained using two different scaling methods namely: The Rescaled Range (R/S) and the detrended fluctuation analysis(DFA). The delay vector variance (DVV), Largest Lyapunov Exponent (λ1) and Correlation Dimension (D2) methods were used to investigate nonlinearity and the results confirm the presence of deterministic nonlinear profile in the radio refractivity time series. The recurrence quantification analysis (RQA) was used to quantify the degree of chaoticity in the radio refractivity across the different climatic zones. RQA was found to be a good measure for identifying unique fingerprint and signature of chaotic time series data. Microwave radio refractivity was found to be persistent and chaotic in all the study locations. The dynamics of radio refractivity increases in complexity and chaoticity from the Coastal region towards the Sahelian climate. The design, development and deployment of robust and reliable microwave communication link in the region will be greatly affected by the chaotic nature of radio refractivity in the region.

Comparison of the Scaling Properties of EUV Intensity Fluctuations in Coronal Holes to those in Regions of Quiet Sun

NASA Astrophysics Data System (ADS)

Cadavid, Ana Cristina; Lawrence, John K.; Jennings, Peter John

2017-08-01

We investigate the scaling properties of EUV intensity fluctuations seen in low-latitude coronal holes (CH) and in regions of Quiet Sun (QS), in signals obtained with the SDO/AIA instrument in the 193 Å waveband. Contemporaneous time series in the 171 and 211 Å wavebands are used for comparison among emissions at different heights in the transition region and low corona. Potential-field extrapolations of contemporaneous SDO/HMI line-of-sight magnetic fields provide a context in the physical environment. Detrended fluctuation analysis (DFA) shows that the variance of the fluctuations obeys a power-law as a function of temporal scales with periods in the range ~15-60 min. This scaling is characterized by a generalized Hurst exponent α. In QS regions, and in regions within CHs that include magnetic bipoles, the scaling exponent lies in the range 1.0 < α < 1.5, and it thus corresponds to anti-correlated, turbulent-like, dynamical processes. Regions inside the coronal holes primarily associated with magnetic field of a dominant single polarity, have a generalized exponent (0.5 < α < 1) corresponding to positively correlated (“persistent”) processes. The results indicate the influence of the magnetic fields on the dynamics of the emission.

Nonlinear stratospheric variability: multifractal de-trended fluctuation analysis and singularity spectra

PubMed Central

Domeisen, Daniela I. V.

2016-01-01

Characterizing the stratosphere as a turbulent system, temporal fluctuations often show different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. In this study, the different scaling laws in the long-term stratospheric variability are studied using multifractal de-trended fluctuation analysis (MF-DFA). The analysis is performed comparing four re-analysis products and different realizations of an idealized numerical model, isolating the role of topographic forcing and seasonal variability, as well as the absence of climate teleconnections and small-scale forcing. The Northern Hemisphere (NH) shows a transition of scaling exponents for time scales shorter than about 1 year, for which the variability is multifractal and scales in time with a power law corresponding to a red spectrum, to longer time scales, for which the variability is monofractal and scales in time with a power law corresponding to white noise. Southern Hemisphere (SH) variability also shows a transition at annual scales. The SH also shows a narrower dynamical range in multifractality than the NH, as seen in the generalized Hurst exponent and in the singularity spectra. The numerical integrations show that the models are able to reproduce the low-frequency variability but are not able to fully capture the shorter term variability of the stratosphere. PMID:27493560

DNA viewed as an out-of-equilibrium structure

NASA Astrophysics Data System (ADS)

Provata, A.; Nicolis, C.; Nicolis, G.

2014-05-01

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ2 tests shows that DNA can not be described as a low order Markov chain of order up to r =6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

DNA viewed as an out-of-equilibrium structure.

PubMed

Provata, A; Nicolis, C; Nicolis, G

2014-05-01

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ^{2} tests shows that DNA can not be described as a low order Markov chain of order up to r=6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

Long memory in patterns of mobile phone usage

NASA Astrophysics Data System (ADS)

Owczarczuk, Marcin

2012-02-01

In this article we show that usage of a mobile phone, i.e. daily series of number of calls made by a customer, exhibits long memory. We use a sample of 4502 postpaid users from a Polish mobile operator and study their two-year billing history. We estimate Hurst exponent by nine estimators: aggregated variance method, differencing the variance, absolute values of the aggregated series, Higuchi's method, residuals of regression, the R/S method, periodogram method, modified periodogram method and Whittle estimator. We also analyze empirically relations between estimators. Long memory implies an inertial effect in clients' behavior which may be used by mobile operators to accelerate usage and gain additional profit.

Schramm-Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

NASA Astrophysics Data System (ADS)

Posé, N.; Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.

Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm-Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for H=-1 and H=0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

Study of memory effects in international market indices

NASA Astrophysics Data System (ADS)

Mariani, M. C.; Florescu, I.; Beccar Varela, M. P.; Ncheuguim, E.

2010-04-01

Long term memory effects in stock market indices that represent internationally diversified stocks are analyzed in this paper and the results are compared with the S&P 500 index. The Hurst exponent and the Detrended fluctuation analysis (DFA) technique are the tools used for this analysis. The financial time-series data of these indices are tested with the Normalized Truncated Levy Flight to check whether the evolution of these indices is explained by the TLF. Some features that seem to be specific for international indices are discovered and briefly discussed. In particular, a potential investor seems to be faced with new investment opportunities in emerging markets during and especially after a crisis.

Roughness of stylolites: implications of 3D high resolution topography measurements.

PubMed

Schmittbuhl, J; Renard, F; Gratier, J P; Toussaint, R

2004-12-03

Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling invariance. At large scales, the Hurst exponent is zeta(1) approximately 0.5 and very different from that at small scales where zeta(2) approximately 1.2. A crossover length scale at around L(c)=1 mm is well characterized. Measurements are consistent with a Langevin equation that describes the growth of a stylolitic interface as a competition between stabilizing long range elastic interactions at large scales or local surface tension effects at small scales and a destabilizing quenched material disorder.

Orthogonal system of fractural and integrated diagnostic features in vibration analysis

NASA Astrophysics Data System (ADS)

Kostyukov, V. N.; Boychenko, S. N.

2017-08-01

The paper presents the results obtained in the studies of the orthogonality of the vibration diagnostic features system comprising the integrated features, particularly - root mean square values of vibration acceleration, vibration velocity, vibration displacement and fractal feature (Hurst exponent). To diagnose the condition of the equipment by the vibration signal, the orthogonality of the vibration diagnostic features is important. The fact of orthogonality shows that the system of features is not superfluous and allows the maximum coverage of the state space of the object being diagnosed. This, in turn, increases reliability of the machinery condition monitoring results. The studies were carried out on the models of vibration signals using the programming language R.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamışlıoğlu, Miraç, E-mail: m.kamislioglu@gmail.com; Külahcı, Fatih, E-mail: fatihkulahci@firat.edu.tr

Nonlinear time series analysis techniques have large application areas on the geoscience and geophysics fields. Modern nonlinear methods are provided considerable evidence for explain seismicity phenomena. In this study nonlinear time series analysis, fractal analysis and spectral analysis have been carried out for researching the chaotic behaviors of release radon gas ({sup 222}Rn) concentration occurring during seismic events. Nonlinear time series analysis methods (Lyapunov exponent, Hurst phenomenon, correlation dimension and false nearest neighbor) were applied for East Anatolian Fault Zone (EAFZ) Turkey and its surroundings where there are about 35,136 the radon measurements for each region. In this paper weremore » investigated of {sup 222}Rn behavior which it’s used in earthquake prediction studies.« less

Network Analyses for Space-Time High Frequency Wind Data

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Kanevski, Mikhail

2017-04-01

Recently, network science has shown an important contribution to the analysis, modelling and visualization of complex time series. Numerous existing methods have been proposed for constructing networks. This work studies spatio-temporal wind data by using networks based on the Granger causality test. Furthermore, a visual comparison is carried out with several frequencies of data and different size of moving window. The main attention is paid to the temporal evolution of connectivity intensity. The Hurst exponent is applied on the provided time series in order to explore if there is a long connectivity memory. The results explore the space time structure of wind data and can be applied to other environmental data. The used dataset presents a challenging case study. It consists of high frequency (10 minutes) wind data from 120 measuring stations in Switzerland, for a time period of 2012-2013. The distribution of stations covers different geomorphological zones and elevation levels. The results are compared with the Person correlation network as well.

Investigating Long-Range Dependence in American Treasury Bills Variations and Volatilities during Stable and Unstable Periods

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2016-05-01

Detrended fluctuation analysis (DFA) is used to examine long-range dependence in variations and volatilities of American treasury bills (TB) during periods of low and high movements in TB rates. Volatility series are estimated by generalized autoregressive conditional heteroskedasticity (GARCH) model under Gaussian, Student, and the generalized error distribution (GED) assumptions. The DFA-based Hurst exponents from 3-month, 6-month, and 1-year TB data indicates that in general the dynamics of the TB variations process is characterized by persistence during stable time period (before 2008 international financial crisis) and anti-persistence during unstable time period (post-2008 international financial crisis). For volatility series, it is found that; for stable period; 3-month volatility process is more likely random, 6-month volatility process is anti-persistent, and 1-year volatility process is persistent. For unstable period, estimation results show that the generating process is persistent for all maturities and for all distributional assumptions.

Characterization of exchange rate regimes based on scaling and correlation properties of volatility for ASEAN-5 countries

NASA Astrophysics Data System (ADS)

Muniandy, Sithi V.; Uning, Rosemary

2006-11-01

Foreign currency exchange rate policies of ASEAN member countries have undergone tremendous changes following the 1997 Asian financial crisis. In this paper, we study the fractal and long-memory characteristics in the volatility of five ASEAN founding members’ exchange rates with respect to US dollar. The impact of exchange rate policies implemented by the ASEAN-5 countries on the currency fluctuations during pre-, mid- and post-crisis are briefly discussed. The time series considered are daily price returns, absolute returns and aggregated absolute returns, each partitioned into three segments based on the crisis regimes. These time series are then modeled using fractional Gaussian noise, fractionally integrated ARFIMA (0,d,0) and generalized Cauchy process. The first two stationary models provide the description of long-range dependence through Hurst and fractional differencing parameter, respectively. Meanwhile, the generalized Cauchy process offers independent estimation of fractal dimension and long memory exponent. In comparison, among the three models we found that the generalized Cauchy process showed greater sensitivity to transition of exchange rate regimes that were implemented by ASEAN-5 countries.

[Hydrologic variability and sensitivity based on Hurst coefficient and Bartels statistic].

PubMed

Lei, Xu; Xie, Ping; Wu, Zi Yi; Sang, Yan Fang; Zhao, Jiang Yan; Li, Bin Bin

2018-04-01

Due to the global climate change and frequent human activities in recent years, the pure stochastic components of hydrological sequence is mixed with one or several of the variation ingredients, including jump, trend, period and dependency. It is urgently needed to clarify which indices should be used to quantify the degree of their variability. In this study, we defined the hydrological variability based on Hurst coefficient and Bartels statistic, and used Monte Carlo statistical tests to test and analyze their sensitivity to different variants. When the hydrological sequence had jump or trend variation, both Hurst coefficient and Bartels statistic could reflect the variation, with the Hurst coefficient being more sensitive to weak jump or trend variation. When the sequence had period, only the Bartels statistic could detect the mutation of the sequence. When the sequence had a dependency, both the Hurst coefficient and the Bartels statistics could reflect the variation, with the latter could detect weaker dependent variations. For the four variations, both the Hurst variability and Bartels variability increased with the increases of variation range. Thus, they could be used to measure the variation intensity of the hydrological sequence. We analyzed the temperature series of different weather stations in the Lancang River basin. Results showed that the temperature of all stations showed the upward trend or jump, indicating that the entire basin had experienced warming in recent years and the temperature variability in the upper and lower reaches was much higher. This case study showed the practicability of the proposed method.

Multi-scale correlations in different futures markets

NASA Astrophysics Data System (ADS)

Bartolozzi, M.; Mellen, C.; di Matteo, T.; Aste, T.

2007-07-01

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.

Coherent changes of multifractal properties of continuous acoustic emission at failure of heterogeneous materials

NASA Astrophysics Data System (ADS)

Panteleev, Ivan; Bayandin, Yuriy; Naimark, Oleg

2017-12-01

This work performs a correlation analysis of the statistical properties of continuous acoustic emission recorded in different parts of marble and fiberglass laminate samples under quasi-static deformation. A spectral coherent measure of time series, which is a generalization of the squared coherence spectrum on a multidimensional series, was chosen. The spectral coherent measure was estimated in a sliding time window for two parameters of the acoustic emission multifractal singularity spectrum: the spectrum width and the generalized Hurst exponent realizing the maximum of the singularity spectrum. It is shown that the preparation of the macrofracture focus is accompanied by the synchronization (coherent behavior) of the statistical properties of acoustic emission in allocated frequency intervals.

Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market

NASA Astrophysics Data System (ADS)

Kuroda, Koji; Maskawa, Jun-ichi; Murai, Joshin

2013-08-01

Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.

Robust non-Gaussian statistics and long-range correlation of total ozone

NASA Astrophysics Data System (ADS)

Toumi, R.; Syroka, J.; Barnes, C.; Lewis, P.

2001-01-01

Three long-term total ozone time series at Camborne, Lerwick and Arosa are examined for their statistical properties. Non-Gaussian behaviour is seen for all locations. There are large interannual fluctuations in the higher moments of the probability distribution. However, only the mean for all stations and summer standard deviation at Lerwick show significant trends. This suggests that there has been no long-term change in the stratospheric circulation, but there are decadal variations. The time series can be also characterised as scale invariant with a Hurst exponent of about 0.8 for all three sites. The Arosa time series was found to be weakly intermittent, in agreement with the non-Gaussian characteristics of the data set

Multifractal structures for the Russian stock market

NASA Astrophysics Data System (ADS)

Ikeda, Taro

2018-02-01

In this paper, we apply the multifractal detrended fluctuation analysis (MFDFA) to the Russian stock price returns. To the best of our knowledge, this paper is the first to reveal the multifractal structures for the Russian stock market by financial crises. The contributions of the paper are twofold. (i) Finding the multifractal structures for the Russian stock market. The generalized Hurst exponents estimated become highly-nonlinear to the order of the fluctuation functions. (ii) Computing the multifractality degree according to Zunino et al. (2008). We find that the multifractality degree of the Russian stock market can be categorized within emerging markets, however, the Russian 1998 crisis and the global financial crisis dampen the degree when we consider the order of the polynomial trends in the MFDFA.

Financial Markets during Highly Anxious Time: Multifractal Fluctuations in Asset Returns

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

Building on the notion that systems and in particular complex systems such as stock exchange markets reveal their structure better when they are under stress, we analyze the multifractal character and nonlinear properties of four major stock market indices during financial meltdowns by means of the multifractal detrended fluctuation analysis (MF-DFA). The three distinct financial crises under investigation are the Black Monday, the Dot-Com and the Great Recession. Scaling and Hurst exponents are derived as well as the singularity spectra. The results show that all indices exhibit strong multifractal properties. The complexity of the markets is higher under the Black Monday event revealed by the width of the singularity spectrum and the higher α0 parameter.

Earthquake scaling laws for rupture geometry and slip heterogeneity

NASA Astrophysics Data System (ADS)

Thingbaijam, Kiran K. S.; Mai, P. Martin; Goda, Katsuichiro

2016-04-01

We analyze an extensive compilation of finite-fault rupture models to investigate earthquake scaling of source geometry and slip heterogeneity to derive new relationships for seismic and tsunami hazard assessment. Our dataset comprises 158 earthquakes with a total of 316 rupture models selected from the SRCMOD database (http://equake-rc.info/srcmod). We find that fault-length does not saturate with earthquake magnitude, while fault-width reveals inhibited growth due to the finite seismogenic thickness. For strike-slip earthquakes, fault-length grows more rapidly with increasing magnitude compared to events of other faulting types. Interestingly, our derived relationship falls between the L-model and W-model end-members. In contrast, both reverse and normal dip-slip events are more consistent with self-similar scaling of fault-length. However, fault-width scaling relationships for large strike-slip and normal dip-slip events, occurring on steeply dipping faults (δ~90° for strike-slip faults, and δ~60° for normal faults), deviate from self-similarity. Although reverse dip-slip events in general show self-similar scaling, the restricted growth of down-dip fault extent (with upper limit of ~200 km) can be seen for mega-thrust subduction events (M~9.0). Despite this fact, for a given earthquake magnitude, subduction reverse dip-slip events occupy relatively larger rupture area, compared to shallow crustal events. In addition, we characterize slip heterogeneity in terms of its probability distribution and spatial correlation structure to develop a complete stochastic random-field characterization of earthquake slip. We find that truncated exponential law best describes the probability distribution of slip, with observable scale parameters determined by the average and maximum slip. Applying Box-Cox transformation to slip distributions (to create quasi-normal distributed data) supports cube-root transformation, which also implies distinctive non-Gaussian slip distributions. To further characterize the spatial correlations of slip heterogeneity, we analyze the power spectral decay of slip applying the 2-D von Karman auto-correlation function (parameterized by the Hurst exponent, H, and correlation lengths along strike and down-slip). The Hurst exponent is scale invariant, H = 0.83 (± 0.12), while the correlation lengths scale with source dimensions (seismic moment), thus implying characteristic physical scales of earthquake ruptures. Our self-consistent scaling relationships allow constraining the generation of slip-heterogeneity scenarios for physics-based ground-motion and tsunami simulations.

Is there any connection between the network morphology and the fluctuations of the stock market index?

NASA Astrophysics Data System (ADS)

Stefan, F. M.; Atman, A. P. F.

2015-02-01

Models which consider behavioral aspects of the investors have attracted increasing interest in the Finance and Econophysics literature in the last years. Different behavioral profiles (imitation, anti-imitation, indifference) were proposed for the investors, which take their decision based on their trust network (neighborhood). Results from agent-based models have shown that most of the features observed in actual stock market indices can be replicated in simulations. Here, we present a deeper investigation of an agent based model considering different network morphologies (regular, random, small-world) for the investors' trust network, in an attempt to answer the question raised in the title. We study the model by considering four scenarios for the investors and different initial conditions to analyze their influence in the stock market fluctuations. We have characterized the stationary limit for each scenario tested, focusing on the changes introduced when complex networks were used, and calculated the Hurst exponent in some cases. Simulations showed interesting results suggesting that the fluctuations of the stock market index are strongly affected by the network morphology, a remarkable result which we believe was never reported or predicted before.

Nonlinear bivariate dependency of price-volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

NASA Astrophysics Data System (ADS)

He, Ling-Yun; Chen, Shu-Peng

2011-01-01

Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.

Temporal variability and memory in sediment transport in an experimental step-pool channel

NASA Astrophysics Data System (ADS)

Saletti, Matteo; Molnar, Peter; Zimmermann, André; Hassan, Marwan A.; Church, Michael

2015-11-01

Temporal dynamics of sediment transport in steep channels using two experiments performed in a steep flume (8%) with natural sediment composed of 12 grain sizes are studied. High-resolution (1 s) time series of sediment transport were measured for individual grain-size classes at the outlet of the flume for different combinations of sediment input rates and flow discharges. Our aim in this paper is to quantify (a) the relation of discharge and sediment transport and (b) the nature and strength of memory in grain-size-dependent transport. None of the simple statistical descriptors of sediment transport (mean, extreme values, and quantiles) display a clear relation with water discharge, in fact a large variability between discharge and sediment transport is observed. Instantaneous transport rates have probability density functions with heavy tails. Bed load bursts have a coarser grain-size distribution than that of the entire experiment. We quantify the strength and nature of memory in sediment transport rates by estimating the Hurst exponent and the autocorrelation coefficient of the time series for different grain sizes. Our results show the presence of the Hurst phenomenon in transport rates, indicating long-term memory which is grain-size dependent. The short-term memory in coarse grain transport increases with temporal aggregation and this reveals the importance of the sampling duration of bed load transport rates in natural streams, especially for large fractions.

Path length entropy analysis of diastolic heart sounds.

PubMed

Griffel, Benjamin; Zia, Mohammad K; Fridman, Vladamir; Saponieri, Cesare; Semmlow, John L

2013-09-01

Early detection of coronary artery disease (CAD) using the acoustic approach, a noninvasive and cost-effective method, would greatly improve the outcome of CAD patients. To detect CAD, we analyze diastolic sounds for possible CAD murmurs. We observed diastolic sounds to exhibit 1/f structure and developed a new method, path length entropy (PLE) and a scaled version (SPLE), to characterize this structure to improve CAD detection. We compare SPLE results to Hurst exponent, Sample entropy and Multiscale entropy for distinguishing between normal and CAD patients. SPLE achieved a sensitivity-specificity of 80%-81%, the best of the tested methods. However, PLE and SPLE are not sufficient to prove nonlinearity, and evaluation using surrogate data suggests that our cardiovascular sound recordings do not contain significant nonlinear properties. Copyright © 2013 Elsevier Ltd. All rights reserved.

A new methodological approach for worldwide beryllium-7 time series analysis

NASA Astrophysics Data System (ADS)

Bianchi, Stefano; Longo, Alessandro; Plastino, Wolfango

2018-07-01

Time series analyses of cosmogenic radionuclide 7Be and 22Na atmospheric activity concentrations and meteorological data observed at twenty-five International Monitoring System (IMS) stations of the Comprehensive Nuclear-Test-Ban Treaty Organisation (CTBTO) have shown great variability in terms of noise structures, harmonic content, cross-correlation patterns and local Hurst exponent behaviour. Noise content and its structure has been extracted and characterised for the two radionuclides time series. It has been found that the yearly component, which is present in most of the time series, is not stationary, but has a percentage weight that varies with time. Analysis of atmospheric activity concentrations of 7Be, measured at IMS stations, has shown them to be influenced by distinct meteorological patterns, mainly by atmospheric pressure and temperature.

Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes.

PubMed

de Castro, C P; Luković, M; Pompanin, G; Andrade, R F S; Herrmann, H J

2018-03-27

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We show numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H ∈ [-1, 0] is statistically equivalent to SLE curves. Our results suggest that the external perimeter also retains the Markovian properties, confirmed by the absence of time correlations in the driving function and the fact that the latter is Gaussian distributed for any specific time. We also confirm that for all H the variance of the winding angle grows logarithmically with size.

Inefficiency in Latin-American market indices

NASA Astrophysics Data System (ADS)

Zunino, L.; Tabak, B. M.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.

2007-11-01

We explore the deviations from efficiency in the returns and volatility returns of Latin-American market indices. Two different approaches are considered. The dynamics of the Hurst exponent is obtained via a wavelet rolling sample approach, quantifying the degree of long memory exhibited by the stock market indices under analysis. On the other hand, the Tsallis q entropic index is measured in order to take into account the deviations from the Gaussian hypothesis. Different dynamic rankings of inefficieny are obtained, each of them contemplates a different source of inefficiency. Comparing with the results obtained for a developed country (US), we confirm a similar degree of long-range dependence for our emerging markets. Moreover, we show that the inefficiency in the Latin-American countries comes principally from the non-Gaussian form of the probability distributions.

Self-Organized Criticality Properties of the Turbulence-Induced Particle Flux at the Plasma Edge of the HT-6M Tokamak

NASA Astrophysics Data System (ADS)

Wang, Wen-Hao; Yu, Chang-Xuan; Wen, Yi-Zhi; Xu, Yu-Hong; Ling, Bi-Li; Gong, Xian-Zu; Liu, Bao-Hua; Wan, Bao-Nian

2001-06-01

The power spectrum and the probability distribution function (PDF) of the turbulence-induced particle flux Γ in the velocity shear layer of the HT-6M edge region have been measured and analysed. Three regions of frequency dependence (f 0, f-1, f-4) have been observed in the spectrum of the flux. The PDF of the flux displays a Γ-1 scaling over one decade in Γ. Using the rescaled-range statistical technique, we find that the degree of the self-similarity (Hurst exponent) of the particle flux in the measured region ranges from 0.64 to 0.83. All of these results may mean that the plasma transport is in a state characterized by self-organized criticality.

Path Length Entropy Analysis of Diastolic Heart Sounds

PubMed Central

Griffel, B.; Zia, M. K.; Fridman, V.; Saponieri, C.; Semmlow, J. L.

2013-01-01

Early detection of coronary artery disease (CAD) using the acoustic approach, a noninvasive and cost-effective method, would greatly improve the outcome of CAD patients. To detect CAD, we analyze diastolic sounds for possible CAD murmurs. We observed diastolic sounds to exhibit 1/f structure and developed a new method, path length entropy (PLE) and a scaled version (SPLE), to characterize this structure to improve CAD detection. We compare SPLE results to Hurst exponent, Sample entropy and Multi-scale entropy for distinguishing between normal and CAD patients. SPLE achieved a sensitivity-specificity of 80%–81%, the best of the tested methods. However, PLE and SPLE are not sufficient to prove nonlinearity, and evaluation using surrogate data suggests that our cardiovascular sound recordings do not contain significant nonlinear properties. PMID:23930808

Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation

NASA Astrophysics Data System (ADS)

Wang, Fang; Li, Zong-shou; Li, Jin-wei

2014-12-01

Feature extraction plays a great important role in image processing and pattern recognition. As a power tool, multifractal theory is recently employed for this job. However, traditional multifractal methods are proposed to analyze the objects with stationary measure and cannot for non-stationary measure. The works of this paper is twofold. First, the definition of stationary image and 2D image feature detection methods are proposed. Second, a novel feature extraction scheme for non-stationary image is proposed by local multifractal detrended fluctuation analysis (Local MF-DFA), which is based on 2D MF-DFA. A set of new multifractal descriptors, called local generalized Hurst exponent (Lhq) is defined to characterize the local scaling properties of textures. To test the proposed method, both the novel texture descriptor and other two multifractal indicators, namely, local Hölder coefficients based on capacity measure and multifractal dimension Dq based on multifractal differential box-counting (MDBC) method, are compared in segmentation experiments. The first experiment indicates that the segmentation results obtained by the proposed Lhq are better than the MDBC-based Dq slightly and superior to the local Hölder coefficients significantly. The results in the second experiment demonstrate that the Lhq can distinguish the texture images more effectively and provide more robust segmentations than the MDBC-based Dq significantly.

Statistical Properties of Photospheric Magnetic Elements Observed by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory

NASA Astrophysics Data System (ADS)

Javaherian, M.; Safari, H.; Dadashi, N.; Aschwanden, M. J.

2017-11-01

Magnetic elements of the solar surface are studied (using the 6173 Å Fe i line) in magnetograms recorded with the high-resolution Solar Dynamics Observatory (SDO)/ Helioseismic and Magnetic Imager (HMI). To extract some statistical and physical properties of these elements ( e.g. filling factors, magnetic flux, size, and lifetimes), we employed the region-based method called Yet Another Feature Tracking Algorithm ( YAFTA). An area of 400^''×400^'' was selected to investigate the magnetic characteristics in 2011. The correlation coefficient between filling factors of negative and positive polarities is 0.51. A broken power-law fit was applied to the frequency distribution of size and flux. Exponents of the power-law distributions for sizes smaller and greater than 16 arcsec2 were found to be -2.24 and -4.04, respectively. The exponents of power-law distributions for fluxes lower and greater than 2.63× 10^{19} Mx were found to be -2.11 and -2.51, respectively. The relationship between the size [S] and flux [F] of elements can be expressed by a power-law behavior of the form of S∝ F^{0.69}. The lifetime and its relationship with the flux and size of quiet-Sun (QS) elements during three days were studied. The code detected patches with lifetimes of about 15 hours, which we call long-duration events. We found that more than 95% of the magnetic elements have lifetimes shorter than 100 minutes. About 0.05% of the elements had lifetimes of more than six hours. The relationships between size [S], lifetime [T], and flux [F] for patches in the QS yield power-law relationships S∝ T^{0.25} and F∝ T^{0.38}, respectively. Executing a detrended-fluctuation analysis of the time series of new emerged magnetic elements, we found a Hurst exponent of 0.82, which implies a long-range temporal correlation in the system.

Long-term ground deformation patterns of Bucharest using multi-temporal InSAR and multivariate dynamic analyses: a possible transpressional system?

PubMed Central

Armaş, Iuliana; Mendes, Diana A.; Popa, Răzvan-Gabriel; Gheorghe, Mihaela; Popovici, Diana

2017-01-01

The aim of this exploratory research is to capture spatial evolution patterns in the Bucharest metropolitan area using sets of single polarised synthetic aperture radar (SAR) satellite data and multi-temporal radar interferometry. Three sets of SAR data acquired during the years 1992–2010 from ERS-1/-2 and ENVISAT, and 2011–2014 from TerraSAR-X satellites were used in conjunction with the Small Baseline Subset (SBAS) and persistent scatterers (PS) high-resolution multi-temporal interferometry (InSAR) techniques to provide maps of line-of-sight displacements. The satellite-based remote sensing results were combined with results derived from classical methodologies (i.e., diachronic cartography) and field research to study possible trends in developments over former clay pits, landfill excavation sites, and industrial parks. The ground displacement trend patterns were analysed using several linear and nonlinear models, and techniques. Trends based on the estimated ground displacement are characterised by long-term memory, indicated by low noise Hurst exponents, which in the long-term form interesting attractors. We hypothesize these attractors to be tectonic stress fields generated by transpressional movements. PMID:28252103

Long-term ground deformation patterns of Bucharest using multi-temporal InSAR and multivariate dynamic analyses: a possible transpressional system?

PubMed

Armaş, Iuliana; Mendes, Diana A; Popa, Răzvan-Gabriel; Gheorghe, Mihaela; Popovici, Diana

2017-03-02

The aim of this exploratory research is to capture spatial evolution patterns in the Bucharest metropolitan area using sets of single polarised synthetic aperture radar (SAR) satellite data and multi-temporal radar interferometry. Three sets of SAR data acquired during the years 1992-2010 from ERS-1/-2 and ENVISAT, and 2011-2014 from TerraSAR-X satellites were used in conjunction with the Small Baseline Subset (SBAS) and persistent scatterers (PS) high-resolution multi-temporal interferometry (InSAR) techniques to provide maps of line-of-sight displacements. The satellite-based remote sensing results were combined with results derived from classical methodologies (i.e., diachronic cartography) and field research to study possible trends in developments over former clay pits, landfill excavation sites, and industrial parks. The ground displacement trend patterns were analysed using several linear and nonlinear models, and techniques. Trends based on the estimated ground displacement are characterised by long-term memory, indicated by low noise Hurst exponents, which in the long-term form interesting attractors. We hypothesize these attractors to be tectonic stress fields generated by transpressional movements.

The Dynamical Classification of Centaurs which Evolve into Comets

NASA Astrophysics Data System (ADS)

Wood, Jeremy R.; Horner, Jonathan; Hinse, Tobias; Marsden, Stephen; Swinburne University of Technology

2016-10-01

Centaurs are small Solar system bodies with semi-major axes between Jupiter and Neptune and perihelia beyond Jupiter. Centaurs can be further subclassified into two dynamical categories - random walk and resonance hopping. Random walk Centaurs have mean square semi-major axes (< a2 >) which vary in time according to a generalized diffusion equation where < a2 > ~t2H. H is the Hurst exponent with 0 < H < 1, and t is time. The behavior of < a2 > for resonance hopping Centaurs is not well described by generalized diffusion.The aim of this study is to determine which dynamical type of Centaur is most likely to evolve into each class of comet. 31,722 fictional massless test particles were integrated for 3 Myr in the 6-body problem (Sun, Jovian planets, test particle). Initially each test particle was a member of one of four groups. The semi-major axes of all test particles in a group were clustered within 0.27 au from a first order, interior Mean Motion resonance of Neptune. The resonances were centered at 18.94 au, 22.95 au, 24.82 au and 28.37 au.If the perihelion of a test particle reached < 4 au then the test particle was considered to be a comet and classified as either a random walk or resonance hopping Centaur. The results showed that over 4,000 test particles evolved into comets within 3 Myr. 59% of these test particles were random walk and 41% were resonance hopping. The behavior of the semi-major axis in time was usually well described by generalized diffusion for random walk Centaurs (ravg = 0.98) and poorly described for resonance hopping Centaurs (ravg = 0.52). The average Hurst exponent was 0.48 for random walk Centaurs and 0.20 for resonance hopping Centaurs. Random walk Centaurs were more likely to evolve into short period comets while resonance hopping Centaurs were more likely to evolve into long period comets. For each initial cluster, resonance hopping Centaurs took longer to evolve into comets than random walk Centaurs. Overall the population of random walk Centaurs averaged 143 kyr to evolve into comets, and the population of resonance hopping Centaurs averaged 164 kyr.

(Multi)fractality of Earthquakes by use of Wavelet Analysis

NASA Astrophysics Data System (ADS)

Enescu, B.; Ito, K.; Struzik, Z. R.

2002-12-01

The fractal character of earthquakes' occurrence, in time, space or energy, has by now been established beyond doubt and is in agreement with modern models of seismicity. Moreover, the cascade-like generation process of earthquakes -with one "main" shock followed by many aftershocks, having their own aftershocks- may well be described through multifractal analysis, well suited for dealing with such multiplicative processes. The (multi)fractal character of seismicity has been analysed so far by using traditional techniques, like the box-counting and correlation function algorithms. This work introduces a new approach for characterising the multifractal patterns of seismicity. The use of wavelet analysis, in particular of the wavelet transform modulus maxima, to multifractal analysis was pioneered by Arneodo et al. (1991, 1995) and applied successfully in diverse fields, such as the study of turbulence, the DNA sequences or the heart rate dynamics. The wavelets act like a microscope, revealing details about the analysed data at different times and scales. We introduce and perform such an analysis on the occurrence time of earthquakes and show its advantages. In particular, we analyse shallow seismicity, characterised by a high aftershock "productivity", as well as intermediate and deep seismic activity, known for its scarcity of aftershocks. We examine as well declustered (aftershocks removed) versions of seismic catalogues. Our preliminary results show some degree of multifractality for the undeclustered, shallow seismicity. On the other hand, at large scales, we detect a monofractal scaling behaviour, clearly put in evidence for the declustered, shallow seismic activity. Moreover, some of the declustered sequences show a long-range dependent (LRD) behaviour, characterised by a Hurst exponent, H > 0.5, in contrast with the memory-less, Poissonian model. We demonstrate that the LRD is a genuine characteristic and is not an effect of the time series probability distribution function. One of the most attractive features of wavelet analysis is its ability to determine a local Hurst exponent. We show that this feature together with the possibility of extending the analysis to spatial patterns may constitute a valuable approach to search for anomalous (precursory?) patterns of seismic activity.

A Novel EEG Based Spectral Analysis of Persistent Brain Function Alteration in Athletes with Concussion History.

PubMed

Munia, Tamanna T K; Haider, Ali; Schneider, Charles; Romanick, Mark; Fazel-Rezai, Reza

2017-12-08

The neurocognitive sequelae of a sport-related concussion and its management are poorly defined. Detecting deficits are vital in making a decision about the treatment plan as it can persist one year or more following a brain injury. The reliability of traditional cognitive assessment tools is debatable, and thus attention has turned to assessments based on electroencephalogram (EEG) to evaluate subtle post-concussive alterations. In this study, we calculated neurocognitive deficits combining EEG analysis with three standard post-concussive assessment tools. Data were collected for all testing modalities from 21 adolescent athletes (seven concussive and fourteen healthy) in three different trials. For EEG assessment, along with linear frequency-based features, we introduced a set of time-frequency (Hjorth Parameters) and nonlinear features (approximate entropy and Hurst exponent) for the first time to explore post-concussive deficits. Besides traditional frequency-band analysis, we also presented a new individual frequency-based approach for EEG assessment. While EEG analysis exhibited significant discrepancies between the groups, none of the cognitive assessment resulted in significant deficits. Therefore, the evidence from the study highlights that our proposed EEG analysis and markers are more efficient at deciphering post-concussion residual neurocognitive deficits and thus has a potential clinical utility of proper concussion assessment and management.

Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Analyzing the Cross-Correlation Between Onshore and Offshore RMB Exchange Rates Based on Multifractal Detrended Cross-Correlation Analysis (MF-DCCA)

NASA Astrophysics Data System (ADS)

Xie, Chi; Zhou, Yingying; Wang, Gangjin; Yan, Xinguo

We use the multifractal detrended cross-correlation analysis (MF-DCCA) method to explore the multifractal behavior of the cross-correlation between exchange rates of onshore RMB (CNY) and offshore RMB (CNH) against US dollar (USD). The empirical data are daily prices of CNY/USD and CNH/USD from May 1, 2012 to February 29, 2016. The results demonstrate that: (i) the cross-correlation between CNY/USD and CNH/USD is persistent and its fluctuation is smaller when the order of fluctuation function is negative than that when the order is positive; (ii) the multifractal behavior of the cross-correlation between CNY/USD and CNH/USD is significant during the sample period; (iii) the dynamic Hurst exponents obtained by the rolling windows analysis show that the cross-correlation is stable when the global economic situation is good and volatile in bad situation; and (iv) the non-normal distribution of original data has a greater effect on the multifractality of the cross-correlation between CNY/USD and CNH/USD than the temporary correlation.

Vegetation dynamics and responses to climate change and human activities in Central Asia.

PubMed

Jiang, Liangliang; Guli Jiapaer; Bao, Anming; Guo, Hao; Ndayisaba, Felix

2017-12-01

Knowledge of the current changes and dynamics of different types of vegetation in relation to climatic changes and anthropogenic activities is critical for developing adaptation strategies to address the challenges posed by climate change and human activities for ecosystems. Based on a regression analysis and the Hurst exponent index method, this research investigated the spatial and temporal characteristics and relationships between vegetation greenness and climatic factors in Central Asia using the Normalized Difference Vegetation Index (NDVI) and gridded high-resolution station (land) data for the period 1984-2013. Further analysis distinguished between the effects of climatic change and those of human activities on vegetation dynamics by means of a residual analysis trend method. The results show that vegetation pixels significantly decreased for shrubs and sparse vegetation compared with those for the other vegetation types and that the degradation of sparse vegetation was more serious in the Karakum and Kyzylkum Deserts, the Ustyurt Plateau and the wetland delta of the Large Aral Sea than in other regions. The Hurst exponent results indicated that forests are more sustainable than grasslands, shrubs and sparse vegetation. Precipitation is the main factor affecting vegetation growth in the Kazakhskiy Melkosopochnik. Moreover, temperature is a controlling factor that influences the seasonal variation of vegetation greenness in the mountains and the Aral Sea basin. Drought is the main factor affecting vegetation degradation as a result of both increased temperature and decreased precipitation in the Kyzylkum Desert and the northern Ustyurt Plateau. The residual analysis highlighted that sparse vegetation and the degradation of some shrubs in the southern part of the Karakum Desert, the southern Ustyurt Plateau and the wetland delta of the Large Aral Sea were mainly triggered by human activities: the excessive exploitation of water resources in the upstream areas of the Amu Darya basin and oil and natural gas extraction in the southern part of the Karakum Desert and the southern Ustyurt Plateau. The results also indicated that after the collapse of the Soviet Union, abandoned pastures gave rise to increased vegetation in eastern Kazakhstan, Kyrgyzstan and Tajikistan, and abandoned croplands reverted to grasslands in northern Kazakhstan, leading to a decrease in cropland greenness. Shrubs and sparse vegetation were extremely sensitive to short-term climatic variations, and our results demonstrated that these vegetation types were the most seriously degraded by human activities. Therefore, regional governments should strive to restore vegetation to sustain this fragile arid ecological environment. Copyright © 2017 Elsevier B.V. All rights reserved.

Fractal Analysis and Hurst Parameter for Intrapartum Fetal Heart Rate Variability Analysis: A Versatile Alternative to Frequency Bands and LF/HF Ratio

PubMed Central

Doret, Muriel; Spilka, Jiří; Chudáček, Václav; Gonçalves, Paulo; Abry, Patrice

2015-01-01

Background The fetal heart rate (FHR) is commonly monitored during labor to detect early fetal acidosis. FHR variability is traditionally investigated using Fourier transform, often with adult predefined frequency band powers and the corresponding LF/HF ratio. However, fetal conditions differ from adults and modify spectrum repartition along frequencies. Aims This study questions the arbitrariness definition and relevance of the frequency band splitting procedure, and thus of the calculation of the underlying LF/HF ratio, as efficient tools for characterizing intrapartum FHR variability. Study Design The last 30 minutes before delivery of the intrapartum FHR were analyzed. Subjects Case-control study. A total of 45 singletons divided into two groups based on umbilical cord arterial pH: the Index group with pH ≤ 7.05 (n = 15) and Control group with pH > 7.05 (n = 30). Outcome Measures Frequency band-based LF/HF ratio and Hurst parameter. Results This study shows that the intrapartum FHR is characterized by fractal temporal dynamics and promotes the Hurst parameter as a potential marker of fetal acidosis. This parameter preserves the intuition of a power frequency balance, while avoiding the frequency band splitting procedure and thus the arbitrary choice of a frequency separating bands. The study also shows that extending the frequency range covered by the adult-based bands to higher and lower frequencies permits the Hurst parameter to achieve better performance for identifying fetal acidosis. Conclusions The Hurst parameter provides a robust and versatile tool for quantifying FHR variability, yields better acidosis detection performance compared to the LF/HF ratio, and avoids arbitrariness in spectral band splitting and definitions. PMID:26322889

Does pop music exist? Hierarchical structure in phonographic markets

NASA Astrophysics Data System (ADS)

Buda, Andrzej

2012-11-01

I find a topological arrangement of assets traded in phonographic markets which has associated a meaningful economic taxonomy. I continue using the Minimal Spanning Tree and the correlations between assets, but now outside the stock markets. This is the first attempt to use these methods on phonographic markets where we have artists instead of stocks. The value of an artist is defined by record sales. The graph is obtained starting from the matrix of correlation coefficients computed between the world’s most popular 30 artists by considering the synchronous time evolution of the difference of the logarithm of weekly record sales. This method provides the hierarchical structure of the phonographic market and information on which music genre is meaningful according to customers. Statistical properties (including the Hurst exponent) of weekly record sales in the phonographic market are also discussed.

Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India

NASA Astrophysics Data System (ADS)

Manimaran, P.; Narayana, A. C.

2018-07-01

In this paper, we study the multifractal characteristics and cross-correlation behaviour of Air Pollution Index (API) time series data through multifractal detrended cross-correlation analysis method. We analyse the daily API records of nine air pollutants of the university of Hyderabad campus for a period of three years (2013-2016). The cross-correlation behaviour has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, it is found that the cross-correlation analysis shows anti-correlation behaviour for all possible 36 bivariate time series. We also observe the existence of multifractal nature in all the bivariate time series in which many of them show strong multifractal behaviour. In particular, the hazardous particulate matter PM2.5 and inhalable particulate matter PM10 shows anti-correlated behaviour with all air pollutants.

Multifractal analysis of the time series of daily means of wind speed in complex regions

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Golay, Jean; Telesca, Luciano; Kanevski, Mikhail

2018-04-01

In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be more linked with the local conditions of the highly varying topography of Switzerland. Our findings point out to a persistent behaviour of all the measured wind speed series (indicated by a Hurst exponent significantly larger than 0.5), and to a high multifractality degree indicating a relative dominance of the large fluctuations in the dynamics of wind speed, especially in the Swiss plateau, which is comprised between the Jura and Alp mountain ranges. The study represents a contribution to the understanding of the dynamical mechanisms of wind speed variability in mountainous regions.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Scaling properties of rainfall records in some Mexican zones

NASA Astrophysics Data System (ADS)

Angulo-Fernández, Fercia; Reyes-Ramírez, Israel; Flores-Márquez, Elsa Leticia

2018-04-01

Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun's radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.

Martingales, nonstationary increments, and the efficient market hypothesis

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.; Bassler, Kevin E.; Gunaratne, Gemunu H.

2008-06-01

We discuss the deep connection between nonstationary increments, martingales, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). We explain why a test for a martingale is generally a test for uncorrelated increments. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. But while a Markovian market has no memory to exploit and cannot be beaten systematically, a martingale admits memory that might be exploitable in higher order correlations. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama’s paper on the EMH. We emphasize that the use of the log increment as a variable in data analysis generates spurious fat tails and spurious Hurst exponents.

Irregular-regular mode oscillations inside plasma bubble and its fractal analysis in glow discharge magnetized plasma

NASA Astrophysics Data System (ADS)

Megalingam, Mariammal; Hari Prakash, N.; Solomon, Infant; Sarma, Arun; Sarma, Bornali

2017-04-01

Experimental evidence of different kinds of oscillations in floating potential fluctuations of glow discharge magnetized plasma is being reported. A spherical gridded cage is inserted into the ambient plasma volume for creating plasma bubbles. Plasma is produced between a spherical mesh grid and chamber. The spherical mesh grid of 80% optical transparency is connected to the positive terminal of power supply and considered as anode. Two Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations in different positions within the system, viz., inside and outside the spherical mesh grid. At certain conditions of discharge voltage (Vd) and magnetic field, irregular to regular mode appears, and it shows chronological changes with respect to magnetic field. Further various nonlinear analyses such as Recurrence Plot, Hurst exponent, and Lyapunov exponent have been carried out to investigate the dynamics of oscillation at a range of discharge voltages and external magnetic fields. Determinism, entropy, and Lmax are important measures of Recurrence Quantification Analysis which indicate an irregular to regular transition in the dynamics of the fluctuations. Furthermore, behavior of the plasma oscillation is characterized by the technique called multifractal detrended fluctuation analysis to explore the nature of the fluctuations. It reveals that it has a multifractal nature and behaves as a long range correlated process.

Influence of the Investor's Behavior on the Complexity of the Stock Market

NASA Astrophysics Data System (ADS)

Atman, A. P. F.; Gonçalves, Bruna Amin

2012-04-01

One of the pillars of the finance theory is the efficient-market hypothesis, which is used to analyze the stock market. However, in recent years, this hypothesis has been questioned by a number of studies showing evidence of unusual behaviors in the returns of financial assets ("anomalies") caused by behavioral aspects of the economic agents. Therefore, it is time to initiate a debate about the efficient-market hypothesis and the "behavioral finances." We here introduce a cellular automaton model to study the stock market complexity, considering different behaviors of the economical agents. From the analysis of the stationary standard of investment observed in the simulations and the Hurst exponents obtained for the term series of stock index, we draw conclusions concerning the complexity of the model compared to real markets. We also investigate which conditions of the investors are able to influence the efficient market hypothesis statements.

Fractal and Multifractal Analysis of Human Gait

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.

2003-09-01

We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

Extreme-value statistics of fractional Brownian motion bridges.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2016-11-01

Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t_{+} the process is positive, the maximum m it achieves, and the time t_{max} when this maximum is taken. Using a perturbative expansion around Brownian motion (H=1/2), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and t_{max}. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H>1/2 and H<1/2. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

Fractional Brownian motion and the critical dynamics of zipping polymers.

PubMed

Walter, J-C; Ferrantini, A; Carlon, E; Vanderzande, C

2012-03-01

We consider two complementary polymer strands of length L attached by a common-end monomer. The two strands bind through complementary monomers and at low temperatures form a double-stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature T=T(c) using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as τ∼L(2.26(2)), exceeding the Rouse time ∼L(2.18). We investigate the probability distribution function, velocity autocorrelation function, survival probability, and boundary behavior of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent H=0.44(1). We discuss similarities to and differences from unbiased polymer translocation.

Critical comparison of several order-book models for stock-market fluctuations

NASA Astrophysics Data System (ADS)

Slanina, F.

2008-01-01

Far-from-equilibrium models of interacting particles in one dimension are used as a basis for modelling the stock-market fluctuations. Particle types and their positions are interpreted as buy and sel orders placed on a price axis in the order book. We revisit some modifications of well-known models, starting with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler model and investigate its variants. One of them is the simplified version of the Genoa artificial market. The list of studied models is completed by the models of Maslov and Daniels et al. Generically, in all cases we compare the return distribution, absolute return autocorrelation and the value of the Hurst exponent. It turns out that none of the models reproduces satisfactorily all the empirical data, but the most promising candidates for further development are the Genoa artificial market and the Maslov model with moderate order evaporation.

Some Probabilistic and Statistical Properties of the Seismic Regime of Zemmouri (Algeria) Seismoactive Zone

NASA Astrophysics Data System (ADS)

Baddari, Kamel; Bellalem, Fouzi; Baddari, Ibtihel; Makdeche, Said

2016-10-01

Statistical tests have been used to adjust the Zemmouri seismic data using a distribution function. The Pareto law has been used and the probabilities of various expected earthquakes were computed. A mathematical expression giving the quantiles was established. The extreme values limiting law confirmed the accuracy of the adjustment method. Using the moment magnitude scale, a probabilistic model was made to predict the occurrences of strong earthquakes. The seismic structure has been characterized by the slope of the recurrence plot γ, fractal dimension D, concentration parameter K sr, Hurst exponents H r and H t. The values of D, γ, K sr, H r, and H t diminished many months before the principal seismic shock ( M = 6.9) of the studied seismoactive zone has occurred. Three stages of the deformation of the geophysical medium are manifested in the variation of the coefficient G% of the clustering of minor seismic events.

Executive Functions and Prefrontal Cortex: A Matter of Persistence?

PubMed Central

Ball, Gareth; Stokes, Paul R.; Rhodes, Rebecca A.; Bose, Subrata K.; Rezek, Iead; Wink, Alle-Meije; Lord, Louis-David; Mehta, Mitul A.; Grasby, Paul M.; Turkheimer, Federico E.

2011-01-01

Executive function is thought to originates from the dynamics of frontal cortical networks. We examined the dynamic properties of the blood oxygen level dependent time-series measured with functional MRI (fMRI) within the prefrontal cortex (PFC) to test the hypothesis that temporally persistent neural activity underlies performance in three tasks of executive function. A numerical estimate of signal persistence, the Hurst exponent, postulated to represent the coherent firing of cortical networks, was determined and correlated with task performance. Increasing persistence in the lateral PFC was shown to correlate with improved performance during an n-back task. Conversely, we observed a correlation between persistence and increasing commission error – indicating a failure to inhibit a prepotent response – during a Go/No-Go task. We propose that persistence within the PFC reflects dynamic network formation and these findings underline the importance of frequency analysis of fMRI time-series in the study of executive functions. PMID:21286223

Long-term sea level trends: Natural or anthropogenic?

NASA Astrophysics Data System (ADS)

Becker, M.; Karpytchev, M.; Lennartz-Sassinek, S.

2014-08-01

Detection and attribution of human influence on sea level rise are important topics that have not yet been explored in depth. We question whether the sea level changes (SLC) over the past century were natural in origin. SLC exhibit power law long-term correlations. By estimating Hurst exponent through Detrended Fluctuation Analysis and by applying statistics of Lennartz and Bunde, we search the lower bounds of statistically significant external sea level trends in longest tidal records worldwide. We provide statistical evidences that the observed SLC, at global and regional scales, is beyond its natural internal variability. The minimum anthropogenic sea level trend (MASLT) contributes to the observed sea level rise more than 50% in New York, Baltimore, San Diego, Marseille, and Mumbai. A MASLT is about 1 mm/yr in global sea level reconstructions that is more than half of the total observed sea level trend during the XXth century.

Nonequilibrium fluctuations during diffusion in liquid layers

NASA Astrophysics Data System (ADS)

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H =1 . We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Nonequilibrium fluctuations during diffusion in liquid layers.

PubMed

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H=1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Efficiency or speculation? A time-varying analysis of European sovereign debt

NASA Astrophysics Data System (ADS)

Ferreira, Paulo

2018-01-01

The outbreak of the Greek debt crisis caused turmoil in European markets and drew attention to the problem of public debt and its consequences. The increase in the return rates of sovereign debts was one of these consequences. However, like any other asset, sovereign debt returns are expected to have a memoryless behaviour. Analysing a total of 15 European countries (Eurozone and non-Eurozone), and applying a time-varying analysis of the Hurst exponent, we found evidence of long-range memory in sovereign bonds. When analysing the spreads between each bond and the German one, it is possible to conclude that Eurozone countries' spreads show more evidence of long-range dependence. Considering the Eurozone countries most affected by the Eurozone crisis, that long-range dependence is more evident, but started before the crisis, which could be interpreted as possible speculation by investors.

Long memory of abnormal investor attention and the cross-correlations between abnormal investor attention and trading volume, volatility respectively

NASA Astrophysics Data System (ADS)

Fan, Xiaoqian; Yuan, Ying; Zhuang, Xintian; Jin, Xiu

2017-03-01

Taking Baidu Index as a proxy for abnormal investor attention (AIA), the long memory property in the AIA of Shanghai Stock Exchange (SSE) 50 Index component stocks was empirically investigated using detrended fluctuation analysis (DFA) method. The results show that abnormal investor attention is power-law correlated with Hurst exponents between 0.64 and 0.98. Furthermore, the cross-correlations between abnormal investor attention and trading volume, volatility respectively are studied using detrended cross-correlation analysis (DCCA) and the DCCA cross-correlation coefficient (ρDCCA). The results suggest that there are positive correlations between AIA and trading volume, volatility respectively. In addition, the correlations for trading volume are in general higher than the ones for volatility. By carrying on rescaled range analysis (R/S) and rolling windows analysis, we find that the results mentioned above are effective and significant.

The influence of trading volume on market efficiency: The DCCA approach

NASA Astrophysics Data System (ADS)

Sukpitak, Jessada; Hengpunya, Varagorn

2016-09-01

For a single market, the cross-correlation between market efficiency and trading volume, which is an indicator of market liquidity, is attentively analysed. The study begins with creating time series of market efficiency by applying time-varying Hurst exponent with one year sliding window to daily closing prices. The time series of trading volume corresponding to the same time period used for the market efficiency is derived from one year moving average of daily trading volume. Subsequently, the detrended cross-correlation coefficient is employed to quantify the degree of cross-correlation between the two time series. It was found that values of cross-correlation coefficient of all considered stock markets are close to 0 and are clearly out of range in which correlation being considered significant in almost every time scale. Obtained results show that the market liquidity in term of trading volume hardly has effect on the market efficiency.

Multifractal detrended fluctuation analysis of intensity time series of photons scattered by tracer particles within a polymeric gel

NASA Astrophysics Data System (ADS)

Telesca, Luciano; Haro-Pérez, Catalina; Moreno-Torres, L. Rebeca; Ramirez-Rojas, Alejandro

2018-01-01

Some properties of spatial confinement of tracer colloidal particles within polyacrylamide dispersions are studied by means of the well-known dynamic light scattering (DLS) technique. DLS allows obtaining sequences of elapsed times of scattered photons. In this work, the aqueous polyacrylamide dispersion has no crosslinking and the volume fraction occupied by the tracer particles is 0.02 %. Our experimental setup provides two sequences of photons scattered by the same scattering volume that corresponds to two simultaneous experiments (Channel A and Channel B). By integration of these sequences, the intensity time series are obtained. We find that both channels are antipersistent with Hurst exponent, H ∼0.43 and 0.36, respectively. The antipersistence of the intensity time series indicates a subdiffusive dynamics of the tracers in the polymeric network, which is in agreement with the time dependence of the tracer's mean square displacement.

Generalized Arcsine Laws for Fractional Brownian Motion

NASA Astrophysics Data System (ADS)

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-01

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian Bt starting from the origin, and evolving during time T , one considers the following three observables: (i) the duration t+ the process is positive, (ii) the time tlast the process last visits the origin, and (iii) the time tmax when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion Xt, a non-Markovian Gaussian process indexed by the Hurst exponent H . It generalizes standard Brownian motion (i.e., H =1/2 ). We obtain the three probabilities using a perturbative expansion in ɛ =H -1/2 . While all three probabilities are different, this distinction can only be made at second order in ɛ . Our results are confirmed to high precision by extensive numerical simulations.

Fractal analysis on human dynamics of library loans

NASA Astrophysics Data System (ADS)

Fan, Chao; Guo, Jin-Li; Zha, Yi-Long

2012-12-01

In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.

A better understanding of long-range temporal dependence of traffic flow time series

NASA Astrophysics Data System (ADS)

Feng, Shuo; Wang, Xingmin; Sun, Haowei; Zhang, Yi; Li, Li

2018-02-01

Long-range temporal dependence is an important research perspective for modelling of traffic flow time series. Various methods have been proposed to depict the long-range temporal dependence, including autocorrelation function analysis, spectral analysis and fractal analysis. However, few researches have studied the daily temporal dependence (i.e. the similarity between different daily traffic flow time series), which can help us better understand the long-range temporal dependence, such as the origin of crossover phenomenon. Moreover, considering both types of dependence contributes to establishing more accurate model and depicting the properties of traffic flow time series. In this paper, we study the properties of daily temporal dependence by simple average method and Principal Component Analysis (PCA) based method. Meanwhile, we also study the long-range temporal dependence by Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). The results show that both the daily and long-range temporal dependence exert considerable influence on the traffic flow series. The DFA results reveal that the daily temporal dependence creates crossover phenomenon when estimating the Hurst exponent which depicts the long-range temporal dependence. Furthermore, through the comparison of the DFA test, PCA-based method turns out to be a better method to extract the daily temporal dependence especially when the difference between days is significant.

Spatiotemporal dynamics of grassland aboveground biomass on the Qinghai-Tibet Plateau based on validated MODIS NDVI.

PubMed

Liu, Shiliang; Cheng, Fangyan; Dong, Shikui; Zhao, Haidi; Hou, Xiaoyun; Wu, Xue

2017-06-23

Spatiotemporal dynamics of aboveground biomass (AGB) is a fundamental problem for grassland environmental management on the Qinghai-Tibet Plateau (QTP). Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) data can feasibly be used to estimate AGB at large scales, and their precise validation is necessary to utilize them effectively. In our study, the clip-harvest method was used at 64 plots in QTP grasslands to obtain actual AGB values, and a handheld hyperspectral spectrometer was used to calculate field-measured NDVI to validate MODIS NDVI. Based on the models between NDVI and AGB, AGB dynamics trends during 2000-2012 were analyzed. The results showed that the AGB in QTP grasslands increased during the study period, with 70% of the grasslands undergoing increases mainly in the Qinghai Province. Also, the meadow showed a larger increasing trend than steppe. Future AGB dynamic trends were also investigated using a combined analysis of the slope values and the Hurst exponent. The results showed high sustainability of AGB dynamics trends after the study period. Predictions indicate 60% of the steppe and meadow grasslands would continue to increase in AGB, while 25% of the grasslands would remain in degradation, with most of them distributing in Tibet.

Variations in the Parameters of Background Seismic Noise during the Preparation Stages of Strong Earthquakes in the Kamchatka Region

NASA Astrophysics Data System (ADS)

Kasimova, V. A.; Kopylova, G. N.; Lyubushin, A. A.

2018-03-01

The results of the long (2011-2016) investigation of background seismic noise (BSN) in Kamchatka by the method suggested by Doct. Sci. (Phys.-Math.) A.A. Lyubushin with the use of the data from the network of broadband seismic stations of the Geophysical Survey of the Russian Academy of Sciences are presented. For characterizing the BSN field and its variability, continuous time series of the statistical parameters of the multifractal singularity spectra and wavelet expansion calculated from the records at each station are used. These parameters include the generalized Hurst exponent α*, singularity spectrum support width Δα, wavelet spectral exponent β, minimal normalized entropy of wavelet coefficients En, and spectral measure of their coherent behavior. The peculiarities in the spatiotemporal distribution of the BSN parameters as a probable response to the earthquakes with M w = 6.8-8.3 that occurred in Kamchatka in 2013 and 2016 are considered. It is established that these seismic events were preceded by regular variations in the BSN parameters, which lasted for a few months and consisted in the reduction of the median and mean α*, Δα, and β values estimated over all the stations and in the increase of the En values. Based on the increase in the spectral measure of the coherent behavior of the four-variate time series of the median and mean values of the considered statistics, the effect of the enhancement of the synchronism in the joint (collective) behavior of these parameters during a certain period prior to the mantle earthquake in the Sea of Okhotsk (May 24, 2013, M w = 8.3) is diagnosed. The procedures for revealing the precursory effects in the variations of the BSN parameters are described and the examples of these effects are presented.

Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations

NASA Astrophysics Data System (ADS)

Meng, Hao; Ren, Fei; Gu, Gao-Feng; Xiong, Xiong; Zhang, Yong-Jie; Zhou, Wei-Xing; Zhang, Wei

2012-05-01

Understanding the statistical properties of recurrence intervals (also termed return intervals in econophysics literature) of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have been extensively investigated. However, the impacts of microscopic rules of a complex system on the macroscopic properties of its recurrence intervals are less studied. In this letter, we adopt an order-driven stock model to address this issue for stock returns. We find that the distributions of the scaled recurrence intervals of simulated returns have a power-law scaling with stretched exponential cutoff and the intervals possess multifractal nature, which are consistent with empirical results. We further investigate the effects of long memory in the directions (or signs) and relative prices of the order flow on the characteristic quantities of these properties. It is found that the long memory in the order directions (Hurst index Hs) has a negligible effect on the interval distributions and the multifractal nature. In contrast, the power-law exponent of the interval distribution increases linearly with respect to the Hurst index Hx of the relative prices, and the singularity width of the multifractal nature fluctuates around a constant value when Hx<0.7 and then increases with Hx. No evident effects of Hs and Hx are found on the long memory of the recurrence intervals. Our results indicate that the nontrivial properties of the recurrence intervals of returns are mainly caused by traders' behaviors of persistently placing new orders around the best bid and ask prices.

Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Gu, Rongbao; Chen, Hongtao; Wang, Yudong

2010-07-01

The multifractal nature of WTI and Brent crude oil markets is studied employing the multifractal detrended fluctuation analysis. We find that two crude oil markets become more and more efficient for long-term and two Gulf Wars cannot change time scale behavior of crude oil return series. Considering long-term influence caused by Gulf Wars, we find such “turning windows” in generalized Hurst exponents obtained from three periods divided by two Gulf Wars so that WTI and Brent crude oil returns possess different properties above and below the windows respectively. Comparing with the results obtained from three periods we conclude that, before the First Gulf War, international crude oil markets possessed the highest multifractality degree, small-scope fluctuations presented the strongest persistence and large-scope fluctuations presented the strongest anti-persistence. We find that, for two Gulf Wars, the first one made a greater impact on international oil markets; for two markets, Brent was more influenced by Gulf Wars. In addition, we also verified that the multifractal structures of two markets’ indices are not only mainly attributed to the broad fat-tail distributions and persistence, but also affected by some other factors.

Multifractal analysis for grading complex fractionated electrograms in atrial fibrillation.

PubMed

Orozco-Duque, A; Novak, D; Kremen, V; Bustamante, J

2015-11-01

Complex fractionated atrial electrograms provide an important tool for identifying arrhythmogenic substrates that can be used to guide catheter ablation for atrial fibrillation (AF). However, fractionation is a phenomenon that remains unclear. This paper aims to evaluate the multifractal properties of electrograms in AF in order to propose a method based on multifractal analysis able to discriminate between different levels of fractionation. We introduce a new method, the h-fluctuation index (hFI), where h is the generalised Hurst exponent, to extract information from the shape of the multifractal spectrum. Two multifractal frameworks are evaluated: multifractal detrended fluctuation analysis and wavelet transform modulus maxima. hFI is exemplified through its application in synthetic signals, and it is evaluated in a database of electrograms labeled on the basis of four degrees of fractionation. We compare the performance of hFI with other indexes, and find that hFI outperforms them. The results of the study provide evidence that multifractal analysis is useful for studying fractionation phenomena in AF electrograms, and indicate that hFI can be proposed as a tool for grade fractionation associated with the detection of target sites for ablation in AF.

In-Situ Patterning: Selective Area Deposition and Etching. Materials Research Society Symposium Proceedings. Volume 158

DTIC Science & Technology

1990-11-21

Canterford, Halides of the First RgWL rpsition Metals (Wiley-Interscience, London, 1969). 4. G. Koren and J. E. Hurst Jr., AppI, Phys. A 45, 301 (1988). 5. T...Nakayama, Surf. Sci. 12., 101 (1983). 6. J. J. Ritsko, F. Ho, and J. Hurst , Appl., Phys. Lett., 3, 78, (1988...Ho, and - - Hurst , Appl. Phys. Lett. 53,78 (1988), andJ. Hurst , private communication. [2] W. Sesselmann,-E.-E. Marinero, and T. J. Chuang, Appl

The evolution of slip surface roughness during earthquake propagation in carbonate faults

NASA Astrophysics Data System (ADS)

Zhu, B.; De Paola, N.; Llewellin, E. W.; Holdsworth, R.

2014-12-01

Slip surface roughness is understood to control the dynamics of earthquake propagation. Quantifying the micro- and nano-scale roughness of slip surfaces can give insight into the grain-scale processes controlling the strength of faults during earthquake propagation. Friction experiments were performed on fine-grained calcite gouges, at speed 1 ms-1, normal stress 18 MPa, displacements 0.009-1.46 m, and room temperature and humidity. Results show a two stage-evolution (S1-2) of the fault strength, with an initial increase up to peak value 0.82 (S1), followed by a sudden decrease to a low, steady-state value 0.18 (S2). Samples retrieved at the end of S1 show the development of a cohesive slip zone (SZ), made of micron-scale, angular clasts formed by brittle fracturing and cataclasis. The SZ of samples deformed up to S2, is composed of nanograin aggregates which exhibit polygonal grain boundaries indicating high temperature grain boundary sliding creep deformation. In both cases, the SZ is bounded by a sharply defined slip surface. The 3-D geometry of seven experimental slip surfaces (40μm×40μm) has been reconstructed by digital processing of sets of 1800 images of SZ cross sections acquired at 20 nm intervals perpendicular to the slip direction, using a slicing (Focussed Ion Beam) and viewing (Field Emission Scanning Electron Microscope) technique. Spectrum power density analyses show that nano- and micron-scale slip surface roughness is anisotropic for both S1 and S2 slip surfaces. At the nano- and micron-scale, root mean square values decrease with length for S1 slip surfaces, but only slightly for S2 surfaces, and are anisotropic in the slip-normal and slip-parallel directions. The anisotropy is reduced at the nano-scale, although S2 slip surfaces are still smoother parallel to slip than normal to slip. Hurst exponents vary through scales, and are anisotropic in the directions parallel and normal to slip. Variable Hurst exponents indicate that slip surface roughness is scale-dependent with anisotropic, not self-affine behaviour at the micro/nano-scale, in contrast to the self-affine behaviour inferred at the mm to km scales. Dynamic weakening and creep deformation, observed during S2, coincide with an evolution towards less anisotropic and scale-dependent slip surface roughness at the nanoscale.

Is fault surface roughness indicative of fault mechanisms? Observations from experimental Limestone faults

NASA Astrophysics Data System (ADS)

Sagy, A.; Tesei, T.; Collettini, C.

2016-12-01

Geometrical irregularity of contacting surfaces is a fundamental factor controlling friction and energy dissipation during sliding. We performed direct shear experiments on 20x20 cm limestone surfaces by applying constant normal load (40-200 kN) and sliding velocity 1-300 µm/s. Before shearing, the surfaces were polished with maximal measured amplitudes of less than 0.1 mm. After shear, elongated islands of shear zones are observed, characterized by grooves ploughed into the limestone surfaces and by layers of fine grain wear. These structures indicate that the contact areas during shear are scattered and occupy a limited portion of the entire surface area. The surfaces was scanned by a laser profilometer that measures topography using 640 parallel beams in a single run, offer up to 10 µm accuracy and working ranges of 200 mm. Two distinctive types of topographical end members are defined: rough wavy sections and smooth polished ones. The rough zones display ridges with typical amplitudes of 0.1-1 mm that cross the grooves perpendicular to the slip direction. These features are associated with penetrative brittle damage and with fragmentation. The smoother zones display reflective mirror-like surfaces bordered by topographical sharp steps at heights of 0.3-0.5 mm. These sections are localized inside the wear layer or between the wear layer and the host rock, and are not associated with observed penetrative damage. Preliminary statistical analysis suggests that the roughness of the ridges zones can be characterized using a power-low relationship between profile length and mean roughness, with relatively high values of Hurst exponents (e.g. H > 0.65) parallel to the slip direction. The polished zones, on the other hand, corresponded to lower values of Hurst exponents (e.g. H ≤ 0.6). Both structural and roughness measurements indicate that the distinctive topographic variations on the surfaces reflect competing mechanical processes which occur simultaneously during shear. The wavy ridged zone is the surface expression of penetrative cracking and fragmentation which widen the shear zone, while the smooth zones reflect localized flow and plastic deformation of the wear material. The similarity in topography of shear structures between experimental and natural faults suggests similar mechanical processes.

Correlation and Return Interval Analysis of Tree Rings Based Temperature and Precipitation Reconstructions

NASA Astrophysics Data System (ADS)

Bunde, A.; Ludescher, J.; Luterbacher, J.; von Storch, H.

2012-04-01

We analyze tree rings based summer temperature and precipitation reconstructions from Central Europe covering the past 2500y [1], by (i) autocorrelation functions, (ii) detrended fluctuation analysis (DFA2) and (iii) the Haar wavelet technique (WT2). We also study (iv) the PDFs of the return intervals for return periods of 5y, 10y, 20y, and 40y. All results provide evidence that the data cannot be described by an AR1 process, but are long-term correlated with a Hurst exponent H close to 1 for summer temperature data and around 0.9 for summer precipitation. These results, however, are not in agreement with neither observational data of the past two centuries nor millennium simulations with contemporary climate models, which both suggest H close to 0.65 for the temperature data and H close to 0.5 for the precipitation data. In particular the strong contrast in precipitation (highly correlated for the reconstructed data, white noise for the observational and model data) rises concerns on tree rings based climate reconstructions, which will have to be taken into account in future investigations. [1] Büntgen, U., Tegel, W., Nicolussi, K., McCormick, M., Frank, D., Trouet, V., Kaplan, J.O., Herzig, F., Heussner, K.-U., Wanner, H., Luterbacher, J., and Esper, J., 2011: 2500 Years of European Climate Variability and Human Susceptibility. SCIENCE, 331, 578-582.

Hurst Estimation of Scale Invariant Processes with Stationary Increments and Piecewise Linear Drift

NASA Astrophysics Data System (ADS)

Modarresi, N.; Rezakhah, S.

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first, we determine the scale intervals, their linear drifts and eliminate them. Then, a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion (fBm).

Analysis and Classification of Traffic in Wireless Sensor Network

DTIC Science & Technology

2007-03-01

34 1. Hurst Parameter ................................................................................35 2. Self-Similarity...traffic is self-similar, buffer size can be better designed from the forecasted traffic workload. 1. Hurst Parameter To determine the extent of self...similarity in WSN traffic, the Hurst parameter, H, is used. H also calculates the length of the long range dependence of a stochastic process. If H

Rescaled Range analysis of Induced Seismicity: rapid classification of clusters in seismic crisis

NASA Astrophysics Data System (ADS)

Bejar-Pizarro, M.; Perez Lopez, R.; Benito-Parejo, M.; Guardiola-Albert, C.; Herraiz, M.

2017-12-01

Different underground fluid operations, mainly gas storing, fracking and water pumping, can trigger Induced Seismicity (IS). This seismicity is normally featured by small-sized earthquakes (M<2.5), although particular cases reach magnitude as great as 5. It has been up for debate whether earthquakes greater than 5 can be triggered by IS or this level of magnitude only corresponds to tectonic earthquakes caused by stress change. Whatever the case, the characterization of IS for seismic clusters and seismic series recorded close but not into the gas storage, is still under discussion. Time-series of earthquakes obey non-linear patterns where the Hurst exponent describes the persistency or anti-persistency of the sequence. Natural seismic sequences have an H-exponent close to 0.7, which combined with the b-value time evolution during the time clusters, give us valuable information about the stationarity of the phenomena. Tectonic earthquakes consist in a main shock with a decay of time-occurrence of seismic shocks obeying the Omori's empirical law. On the contrary, IS does not exhibit a main shock and the time occurrence depends on the injection operations instead of on the tectonic energy released. In this context, the H-exponent can give information about the origin of the sequence. In 2013, a seismic crisis was declared from the Castor underground gas storing located off-shore in the Mediterranean Sea, close to the Northeastern Spanish cost. The greatest induced earthquake was 3.7. However, a 4.2 earthquake, probably of tectonic origin, occurred few days after the operations stopped. In this work, we have compared the H-exponent and the b-value time evolution according to the timeline of gas injection. Moreover, we have divided the seismic sequence into two groups: (1) Induced Seismicity and (2) Triggered Seismicity. The rescaled range analysis allows the differentiation between natural and induced seismicity and gives information about the persistency and long-term memory of the seismic crisis. These results are a part of the Spanish project SISMOSIMA (CGL2013-47412-C2-2P).

The Legacy of Benoit Mandelbrot in Geophysics

NASA Astrophysics Data System (ADS)

Turcotte, D. L.

2001-12-01

The concept of fractals (fractional dimension) was introduced by Benoit Mandelbrot in his famous 1967 Science paper. The initial application was to the length of the coastline of Britain. A milestone in the appreciation of the fractal concept by geophysicists was the Union session of the AGU on fractals led off by Benoit in 1986. Although fractals have found important applications in almost every branch of the physical, biological, and social sciences, fractals have been particularly useful in geophysics. Drainage networks are fractal. The frequency-magnitude distribution of earthquakes is fractal. The scale invariance of landscapes and many other geological processes is due to the applicability of power-law (fractal) distributions. Clouds are often fractal. Porosity distributions are fractal. In an almost independent line of research, Benoit in collaboration with James Wallace and others developed the concept of self-affine fractals. The original applications were primarily to time series in hydrology and built on the foundation laid by Henry Hurst. Fractional Gaussian noises and fractional Brownian motions are ubiquitous in geophysics. These are expressed in terms of the power-law relation between the power-spectral density S and frequency f, S ~ f{ β }, examples are β = 0 (white noise), β = 1 (1/f noise), β = 2 (Brownian motion). Of particular importance in geophysics are fractional noises with β = 0.5, these are stationary but have long-range persistent and have a Hurst exponent H = 0.7. Examples include river flows, tree rings, sunspots, varves, etc. Two of Benoit Mandelbrot's major contributions in geophysics as in other fields are: (1) an appreciation of the importance of fat-tail, power-law (fractal) distributions and (2) an appreciation of the importance of self-similar long-range persistence in both stationary time series (noises) and nonstationary time series (walks).

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

Generalized Arcsine Laws for Fractional Brownian Motion.

PubMed

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-26

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

Understanding the source of multifractality in financial markets

NASA Astrophysics Data System (ADS)

Barunik, Jozef; Aste, Tomaso; Di Matteo, T.; Liu, Ruipeng

2012-09-01

In this paper, we use the generalized Hurst exponent approach to study the multi-scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multi-scaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal model, autoregressive fractionally integrated moving average processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality.

A multifractal detrended fluctuation analysis of financial market efficiency: Comparison using Dow Jones sector ETF indices

NASA Astrophysics Data System (ADS)

Tiwari, Aviral Kumar; Albulescu, Claudiu Tiberiu; Yoon, Seong-Min

2017-10-01

This study challenges the efficient market hypothesis, relying on the Dow Jones sector Exchange-Traded Fund (ETF) indices. For this purpose, we use the generalized Hurst exponent and multifractal detrended fluctuation analysis (MF-DFA) methods, using daily data over the timespan from 2000 to 2015. We compare the sector ETF indices in terms of market efficiency between short- and long-run horizons, small and large fluctuations, and before and after the global financial crisis (GFC). Our findings can be summarized as follows. First, there is clear evidence that the sector ETF markets are multifractal in nature. We also find a crossover in the multifractality of sector ETF market dynamics. Second, the utilities and consumer goods sector ETF markets are more efficient compared with the financial and telecommunications sector ETF markets, in terms of price prediction. Third, there are noteworthy discrepancies in terms of market efficiency, between the short- and long-term horizons. Fourth, the ETF market efficiency is considerably diminished after the global financial crisis.

Stochastic nature of series of waiting times.

PubMed

Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H; Salehi, E; Behjat, E; Qorbani, M; Nezhad, M Khazaei; Zirak, M; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M Reza Rahimi

2013-06-01

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the "waiting times" series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2

Stochastic nature of series of waiting times

NASA Astrophysics Data System (ADS)

Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H.; Salehi, E.; Behjat, E.; Qorbani, M.; Khazaei Nezhad, M.; Zirak, M.; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M. Reza Rahimi

2013-06-01

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2

Experimental evidence of the self-similarity and long-range correlations of the edge fluctuations in HT-6M tokamak

NASA Astrophysics Data System (ADS)

Wang, Wen-hao; Yu, Chang-xuan; Wen, Yi-zhi; Xu, Yu-hong; Ling, Bi-li; Gong, Xian-zu; Liu, Bao-hua; Wan, Bao-nian

2001-02-01

For a better understanding of long timescale transport dynamics, the rescaled range analysis techniques, the autocorrelation function (ACF) and the probability distribution function (PDF) are used to investigate long-range dependences in edge plasma fluctuations in an HT-6M tokamak. The results reveal the self-similar characters of the electrostatic fluctuations with self-similarity parameters (Hurst exponent) ranging from 0.64 to 0.79, taking into consideration the Er×B rotation-sheared effect. Fluctuation ACFs of both the ion saturation current and the floating potential, as well as PDF of the turbulence-induced particle flux, have two distinct timescales. One corresponds to the decorrelation timescale of local fluctuations (µs) and the other lasts to the order of the confinement time (ms). All these experimental results suggest that some of the mechanisms of the underlying turbulence are consistent with plasma transport as characterized by self-organized criticality (SOC).

Minding Impacting Events in a Model of Stochastic Variance

PubMed Central

Duarte Queirós, Sílvio M.; Curado, Evaldo M. F.; Nobre, Fernando D.

2011-01-01

We introduce a generalization of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold, , and another one when the local standard deviation outnumbers . In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterized by large values of the Hurst exponent (), which are ubiquitous features in complex systems. PMID:21483864

On the multifractal effects generated by monofractal signals

NASA Astrophysics Data System (ADS)

Grech, Dariusz; Pamuła, Grzegorz

2013-12-01

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result of finite length of used data series and is additionally amplified by the long-term memory the data eventually may contain. We provide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized Hurst exponent values Δh or a threshold in the width of multifractal spectrum Δα below which multifractal properties of the system are only apparent, i.e. do not exist, despite Δα≠0 or Δh≠0. We find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent γ. Its strength decays according to power law with respect to the length of time series. The influence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated. This provides additional set of semi-analytical results. The obtained formulas are significant in any interdisciplinary application of multifractality, including physics, financial data analysis or physiology, because they allow to separate the ‘true’ multifractal phenomena from the apparent (artificial) multifractal effects. They should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not.

Multifractality and autoregressive processes of dry spell lengths in Europe: an approach to their complexity and predictability

NASA Astrophysics Data System (ADS)

Lana, X.; Burgueño, A.; Serra, C.; Martínez, M. D.

2017-01-01

Dry spell lengths, DSL, defined as the number of consecutive days with daily rain amounts below a given threshold, may provide relevant information about drought regimes. Taking advantage of a daily pluviometric database covering a great extension of Europe, a detailed analysis of the multifractality of the dry spell regimes is achieved. At the same time, an autoregressive process is applied with the aim of predicting DSL. A set of parameters, namely Hurst exponent, H, estimated from multifractal spectrum, f( α), critical Hölder exponent, α 0, for which f( α) reaches its maximum value, spectral width, W, and spectral asymmetry, B, permits a first clustering of European rain gauges in terms of the complexity of their DSL series. This set of parameters also allows distinguishing between time series describing fine- or smooth-structure of the DSL regime by using the complexity index, CI. Results of previous monofractal analyses also permits establishing comparisons between smooth-structures, relatively low correlation dimensions, notable predictive instability and anti-persistence of DSL for European areas, sometimes submitted to long droughts. Relationships are also found between the CI and the mean absolute deviation, MAD, and the optimum autoregressive order, OAO, of an ARIMA( p, d,0) autoregressive process applied to the DSL series. The detailed analysis of the discrepancies between empiric and predicted DSL underlines the uncertainty over predictability of long DSL, particularly for the Mediterranean region.

A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence

NASA Astrophysics Data System (ADS)

Mavridis, M.; Isliker, H.; Vlahos, L.; Görler, T.; Jenko, F.; Told, D.

2014-10-01

An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties of radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.

A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mavridis, M.; Isliker, H.; Vlahos, L.

2014-10-15

An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties ofmore » radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.« less

A Dynamical Systems Explanation of the Hurst Effect and Atmospheric Low-Frequency Variability

PubMed Central

Franzke, Christian L. E.; Osprey, Scott M.; Davini, Paolo; Watkins, Nicholas W.

2015-01-01

The Hurst effect plays an important role in many areas such as physics, climate and finance. It describes the anomalous growth of range and constrains the behavior and predictability of these systems. The Hurst effect is frequently taken to be synonymous with Long-Range Dependence (LRD) and is typically assumed to be produced by a stationary stochastic process which has infinite memory. However, infinite memory appears to be at odds with the Markovian nature of most physical laws while the stationarity assumption lacks robustness. Here we use Lorenz's paradigmatic chaotic model to show that regime behavior can also cause the Hurst effect. By giving an alternative, parsimonious, explanation using nonstationary Markovian dynamics, our results question the common belief that the Hurst effect necessarily implies a stationary infinite memory process. We also demonstrate that our results can explain atmospheric variability without the infinite memory previously thought necessary and are consistent with climate model simulations. PMID:25765880

a Predictive Model of Permeability for Fractal-Based Rough Rock Fractures during Shear

NASA Astrophysics Data System (ADS)

Huang, Na; Jiang, Yujing; Liu, Richeng; Li, Bo; Zhang, Zhenyu

This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent (H), in which H = 3 - Df, where Df is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between H and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.

War neuroses and Arthur Hurst: a pioneering medical film about the treatment of psychiatric battle casualties.

PubMed

Jones, Edgar

2012-07-01

From 1917 to 1918, Major Arthur Hurst filmed shell-shocked patients home from the war in France. Funded by the Medical Research Committee, and using Pathé cameramen, he recorded soldiers who suffered from intractable movement disorders as they underwent treatment at the Royal Victoria Hospital in Netley and undertook programs of occupational therapy at Seale Hayne in Devon. As one of the earliest UK medical films, Hurst's efforts may have drawn inspiration from the official documentary of the Battle of the Somme and films made in 1916 by French Army neurologists. Although initially motivated to make use of a novel medium to illustrate lectures, Hurst was alert to the wider appeal of the motion picture and saw an opportunity to position himself in the postwar medical hierarchy. Some "before treatment" shots were reenacted for the camera. Hurst, like some other shell shock doctors, openly used deception as a therapeutic measure. On the basis that the ends justified the means, they defended this procedure as ethical. Clinicians also took advantage of changes in military regulations to address functional symptoms. Claims made of "cures" in the film and associated publications by Hurst were challenged by other doctors treating shell shock. The absence of follow-up data and evidence from war pension files suggested that Hurst may have overstated the effectiveness of his methods. Nevertheless, the message conveyed in the film that chronic cases could be treated in a single session had a powerful resonance for ambitious or charismatic doctors and was revived in World War II.

A new image segmentation method based on multifractal detrended moving average analysis

NASA Astrophysics Data System (ADS)

Shi, Wen; Zou, Rui-biao; Wang, Fang; Su, Le

2015-08-01

In order to segment and delineate some regions of interest in an image, we propose a novel algorithm based on the multifractal detrended moving average analysis (MF-DMA). In this method, the generalized Hurst exponent h(q) is calculated for every pixel firstly and considered as the local feature of a surface. And then a multifractal detrended moving average spectrum (MF-DMS) D(h(q)) is defined by the idea of box-counting dimension method. Therefore, we call the new image segmentation method MF-DMS-based algorithm. The performance of the MF-DMS-based method is tested by two image segmentation experiments of rapeseed leaf image of potassium deficiency and magnesium deficiency under three cases, namely, backward (θ = 0), centered (θ = 0.5) and forward (θ = 1) with different q values. The comparison experiments are conducted between the MF-DMS method and other two multifractal segmentation methods, namely, the popular MFS-based and latest MF-DFS-based methods. The results show that our MF-DMS-based method is superior to the latter two methods. The best segmentation result for the rapeseed leaf image of potassium deficiency and magnesium deficiency is from the same parameter combination of θ = 0.5 and D(h(- 10)) when using the MF-DMS-based method. An interesting finding is that the D(h(- 10)) outperforms other parameters for both the MF-DMS-based method with centered case and MF-DFS-based algorithms. By comparing the multifractal nature between nutrient deficiency and non-nutrient deficiency areas determined by the segmentation results, an important finding is that the gray value's fluctuation in nutrient deficiency area is much severer than that in non-nutrient deficiency area.

Classification of emotional states from electrocardiogram signals: a non-linear approach based on hurst

PubMed Central

2013-01-01

Background Identifying the emotional state is helpful in applications involving patients with autism and other intellectual disabilities; computer-based training, human computer interaction etc. Electrocardiogram (ECG) signals, being an activity of the autonomous nervous system (ANS), reflect the underlying true emotional state of a person. However, the performance of various methods developed so far lacks accuracy, and more robust methods need to be developed to identify the emotional pattern associated with ECG signals. Methods Emotional ECG data was obtained from sixty participants by inducing the six basic emotional states (happiness, sadness, fear, disgust, surprise and neutral) using audio-visual stimuli. The non-linear feature ‘Hurst’ was computed using Rescaled Range Statistics (RRS) and Finite Variance Scaling (FVS) methods. New Hurst features were proposed by combining the existing RRS and FVS methods with Higher Order Statistics (HOS). The features were then classified using four classifiers – Bayesian Classifier, Regression Tree, K- nearest neighbor and Fuzzy K-nearest neighbor. Seventy percent of the features were used for training and thirty percent for testing the algorithm. Results Analysis of Variance (ANOVA) conveyed that Hurst and the proposed features were statistically significant (p < 0.001). Hurst computed using RRS and FVS methods showed similar classification accuracy. The features obtained by combining FVS and HOS performed better with a maximum accuracy of 92.87% and 76.45% for classifying the six emotional states using random and subject independent validation respectively. Conclusions The results indicate that the combination of non-linear analysis and HOS tend to capture the finer emotional changes that can be seen in healthy ECG data. This work can be further fine tuned to develop a real time system. PMID:23680041

Experimental study of the moisture distribution on the wetting front during drainage and imbibition in a 2D sand chamber

NASA Astrophysics Data System (ADS)

Wei, Yunbo; Chen, Kouping; Wu, Jichun; Zhu, Xiaobin

2018-06-01

In the present study, the moisture distribution on the wetting front during drainage and imbibition in a 2D sand chamber is studied thoroughly. Based on the high-resolution data measured by light transmission method, the moisture distribution is observed and then analyzed quantitatively. During drainage and imbibition, different moisture distributions are observed: (a) during drainage, moisture contents fluctuate in a larger range and fingers can be seen on the wetting front; (b) while during imbibition, moisture contents fluctuate in a smaller range and the wetting front is more regular. The Hurst coefficients are successful in capturing different characteristics of the moisture distribution between drainage and imbibition. During imbibition, the Hurst coefficients are around 0.2 on the wetting front; while during drainage, the Hurst coefficients are around 0.5. As the porosity changes from 0.336 to 0.383, the moisture distribution in the sand chamber does not display obvious change. While as the imbibition rate increases from 5 ml/min to 400 ml/min, the moisture distribution on the wetting front becomes more uniform.

Analysis of porosity distribution of large-scale porous media and their reconstruction by Langevin equation.

PubMed

Jafari, G Reza; Sahimi, Muhammad; Rasaei, M Reza; Tabar, M Reza Rahimi

2011-02-01

Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs ϕ(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=ϕ(h+δh)-ϕ(h) is a stationary and Markov process, characterized by a Markov length scale h(M). The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y(0),h(0)) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured. ©2011 American Physical Society

The Hurst Phenomenon in Error Estimates Related to Atmospheric Turbulence

NASA Astrophysics Data System (ADS)

Dias, Nelson Luís; Crivellaro, Bianca Luhm; Chamecki, Marcelo

2018-05-01

The Hurst phenomenon is a well-known feature of long-range persistence first observed in hydrological and geophysical time series by E. Hurst in the 1950s. It has also been found in several cases in turbulence time series measured in the wind tunnel, the atmosphere, and in rivers. Here, we conduct a systematic investigation of the value of the Hurst coefficient H in atmospheric surface-layer data, and its impact on the estimation of random errors. We show that usually H > 0.5 , which implies the non-existence (in the statistical sense) of the integral time scale. Since the integral time scale is present in the Lumley-Panofsky equation for the estimation of random errors, this has important practical consequences. We estimated H in two principal ways: (1) with an extension of the recently proposed filtering method to estimate the random error (H_p ), and (2) with the classical rescaled range introduced by Hurst (H_R ). Other estimators were tried but were found less able to capture the statistical behaviour of the large scales of turbulence. Using data from three micrometeorological campaigns we found that both first- and second-order turbulence statistics display the Hurst phenomenon. Usually, H_R is larger than H_p for the same dataset, raising the question that one, or even both, of these estimators, may be biased. For the relative error, we found that the errors estimated with the approach adopted by us, that we call the relaxed filtering method, and that takes into account the occurrence of the Hurst phenomenon, are larger than both the filtering method and the classical Lumley-Panofsky estimates. Finally, we found that there is no apparent relationship between H and the Obukhov stability parameter. The relative errors, however, do show stability dependence, particularly in the case of the error of the kinematic momentum flux in unstable conditions, and that of the kinematic sensible heat flux in stable conditions.

Spatio-Temporal Pattern Analysis for Regional Climate Change Using Mathematical Morphology

NASA Astrophysics Data System (ADS)

Das, M.; Ghosh, S. K.

2015-07-01

Of late, significant changes in climate with their grave consequences have posed great challenges on humankind. Thus, the detection and assessment of climatic changes on a regional scale is gaining importance, since it helps to adopt adequate mitigation and adaptation measures. In this paper, we have presented a novel approach for detecting spatio-temporal pattern of regional climate change by exploiting the theory of mathematical morphology. At first, the various climatic zones in the region have been identified by using multifractal cross-correlation analysis (MF-DXA) of different climate variables of interest. Then, the directional granulometry with four different structuring elements has been studied to detect the temporal changes in spatial distribution of the identified climatic zones in the region and further insights have been drawn with respect to morphological uncertainty index and Hurst exponent. The approach has been evaluated with the daily time series data of land surface temperature (LST) and precipitation rate, collected from Microsoft Research - Fetch Climate Explorer, to analyze the spatio-temporal climatic pattern-change in the Eastern and North-Eastern regions of India throughout four quarters of the 20th century.

Statistical, time series, and fractal analysis of full stretch of river Yamuna (India) for water quality management.

PubMed

Parmar, Kulwinder Singh; Bhardwaj, Rashmi

2015-01-01

River water is a major resource of drinking water on earth. Management of river water is highly needed for surviving. Yamuna is the main river of India, and monthly variation of water quality of river Yamuna, using statistical methods have been compared at different sites for each water parameters. Regression, correlation coefficient, autoregressive integrated moving average (ARIMA), box-Jenkins, residual autocorrelation function (ACF), residual partial autocorrelation function (PACF), lag, fractal, Hurst exponent, and predictability index have been estimated to analyze trend and prediction of water quality. Predictive model is useful at 95% confidence limits and all water parameters reveal platykurtic curve. Brownian motion (true random walk) behavior exists at different sites for BOD, AMM, and total Kjeldahl nitrogen (TKN). Quality of Yamuna River water at Hathnikund is good, declines at Nizamuddin, Mazawali, Agra D/S, and regains good quality again at Juhikha. For all sites, almost all parameters except potential of hydrogen (pH), water temperature (WT) crosses the prescribed limits of World Health Organization (WHO)/United States Environmental Protection Agency (EPA).

Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA

PubMed Central

Namazi, Hamidreza; Kiminezhadmalaie, Mona

2015-01-01

Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers. PMID:26539245

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

Universal scaling and nonlinearity of aggregate price impact in financial markets.

PubMed

Patzelt, Felix; Bouchaud, Jean-Philippe

2018-01-01

How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different time scales. Here we reveal that price impact has a universal nonlinear shape for trades aggregated on any intraday scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order-flow imbalance is not associated with large returns. To the contrary, it is observed when the price is pinned to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the midprice falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intraday scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intraday time scales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking.

Universal scaling and nonlinearity of aggregate price impact in financial markets

NASA Astrophysics Data System (ADS)

Patzelt, Felix; Bouchaud, Jean-Philippe

2018-01-01

How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different time scales. Here we reveal that price impact has a universal nonlinear shape for trades aggregated on any intraday scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order-flow imbalance is not associated with large returns. To the contrary, it is observed when the price is pinned to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the midprice falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intraday scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intraday time scales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking.

Covered interest parity arbitrage and temporal long-term dependence between the US dollar and the Yen

NASA Astrophysics Data System (ADS)

Batten, Jonathan A.; Szilagyi, Peter G.

2007-03-01

Using a daily time series from 1983 to 2005 of currency prices in spot and forward USD/Yen markets and matching equivalent maturity short-term US and Japanese interest rates, we investigate the sensitivity of the difference between actual prices in forward markets to those calculated from differentials in short-term interest rates. According to a fundamental theorem in financial economics termed covered interest parity (CIP), the actual and estimated prices should be identical once transaction and other costs are accommodated. The paper presents three important findings: first, we find evidence of considerable variation in CIP deviations from equilibrium; second, these deviations have diminished significantly and by 2000 have been almost eliminated; third, an analysis of the CIP deviations using the local Hurst exponent finds episodes of time-varying dependence over the various sample periods, which appear to be linked to episodes of dollar decline/Yen appreciation, or vice versa. The finding of temporal long-term dependence in CIP deviations is consistent with recent evidence of temporal long-term dependence in the returns of currency, stock and commodity markets.

Heterogeneous porous media: Fronts and noise

NASA Astrophysics Data System (ADS)

Chaouchel, M.; Rakotomalala, N.; Salin, D.; Xu, B.; Yortsos, Y. C.

Capillary effects can be important in immiscible flows in heterogeneous media, particularly at low capillary numbers (Ca). We present experiments and simulations of slow drainage in 3-D porous media, either homogeneous and in the presence of buoyancy or heterogeneous and in its absence. An acoustic technique allows for an accurate study of the 3-D fronts and the cross-over region. Our results suggest that both cases can be described by invasion percolation in a gradient. Both front tails scale with the corresponding Bond numbers as σft≈B-47 in agreement with the theory. An analogous scaling for viscous effects is also given. The noise of these fronts are found correlated in the form of a fractional Brownian motion (fBm) of a Hurst exponent H≈.5. At higher Ca, experiments performed in 3-D porous media with sharp changes in permeability, exhibit a saturation profile response closely linked to the permeability variations. This viscous response to heterogeneity provides an opportunity to investigate and determine correlated (even at all scales, i.e. fBm), permeability fields.

Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence.

PubMed

Olivares, Felipe; Zunino, Luciano; Gulich, Damián; Pérez, Darío G; Rosso, Osvaldo A

2017-10-01

We have experimentally quantified the temporal structural diversity from the coordinate fluctuations of a laser beam propagating through isotropic optical turbulence. The main focus here is on the characterization of the long-range correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. To fulfill this goal, a laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementing the symbolic technique based on ordinal patterns to estimate the well-known permutation entropy. We show that the permutation entropy estimations at multiple time scales evidence an interplay between different dynamical behaviors. More specifically, a crossover between two different scaling regimes is observed. We confirm a transition from an integrated stochastic process contaminated with electronic noise to a fractional Brownian motion with a Hurst exponent H=5/6 as the sampling time increases. Besides, we are able to quantify, from the estimated entropy, the amount of electronic noise as a function of the turbulence strength. We have also demonstrated that these experimental observations are in very good agreement with numerical simulations of noisy fractional Brownian motions with a well-defined crossover between two different scaling regimes.

Mach wave properties in the presence of source and medium heterogeneity

NASA Astrophysics Data System (ADS)

Vyas, J. C.; Mai, P. M.; Galis, M.; Dunham, Eric M.; Imperatori, W.

2018-06-01

We investigate Mach wave coherence for kinematic supershear ruptures with spatially heterogeneous source parameters, embedded in 3D scattering media. We assess Mach wave coherence considering: 1) source heterogeneities in terms of variations in slip, rise time and rupture speed; 2) small-scale heterogeneities in Earth structure, parameterized from combinations of three correlation lengths and two standard deviations (assuming von Karman power spectral density with fixed Hurst exponent); and 3) joint effects of source and medium heterogeneities. Ground-motion simulations are conducted using a generalized finite-difference method, choosing a parameterization such that the highest resolved frequency is ˜5 Hz. We discover that Mach wave coherence is slightly diminished at near fault distances (< 10 km) due to spatially variable slip and rise time; beyond this distance the Mach wave coherence is more strongly reduced by wavefield scattering due to small-scale heterogeneities in Earth structure. Based on our numerical simulations and theoretical considerations we demonstrate that the standard deviation of medium heterogeneities controls the wavefield scattering, rather than the correlation length. In addition, we find that peak ground accelerations in the case of combined source and medium heterogeneities are consistent with empirical ground motion prediction equations for all distances, suggesting that in nature ground shaking amplitudes for supershear ruptures may not be elevated due to complexities in the rupture process and seismic wave-scattering.

A Smoothing Technique for the Multifractal Analysis of a Medium Voltage Feeders Electric Current

NASA Astrophysics Data System (ADS)

de Santis, Enrico; Sadeghian, Alireza; Rizzi, Antonello

2017-12-01

The current paper presents a data-driven detrending technique allowing to smooth complex sinusoidal trends from a real-world electric load time series before applying the Detrended Multifractal Fluctuation Analysis (MFDFA). The algorithm we call Smoothed Sort and Cut Fourier Detrending (SSC-FD) is based on a suitable smoothing of high power periodicities operating directly in the Fourier spectrum through a polynomial fitting technique of the DFT. The main aim consists of disambiguating the characteristic slow varying periodicities, that can impair the MFDFA analysis, from the residual signal in order to study its correlation properties. The algorithm performances are evaluated on a simple benchmark test consisting of a persistent series where the Hurst exponent is known, with superimposed ten sinusoidal harmonics. Moreover, the behavior of the algorithm parameters is assessed computing the MFDFA on the well-known sunspot data, whose correlation characteristics are reported in literature. In both cases, the SSC-FD method eliminates the apparent crossover induced by the synthetic and natural periodicities. Results are compared with some existing detrending methods within the MFDFA paradigm. Finally, a study of the multifractal characteristics of the electric load time series detrendended by the SSC-FD algorithm is provided, showing a strong persistent behavior and an appreciable amplitude of the multifractal spectrum that allows to conclude that the series at hand has multifractal characteristics.

Labor estimation by informational objective assessment (LEIOA) for preterm delivery prediction.

PubMed

Malaina, Iker; Aranburu, Larraitz; Martínez, Luis; Fernández-Llebrez, Luis; Bringas, Carlos; De la Fuente, Ildefonso M; Pérez, Martín Blás; González, Leire; Arana, Itziar; Matorras, Roberto

2018-05-01

To introduce LEIOA, a new screening method to forecast which patients admitted to the hospital because of suspected threatened premature delivery will give birth in < 7 days, so that it can be used to assist in the prognosis and treatment jointly with other clinical tools. From 2010 to 2013, 286 tocographies from women with gestational ages comprehended between 24 and 37 weeks were collected and studied. Then, we developed a new predictive model based on uterine contractions which combine the Generalized Hurst Exponent and the Approximate Entropy by logistic regression (LEIOA model). We compared it with a model using exclusively obstetric variables, and afterwards, we joined both to evaluate the gain. Finally, a cross validation was performed. The combination of LEIOA with the medical model resulted in an increase (in average) of predictive values of 12% with respect to the medical model alone, giving a sensitivity of 0.937, a specificity of 0.747, a positive predictive value of 0.907 and a negative predictive value of 0.819. Besides, adding LEIOA reduced the percentage of incorrectly classified cases by the medical model by almost 50%. Due to the significant increase in predictive parameters and the reduction of incorrectly classified cases when LEIOA was combined with the medical variables, we conclude that it could be a very useful tool to improve the estimation of the immediacy of preterm delivery.

War Neuroses and Arthur Hurst: A Pioneering Medical Film about the Treatment of Psychiatric Battle Casualties

PubMed Central

Jones, Edgar

2016-01-01

From 1917 to 1918, Major Arthur Hurst filmed shell-shocked patients home from the war in France. Funded by the Medical Research Committee, and using Pathé cameramen, he recorded soldiers who suffered from intractable movement disorders as they underwent treatment at the Royal Victoria Hospital in Netley and undertook programs of occupational therapy at Seale Hayne in Devon. As one of the earliest UK medical films, Hurst’s efforts may have drawn inspiration from the official documentary of the Battle of the Somme and films made in 1916 by French Army neurologists. Although initially motivated to make use of a novel medium to illustrate lectures, Hurst was alert to the wider appeal of the motion picture and saw an opportunity to position himself in the postwar medical hierarchy. Some “before treatment” shots were reenacted for the camera. Hurst, like some other shell shock doctors, openly used deception as a therapeutic measure. On the basis that the ends justified the means, they defended this procedure as ethical. Clinicians also took advantage of changes in military regulations to address functional symptoms. Claims made of “cures” in the film and associated publications by Hurst were challenged by other doctors treating shell shock. The absence of follow-up data and evidence from war pension files suggested that Hurst may have overstated the effectiveness of his methods. Nevertheless, the message conveyed in the film that chronic cases could be treated in a single session had a powerful resonance for ambitious or charismatic doctors and was revived in World War II. PMID:21596724

Markov vs. Hurst-Kolmogorov behaviour identification in hydroclimatic processes

NASA Astrophysics Data System (ADS)

Dimitriadis, Panayiotis; Gournari, Naya; Koutsoyiannis, Demetris

2016-04-01

Hydroclimatic processes are usually modelled either by exponential decay of the autocovariance function, i.e., Markovian behaviour, or power type decay, i.e., long-term persistence (or else Hurst-Kolmogorov behaviour). For the identification and quantification of such behaviours several graphical stochastic tools can be used such as the climacogram (i.e., plot of the variance of the averaged process vs. scale), autocovariance, variogram, power spectrum etc. with the former usually exhibiting smaller statistical uncertainty as compared to the others. However, most methodologies including these tools are based on the expected value of the process. In this analysis, we explore a methodology that combines both the practical use of a graphical representation of the internal structure of the process as well as the statistical robustness of the maximum-likelihood estimation. For validation and illustration purposes, we apply this methodology to fundamental stochastic processes, such as Markov and Hurst-Kolmogorov type ones. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

Spatial variability of detrended soil plow layer penetrometer resistance transect in a sugarcane field

NASA Astrophysics Data System (ADS)

Pérez, Luis D.; Cumbrera, Ramiro; Mato, Juan; Millán, Humberto; Tarquis, Ana M.

2015-04-01

Spatial variability of soil properties is relevant for identifying those zones with physical degradation. In this sense, one has to face the problem of identifying the origin and distribution of spatial variability patterns (Brouder et al., 2001; Millán et al., 2012). The objective of the present work was to quantify the spatial structure of soil penetrometer resistance (PR) collected from a transect data consisted of 221 points equidistant. In each sampling, readings were obtained from 0 cm till 70 cm of depth, with an interval of 5 cm (Pérez, 2012). The study was conducted on a Vertisol (Typic Hapludert) dedicated to sugarcane (Saccharum officinarum L.) production during the last sixty years (Pérez et al., 2010). Recently, scaling approach has been applied on the determination of the scaling data properties (Tarquis et al., 2008; Millán et al., 2012; Pérez, 2012). We focus in the Hurst analysis to characterize the data variability for each depth. Previously a detrended analysis was conducted in order to better study de intrinsic variability of the series. The Hurst exponent (H) for each depth was estimated showing a characteristic pattern and differentiating PR evolution in depth. References Brouder, S., Hofmann, B., Reetz, H.F., 2001. Evaluating spatial variability of soil parameters for input management. Better Crops 85, 8-11. Millán, H; AM Tarquís, Luís D. Pérez, Juan Mato, Mario González-Posada, 2012. Spatial variability patterns of some Vertisol properties at a field scale using standardized data. Soil and Tillage Research, 120, 76-84. Pérez, Luís D. 2012. Influencia de la maquinaria agrícola sobre la variabilidad espacial de la compactación del suelo. Aplicación de la metodología geoestadística-fractal. PhD thesis, UPM (In Spanish). Pérez, Luís D., Humberto Millán, Mario González-Posada 2010. Spatial complexity of soil plow layer penetrometer resistance as influenced by sugarcane harvesting: A prefractal approach. Soil and Tillage Research, 110(1), 77-86. Tarquis, A.M., N. Bird, M.C. Cartagena, A. Whitmore and Y. Pachepsky, 2008. Multiscale entropy-based analyses of soil transect data. Vadose Zone Journal, 7(2), 563-569.

Fluctuations of the Concentration of Cs-137 Aerosol in Chernobyl,Fukushima and Kawasaki

NASA Astrophysics Data System (ADS)

Ota, Yohei; Hatano, Yuko; Okada, Yukiko; Hirose, Katsumi

2017-04-01

Statistical analysis is applied to a time series of the airborne concentration of Cs-137. In order to extract fractal characteristics of the fluctuations, we employed the Hurst analysis. Interestingly, the Hurst index is around 1/3, which is common to the Chernobyl data, Fukushima data, and Kawasaki data. The Kawasaki data is measured by the Tokyo City University, located at 40km south to Tokyo. We proposed a stochastic differential equation, based on an advection equation with winds fluctuating probabilistically. The averaged solution of the equation is compared with measured data. We found that the index of the power of the time is -4/3, which is common to the three cases, Chernobyl, Fukushima and Kawasaki.

77 FR 33216 - Agency Information Collection Activities

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-05

... OMB for review may be obtained from: Veta P. Hurst, Senior Attorney, (202) 663-4498, Office of Federal... INFORMATION CONTACT: Veta Hurst, Federal Sector Programs, Office of Federal Operations, 131 M Street NE..., mechanical, or other technological collection techniques or other forms of information technology, e.g...

General and specific statistical properties of foreign exchange markets during a financial crash

NASA Astrophysics Data System (ADS)

Li, Wei-Shen; Tsai, Yun-Jie; Shen, Yu-Hsien; Liaw, Sy-Sang

2016-06-01

We investigate minute-by-minute foreign exchange rate (FX) data of 14 currencies with different exchange-rate regimes during a financial crash, and divide these data into several stages according to their respective tendencies: depreciation stage (stage 1), fluctuating stage (stage 2), and appreciation stage (stage 3). The tail distribution of FX rate returns satisfies a power-law structure for different types of currencies. We find the absolute value of the power-law exponent is smaller in emerging markets than in developed markets, especially during the stage 1, and is greatest in pegged currencies. We also find that the correlation properties of the FX rate return series have quite disparate results among the various types of currencies. Currencies in developed markets respectively have weak persistence and anti-persistence in short and long timescales; whereas the pegged currencies and currencies in emerging markets show different degrees of anti-persistence in various timescales. Further analyses on the data in divided stages indicate that emerging markets and pegged currencies have more prominent dual fractal structures after the depreciation stage, while the developed markets do not. Hurst exponent analyses on the sign series yield similar results to that on the original return series for most currencies. The magnitude series of the returns provide some unique results during a crash. The developed market currencies have strong persistence and exhibit a weaker correlation in the depreciation and appreciation stages. In contrast, the currencies of emerging markets as well as pegged currencies fail to show such a transformation, but rather show a constant-correlation behavior in the corresponding stages of a crash. These results indicate that external shocks exert different degrees of influence during different stages of the crash in various markets.

Nonlinear Dynamics, Poor Data, and What to Make of Them?

NASA Astrophysics Data System (ADS)

Ghil, M.; Zaliapin, I. V.

2005-12-01

The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict variability in the geosciences. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this talk we will describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. These fall into two broad categories: (i) methods that try to ferret out regularities of the time series; and (ii) methods aimed at describing the characteristics of irregular processes. The former include singular-spectrum analysis (SSA), the multi-taper method (MTM), and the maximum-entropy method (MEM). The various steps, as well as the advantages and disadvantages of these methods, will be illustrated by their application to several important climatic time series, such as the Southern Oscillation Index (SOI), paleoclimatic time series, and instrumental temperature time series. The SOI index captures major features of interannual climate variability and is used extensively in its prediction. The other time series cover interdecadal and millennial time scales. The second category includes the calculation of fractional dimension, leading Lyapunov exponents, and Hurst exponents. More recently, multi-trend analysis (MTA), binary-decomposition analysis (BDA), and related methods have attempted to describe the structure of time series that include both regular and irregular components. Within the time available, I will try to give a feeling for how these methods work, and how well.

A support vector machine-based method to identify mild cognitive impairment with multi-level characteristics of magnetic resonance imaging.

PubMed

Long, Zhuqing; Jing, Bin; Yan, Huagang; Dong, Jianxin; Liu, Han; Mo, Xiao; Han, Ying; Li, Haiyun

2016-09-07

Mild cognitive impairment (MCI) represents a transitional state between normal aging and Alzheimer's disease (AD). Non-invasive diagnostic methods are desirable to identify MCI for early therapeutic interventions. In this study, we proposed a support vector machine (SVM)-based method to discriminate between MCI patients and normal controls (NCs) using multi-level characteristics of magnetic resonance imaging (MRI). This method adopted a radial basis function (RBF) as the kernel function, and a grid search method to optimize the two parameters of SVM. The calculated characteristics, i.e., the Hurst exponent (HE), amplitude of low-frequency fluctuations (ALFF), regional homogeneity (ReHo) and gray matter density (GMD), were adopted as the classification features. A leave-one-out cross-validation (LOOCV) was used to evaluate the classification performance of the method. Applying the proposed method to the experimental data from 29 MCI patients and 33 healthy subjects, we achieved a classification accuracy of up to 96.77%, with a sensitivity of 93.10% and a specificity of 100%, and the area under the curve (AUC) yielded up to 0.97. Furthermore, the most discriminative features for classification were found to predominantly involve default-mode regions, such as hippocampus (HIP), parahippocampal gyrus (PHG), posterior cingulate gyrus (PCG) and middle frontal gyrus (MFG), and subcortical regions such as lentiform nucleus (LN) and amygdala (AMYG). Therefore, our method is promising in distinguishing MCI patients from NCs and may be useful for the diagnosis of MCI. Copyright © 2016 IBRO. Published by Elsevier Ltd. All rights reserved.

Dynamics of electricity market correlations

NASA Astrophysics Data System (ADS)

Alvarez-Ramirez, J.; Escarela-Perez, R.; Espinosa-Perez, G.; Urrea, R.

2009-06-01

Electricity market participants rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. However, forecasting is hampered by the non-linear and stochastic nature of price time series. Diverse modeling strategies, from neural networks to traditional transfer functions, have been explored. These approaches are based on the assumption that price series contain correlations that can be exploited for model-based prediction purposes. While many works have been devoted to the demand and price modeling, a limited number of reports on the nature and dynamics of electricity market correlations are available. This paper uses detrended fluctuation analysis to study correlations in the demand and price time series and takes the Australian market as a case study. The results show the existence of correlations in both demand and prices over three orders of magnitude in time ranging from hours to months. However, the Hurst exponent is not constant over time, and its time evolution was computed over a subsample moving window of 250 observations. The computations, also made for two Canadian markets, show that the correlations present important fluctuations over a seasonal one-year cycle. Interestingly, non-linearities (measured in terms of a multifractality index) and reduced price predictability are found for the June-July periods, while the converse behavior is displayed during the December-January period. In terms of forecasting models, our results suggest that non-linear recursive models should be considered for accurate day-ahead price estimation. On the other hand, linear models seem to suffice for demand forecasting purposes.

Why the null matters: statistical tests, random walks and evolution.

PubMed

Sheets, H D; Mitchell, C E

2001-01-01

A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the 'scaled maximum', the 'log-rate-interval' (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The 'runs test' in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.

Comparison of Two Multifractal Analysis Methods: Generalized Structure Function and Multifractal Spectrum

NASA Astrophysics Data System (ADS)

Morato, M. Carmen; Castellanos, M. Teresa; Bird, Nigel; Tarquis, Ana M.

2016-04-01

Soil variability has often been a constant expected factor to take in account in soil studies. This variability could be considered to be composed of "functional" variations plus random fluctuations or noise. Multifractal formalism, first proposed by Mandelbrot (1982), is suitable for variables with self-similar distribution on a spatial domain. Multifractal analysis can provide insight into spatial variability of crop or soil parameters. In soil science, it has been quite popular to characterize the scaling property of a variable measured along a transect as a mass distribution of a statistical measure on a length domain of the studied transect. To do this, it divides it into a number of self similar segments and estimate the partition function and mass function. Based on this, the multifractal spectra (MFS) is calculated. However, another technique can be applied focus its attention in the variations of a measure analyzing the moments of the absolute differences at different scales, the Generalized Structure Function (GSF), and extracting the Generalized Hurst exponents. The aim of this study is to compare both techniques in a transect data. A common 1024 m transect across arable fields at Silsoe in Bedfordshire, east-central England were analyzed with these two multifractal methods. Properties studied were total porosity (Porosity), gravimetric water content (GWC) and nitrogen oxide flux (NO2 flux). The results showed in both methods that NO2 flux presents a clear multifractal character and a weak one in the GWC and Porosity cases. Several parameters were calculated from both methods and are discussed. On the other hand, using the partition function all the scale ranges were used, meanwhile in the GSF a shorter range of scales showed linear behavior in the bilog plots used to estimate the parameters. GWC exhibits a linear pattern from increments of 4 till 256 meters, Porosity showed this behavior from 4 till 64 meters. In case of NO2 flux only from 32 to 256 meters showed it. However, the relation between the mass exponent function and the GSF, found in the literature, was positively verified in the three variables.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

PubMed

Poplová, Michaela; Sovka, Pavel; Cifra, Michal

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance

PubMed Central

Poplová, Michaela; Sovka, Pavel

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal. PMID:29216207

Persistence in eye movement during visual search

NASA Astrophysics Data System (ADS)

Amor, Tatiana A.; Reis, Saulo D. S.; Campos, Daniel; Herrmann, Hans J.; Andrade, José S.

2016-02-01

As any cognitive task, visual search involves a number of underlying processes that cannot be directly observed and measured. In this way, the movement of the eyes certainly represents the most explicit and closest connection we can get to the inner mechanisms governing this cognitive activity. Here we show that the process of eye movement during visual search, consisting of sequences of fixations intercalated by saccades, exhibits distinctive persistent behaviors. Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the probability distributions of these measures show a clear preference of participants towards a reading-like mechanism (geometrical persistence), whose features and potential advantages for searching/foraging are discussed. We then perform a Multifractal Detrended Fluctuation Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find that it exhibits a typical multifractal behavior arising from the sequential combination of saccades and fixations. By inspecting the time series composed of only fixational movements, our results reveal instead a monofractal behavior with a Hurst exponent , which indicates the presence of long-range power-law positive correlations (statistical persistence). We expect that our methodological approach can be adopted as a way to understand persistence and strategy-planning during visual search.

The suppression of scale-free fMRI brain dynamics across three different sources of effort: aging, task novelty and task difficulty.

PubMed

Churchill, Nathan W; Spring, Robyn; Grady, Cheryl; Cimprich, Bernadine; Askren, Mary K; Reuter-Lorenz, Patricia A; Jung, Mi Sook; Peltier, Scott; Strother, Stephen C; Berman, Marc G

2016-08-08

There is growing evidence that fluctuations in brain activity may exhibit scale-free ("fractal") dynamics. Scale-free signals follow a spectral-power curve of the form P(f ) ∝ f(-β), where spectral power decreases in a power-law fashion with increasing frequency. In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently suppressed for different sources of cognitive effort. Decreases in the Hurst exponent (H), which quantifies scale-free signal, was related to three different sources of cognitive effort/task engagement: 1) task difficulty, 2) task novelty, and 3) aging effects. These results were consistently observed across multiple datasets and task paradigms. We also demonstrated that estimates of H are robust across a range of time-window sizes. H was also compared to alternative metrics of BOLD variability (SDBOLD) and global connectivity (Gconn), with effort-related decreases in H producing similar decreases in SDBOLD and Gconn. These results indicate a potential global brain phenomenon that unites research from different fields and indicates that fractal scaling may be a highly sensitive metric for indexing cognitive effort/task engagement.

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

A study of a diffusive model of asset returns and an empirical analysis of financial markets

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

A diffusive model for market dynamics is studied and the predictions of the model are compared to real financial markets. The model has a non-constant diffusion coefficient which depends both on the asset value and the time. A general solution for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases, piecewise linear and quadratic diffusion. The effects of discreteness in the market dynamics on the model are also studied. For the quadratic diffusion case, a type of phase transition leading to fat tails is observed as the discrete distribution approaches the continuum limit. It is also found that the model captures some of the empirical stylized facts observed in real markets, including fat-tails and scaling behavior in the distribution of returns. An analysis of empirical data for the EUR/USD currency exchange rate and the S&P 500 index is performed. Both markets show time scaling behavior consistent with a value of 1/2 for the Hurst exponent. Finally, the results show that the distribution of returns for the two markets is well fitted by the model, and the corresponding empirical diffusion coefficients are determined.

The suppression of scale-free fMRI brain dynamics across three different sources of effort: aging, task novelty and task difficulty

PubMed Central

Churchill, Nathan W.; Spring, Robyn; Grady, Cheryl; Cimprich, Bernadine; Askren, Mary K.; Reuter-Lorenz, Patricia A.; Jung, Mi Sook; Peltier, Scott; Strother, Stephen C.; Berman, Marc G.

2016-01-01

There is growing evidence that fluctuations in brain activity may exhibit scale-free (“fractal”) dynamics. Scale-free signals follow a spectral-power curve of the form P(f ) ∝ f−β, where spectral power decreases in a power-law fashion with increasing frequency. In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently suppressed for different sources of cognitive effort. Decreases in the Hurst exponent (H), which quantifies scale-free signal, was related to three different sources of cognitive effort/task engagement: 1) task difficulty, 2) task novelty, and 3) aging effects. These results were consistently observed across multiple datasets and task paradigms. We also demonstrated that estimates of H are robust across a range of time-window sizes. H was also compared to alternative metrics of BOLD variability (SDBOLD) and global connectivity (Gconn), with effort-related decreases in H producing similar decreases in SDBOLD and Gconn. These results indicate a potential global brain phenomenon that unites research from different fields and indicates that fractal scaling may be a highly sensitive metric for indexing cognitive effort/task engagement. PMID:27498696

Multifractal detrended fluctuation analysis of sheep livestock prices in origin

NASA Astrophysics Data System (ADS)

Pavón-Domínguez, P.; Serrano, S.; Jiménez-Hornero, F. J.; Jiménez-Hornero, J. E.; Gutiérrez de Ravé, E.; Ariza-Villaverde, A. B.

2013-10-01

The multifractal detrended fluctuation analysis (MF-DFA) is used to verify whether or not the returns of time series of prices paid to farmers in original markets can be described by the multifractal approach. By way of example, 5 weekly time series of prices of different breeds, slaughter weight and market differentiation from 2000 to 2012 are analyzed. Results obtained from the multifractal parameters and multifractal spectra show that the price series of livestock products are of a multifractal nature. The Hurst exponent shows that these time series are stationary signals, some of which exhibit long memory (Merino milk-fed in Seville and Segureña paschal in Jaen), short memory (Merino paschal in Cordoba and Segureña milk-fed in Jaen) or even are close to an uncorrelated signals (Merino paschal in Seville). MF-DFA is able to discern the different underlying dynamics that play an important role in different types of sheep livestock markets, such as degree and source of multifractality. In addition, the main source of multifractality of these time series is due to the broadness of the probability function, instead of the long-range correlation properties between small and large fluctuations, which play a clearly secondary role.

Asymmetric acceleration/deceleration dynamics in heart rate variability

NASA Astrophysics Data System (ADS)

Alvarez-Ramirez, J.; Echeverria, J. C.; Meraz, M.; Rodriguez, E.

2017-08-01

The heart rate variability (HRV) is an important physiological signal used either to assess the risk of cardiac death or to model the cardiovascular regulatory dynamics. Asymmetries in HRV data have been observed using 2D Poincare plots, which have been linked to a non-equilibrium operation of the cardiac autonomic system. This work further explores the presence of asymmetries but in the serial correlations of the dynamics of HRV data. To this end, detrended fluctuation analysis (DFA) was used to estimate the Hurst exponent both when the heart rate is accelerating and when it is decelerating. The analysis is conducted using data collected from subjects under normal sinus rhythm (NSR), congestive heart failure (CHF) and atrial fibrillation (AF) . For the NSR cases, it was found that correlations are stronger (p < 0 . 05) when the heart rate is accelerating than when it is decelerating over different scales in the range 20-40 beats. In contrast, the opposite behavior was detected for the CHF and AF patients. Possible links between asymmetric correlations in the dynamics and the mechanisms controlling the operation of the heart rate are discussed, as well as their implications for modeling the cardiovascular regulatory dynamics.

Detecting effects of low levels of cytochalasin B in 3T3 fibroblast cultures by analysis of electrical noise obtained from cellular micromotion

PubMed Central

Lovelady, Douglas C.; Friedman, Jennifer; Patel, Sonali; Rabson, David A.; Lo, Chun-Min

2009-01-01

We performed micromotion experiments using electric cell-substrate impedance sensing (ECIS) on a confluent layer of 3T3 fibroblasts exposed to different low levels of the toxin cytochalasin B. This toxin is know to affect actin polymerization and to disrupt cytoskeletal structure and function in cells, changing the morphology of confluent cell cultures and altering the nature of the cellular micromotion, which is measured by ECIS as changes in impedance. By looking at several measures to characterize the long- and short-term correlations in the noise of the impedance time series, we are able to detect the effects of the toxin at concentrations down to 1 μM; there are intriguing hints that the effects may be discernible at levels as low as 0.1 μM. These measures include the power spectrum, the Hurst and detrended-fluctuation-analysis exponents, and the first zero and first 1/e crossings of the autocorrelation function. While most published work with ECIS uses only average impedance values, we demonstrate that noise analysis provides a more sensitive probe. PMID:19026529

Forecasting the portuguese stock market time series by using artificial neural networks

NASA Astrophysics Data System (ADS)

Isfan, Monica; Menezes, Rui; Mendes, Diana A.

2010-04-01

In this paper, we show that neural networks can be used to uncover the non-linearity that exists in the financial data. First, we follow a traditional approach by analysing the deterministic/stochastic characteristics of the Portuguese stock market data and some typical features are studied, like the Hurst exponents, among others. We also simulate a BDS test to investigate nonlinearities and the results are as expected: the financial time series do not exhibit linear dependence. Secondly, we trained four types of neural networks for the stock markets and used the models to make forecasts. The artificial neural networks were obtained using a three-layer feed-forward topology and the back-propagation learning algorithm. The quite large number of parameters that must be selected to develop a neural network forecasting model involves some trial and as a consequence the error is not small enough. In order to improve this we use a nonlinear optimization algorithm to minimize the error. Finally, the output of the 4 models is quite similar, leading to a qualitative forecast that we compare with the results of the application of k-nearest-neighbor for the same time series.

Functional Covariance Networks: Obtaining Resting-State Networks from Intersubject Variability

PubMed Central

Gohel, Suril; Di, Xin; Walter, Martin; Biswal, Bharat B.

2012-01-01

Abstract In this study, we investigate a new approach for examining the separation of the brain into resting-state networks (RSNs) on a group level using resting-state parameters (amplitude of low-frequency fluctuation [ALFF], fractional ALFF [fALFF], the Hurst exponent, and signal standard deviation). Spatial independent component analysis is used to reveal covariance patterns of the relevant resting-state parameters (not the time series) across subjects that are shown to be related to known, standard RSNs. As part of the analysis, nonresting state parameters are also investigated, such as mean of the blood oxygen level-dependent time series and gray matter volume from anatomical scans. We hypothesize that meaningful RSNs will primarily be elucidated by analysis of the resting-state functional connectivity (RSFC) parameters and not by non-RSFC parameters. First, this shows the presence of a common influence underlying individual RSFC networks revealed through low-frequency fluctation (LFF) parameter properties. Second, this suggests that the LFFs and RSFC networks have neurophysiological origins. Several of the components determined from resting-state parameters in this manner correlate strongly with known resting-state functional maps, and we term these “functional covariance networks”. PMID:22765879

Memory and Trend of Precipitation in China during 1966-2013

NASA Astrophysics Data System (ADS)

Du, M.; Sun, F.; Liu, W.

2017-12-01

As climate change has had a significant impact on water cycle, the characteristic and variation of precipitation under climate change turned into a hotspot in hydrology. This study aims to analyze the trend and memory (both short-term and long-term) of precipitation in China. To do that, we apply statistical tests (including Mann-Kendall test, Ljung-Box test and Hurst exponent) to annual precipitation (P), frequency of rainy day (λ) and mean daily rainfall in days when precipitation occurs (α) in China (1966-2013). We also use a resampling approach to determine the field significance. From there, we evaluate the spatial distribution and percentages of stations with significant memory or trend. We find that the percentages of significant downtrends for λ and significant uptrends for α are significantly larger than the critical values at 95% field significance level, probably caused by the global warming. From these results, we conclude that extra care is necessary when significant results are obtained using statistical tests. This is because the null hypothesis could be rejected by chance and this situation is more likely to occur if spatial correlation is ignored according to the results of the resampling approach.

Characterization of the Dynamics of Climate Systems and Identification of Missing Mechanisms Impacting the Long Term Predictive Capabilities of Global Climate Models Utilizing Dynamical Systems Approaches to the Analysis of Observed and Modeled Climate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhatt, Uma S.; Wackerbauer, Renate; Polyakov, Igor V.

The goal of this research was to apply fractional and non-linear analysis techniques in order to develop a more complete characterization of climate change and variability for the oceanic, sea ice and atmospheric components of the Earth System. This research applied two measures of dynamical characteristics of time series, the R/S method of calculating the Hurst exponent and Renyi entropy, to observational and modeled climate data in order to evaluate how well climate models capture the long-term dynamics evident in observations. Fractional diffusion analysis was applied to ARGO ocean buoy data to quantify ocean transport. Self organized maps were appliedmore » to North Pacific sea level pressure and analyzed in ways to improve seasonal predictability for Alaska fire weather. This body of research shows that these methods can be used to evaluate climate models and shed light on climate mechanisms (i.e., understanding why something happens). With further research, these methods show promise for improving seasonal to longer time scale forecasts of climate.« less

The volume and mean depth of Earth's lakes

NASA Astrophysics Data System (ADS)

Cael, B. B.; Heathcote, A. J.; Seekell, D. A.

2017-01-01

Global lake volume estimates are scarce, highly variable, and poorly documented. We developed a rigorous method for estimating global lake depth and volume based on the Hurst coefficient of Earth's surface, which provides a mechanistic connection between lake area and volume. Volume-area scaling based on the Hurst coefficient is accurate and consistent when applied to lake data sets spanning diverse regions. We applied these relationships to a global lake area census to estimate global lake volume and depth. The volume of Earth's lakes is 199,000 km3 (95% confidence interval 196,000-202,000 km3). This volume is in the range of historical estimates (166,000-280,000 km3), but the overall mean depth of 41.8 m (95% CI 41.2-42.4 m) is significantly lower than previous estimates (62-151 m). These results highlight and constrain the relative scarcity of lake waters in the hydrosphere and have implications for the role of lakes in global biogeochemical cycles.

Monitoring the soil degradation by Metastatistical Analysis

NASA Astrophysics Data System (ADS)

Oleschko, K.; Gaona, C.; Tarquis, A.

2009-04-01

The effectiveness of fractal toolbox to capture the critical behavior of soil structural patterns during the chemical and physical degradation was documented by our numerous experiments (Oleschko et al., 2008 a; 2008 b). The spatio-temporal dynamics of these patterns was measured and mapped with high precision in terms of fractal descriptors. All tested fractal techniques were able to detect the statistically significant differences in structure between the perfect spongy and massive patterns of uncultivated and sodium-saline agricultural soils, respectively. For instance, the Hurst exponent, extracted from the Chernozeḿ micromorphological images and from the time series of its physical and mechanical properties measured in situ, detected the roughness decrease (and therefore the increase in H - from 0.17 to 0.30 for images) derived from the loss of original structure complexity. The combined use of different fractal descriptors brings statistical precision into the quantification of natural system degradation and provides a means for objective soil structure comparison (Oleschko et al., 2000). The ability of fractal parameters to capture critical behavior and phase transition was documented for different contrasting situations, including from Andosols deforestation and erosion, to Vertisols high fructuring and consolidation. The Hurst exponent is used to measure the type of persistence and degree of complexity of structure dynamics. We conclude that there is an urgent need to select and adopt a standardized toolbox for fractal analysis and complexity measures in Earth Sciences. We propose to use the second-order (meta-) statistics as subtle measures of complexity (Atmanspacher et al., 1997). The high degree of correlation was documented between the fractal and high-order statistical descriptors (four central moments of stochastic variable distribution) used to the system heterogeneity and variability analysis. We proposed to call this combined fractal/statistical toolbox Metastatistical Analysis and recommend it to the projects directed to soil degradation monitoring. References: 1. Oleschko, K., B.S. Figueroa, M.E. Miranda, M.A. Vuelvas and E.R. Solleiro, Soil & Till. Res. 55, 43 (2000). 2. Oleschko, K., Korvin, G., Figueroa S. B., Vuelvas, M.A., Balankin, A., Flores L., Carreño, D. Fractal radar scattering from soil. Physical Review E.67, 041403, 2003. 3. Zamora-Castro S., Oleschko, K. Flores, L., Ventura, E. Jr., Parrot, J.-F., 2008. Fractal mapping of pore and solids attributes. Vadose Zone Journal, v. 7, Issue2: 473-492. 4. Oleschko, K., Korvin, G., Muñoz, A., Velásquez, J., Miranda, M.E., Carreon, D., Flores, L., Martínez, M., Velásquez-Valle, M., Brambilla, F., Parrot, J.-F. Ronquillo, G., 2008. Fractal mapping of soil moisture content from remote sensed multi-scale data. Nonlinear Proceses in Geophysics Journal, 15: 711-725. 5. Atmanspacher, H., Räth, Ch., Wiedenmann, G., 1997. Statistics and meta-statistics in the concept of complexity. Physica A, 234: 819-829.

Probing the fractal pattern and organization of Bacillus thuringiensis bacteria colonies growing under different conditions using quantitative spectral light scattering polarimetry

NASA Astrophysics Data System (ADS)

Banerjee, Paromita; Soni, Jalpa; Purwar, Harsh; Ghosh, Nirmalya; Sengupta, Tapas K.

2013-03-01

Development of methods for quantification of cellular association and patterns in growing bacterial colony is of considerable current interest, not only to help understand multicellular behavior of a bacterial species but also to facilitate detection and identification of a bacterial species in a given space and under a given set of condition(s). We have explored quantitative spectral light scattering polarimetry for probing the morphological and structural changes taking place during colony formations of growing Bacillus thuringiensis bacteria under different conditions (in normal nutrient agar representing favorable growth environment, in the presence of 1% glucose as an additional nutrient, and 3 mM sodium arsenate as toxic material). The method is based on the measurement of spectral 3×3 Mueller matrices (which involves linear polarization measurements alone) and its subsequent analysis via polar decomposition to extract the intrinsic polarization parameters. Moreover, the fractal micro-optical parameter, namely, the Hurst exponent H, is determined via fractal-Born approximation-based inverse analysis of the polarization-preserving component of the light scattering spectra. Interesting differences are noted in the derived values for the H parameter and the intrinsic polarization parameters (linear diattenuation d, linear retardance δ, and linear depolarization Δ coefficients) of the growing bacterial colonies under different conditions. The bacterial colony growing in presence of 1% glucose exhibit the strongest fractality (lowest value of H), whereas that growing in presence of 3 mM sodium arsenate showed the weakest fractality. Moreover, the values for δ and d parameters are found to be considerably higher for the colony growing in presence of glucose, indicating more structured growth pattern. These findings are corroborated further with optical microscopic studies conducted on the same samples.

Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task

PubMed Central

Ciuciu, P.; Varoquaux, G.; Abry, P.; Sadaghiani, S.; Kleinschmidt, A.

2012-01-01

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes. PMID:22715328

Financial Crisis: A New Measure for Risk of Pension Fund Portfolios

PubMed Central

Cadoni, Marinella; Melis, Roberta; Trudda, Alessandro

2015-01-01

It has been argued that pension funds should have limitations on their asset allocation, based on the risk profile of the different financial instruments available on the financial markets. This issue proves to be highly relevant at times of market crisis, when a regulation establishing limits to risk taking for pension funds could prevent defaults. In this paper we present a framework for evaluating the risk level of a single financial instrument or a portfolio. By assuming that the log asset returns can be described by a multifractional Brownian motion, we evaluate the risk using the time dependent Hurst parameter H(t) which models volatility. To provide a measure of the risk, we model the Hurst parameter with a random variable with mixture of beta distribution. We prove the efficacy of the methodology by implementing it on different risk level financial instruments and portfolios. PMID:26086529

Financial Crisis: A New Measure for Risk of Pension Fund Portfolios.

PubMed

Cadoni, Marinella; Melis, Roberta; Trudda, Alessandro

2015-01-01

It has been argued that pension funds should have limitations on their asset allocation, based on the risk profile of the different financial instruments available on the financial markets. This issue proves to be highly relevant at times of market crisis, when a regulation establishing limits to risk taking for pension funds could prevent defaults. In this paper we present a framework for evaluating the risk level of a single financial instrument or a portfolio. By assuming that the log asset returns can be described by a multifractional Brownian motion, we evaluate the risk using the time dependent Hurst parameter H(t) which models volatility. To provide a measure of the risk, we model the Hurst parameter with a random variable with mixture of beta distribution. We prove the efficacy of the methodology by implementing it on different risk level financial instruments and portfolios.

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

Comparison study of global and local approaches describing critical phenomena on the Polish stock exchange market

NASA Astrophysics Data System (ADS)

Czarnecki, Łukasz; Grech, Dariusz; Pamuła, Grzegorz

2008-12-01

We confront global and local methods to analyze the financial crash-like events on the Polish financial market from the critical phenomena point of view. These methods are based on the analysis of log-periodicity and the local fractal properties of financial time series in the vicinity of phase transitions (crashes). The whole history (1991-2008) of Warsaw Stock Exchange Index (WIG) describing the largest developing financial market in Europe, is analyzed in a daily time horizon. We find that crash-like events on the Polish financial market are described better by the log-divergent price model decorated with log-periodic behavior than the corresponding power-law-divergent price model. Predictions coming from log-periodicity scenario are verified for all main crashes that took place in WIG history. It is argued that crash predictions within log-periodicity model strongly depend on the amount of data taken to make a fit and therefore are likely to contain huge inaccuracies. Turning to local fractal description, we calculate the so-called local (time dependent) Hurst exponent H for the WIG time series and we find the dependence between the behavior of the local fractal properties of the WIG time series and the crashes appearance on the financial market. The latter method seems to work better than the global approach - both for developing as for developed markets. The current situation on the market, particularly related to the Fed intervention in September’07 and the situation on the market immediately after this intervention is also analyzed from the fractional Brownian motion point of view.

Performance Based Logistics: Optimizing Total System Availability and Reducing Program Cost

DTIC Science & Technology

2011-03-14

MONITOR’S REPORT Dr. Paul C. Jussel NUMBER(S) U.S. Army War College 12. DISTRIBUTION / AVAILABILITY STATEMENT Distribution Statement A...Colonel David M. Kaczmarski United States Army Dr. Paul C. Jussel Project Adviser This CRP is submitted in...8911927-1.html# (accessed 10 November 2010) 2 Hurst, Dana . Performance Based Logistics – A Bridge Between Acquisition Reform and Logistics Supply

Visual Analytics of integrated Data Systems for Space Weather Purposes

NASA Astrophysics Data System (ADS)

Rosa, Reinaldo; Veronese, Thalita; Giovani, Paulo

Analysis of information from multiple data sources obtained through high resolution instrumental measurements has become a fundamental task in all scientific areas. The development of expert methods able to treat such multi-source data systems, with both large variability and measurement extension, is a key for studying complex scientific phenomena, especially those related to systemic analysis in space and environmental sciences. In this talk, we present a time series generalization introducing the concept of generalized numerical lattice, which represents a discrete sequence of temporal measures for a given variable. In this novel representation approach each generalized numerical lattice brings post-analytical data information. We define a generalized numerical lattice as a set of three parameters representing the following data properties: dimensionality, size and post-analytical measure (e.g., the autocorrelation, Hurst exponent, etc)[1]. From this representation generalization, any multi-source database can be reduced to a closed set of classified time series in spatiotemporal generalized dimensions. As a case study, we show a preliminary application in space science data, highlighting the possibility of a real time analysis expert system. In this particular application, we have selected and analyzed, using detrended fluctuation analysis (DFA), several decimetric solar bursts associated to X flare-classes. The association with geomagnetic activity is also reported. DFA method is performed in the framework of a radio burst automatic monitoring system. Our results may characterize the variability pattern evolution, computing the DFA scaling exponent, scanning the time series by a short windowing before the extreme event [2]. For the first time, the application of systematic fluctuation analysis for space weather purposes is presented. The prototype for visual analytics is implemented in a Compute Unified Device Architecture (CUDA) by using the K20 Nvidia graphics processing units (GPUs) to reduce the integrated analysis runtime. [1] Veronese et al. doi: 10.6062/jcis.2009.01.02.0021, 2010. [2] Veronese et al. doi:http://dx.doi.org/10.1016/j.jastp.2010.09.030, 2011.

Wavelet versus detrended fluctuation analysis of multifractal structures

NASA Astrophysics Data System (ADS)

Oświȩcimka, Paweł; Kwapień, Jarosław; Drożdż, Stanisław

2006-07-01

We perform a comparative study of applicability of the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maxima (WTMM) method in proper detecting of monofractal and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Lévy flights, and different sorts of multifractal binomial cascades. Our results show that in the majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended. In particular, WTMM gives biased outcomes for the fractional Brownian motion with different values of Hurst exponent, indicating spurious multifractality. In some cases WTMM can also give different results if one applies different wavelets. We do not exclude using WTMM in real data analysis, but it occurs that while one may apply MFDFA in a more automatic fashion, WTMM must be applied with care. In the second part of our work, we perform an analogous analysis on empirical data coming from the American and from the German stock market. For this data both methods detect rich multifractality in terms of broad f(α) , but MFDFA suggests that this multifractality is poorer than in the case of WTMM.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region

NASA Astrophysics Data System (ADS)

Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib

2018-03-01

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.

Fractality of eroded coastlines of correlated landscapes.

PubMed

Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

2011-07-01

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

Scaling range of power laws that originate from fluctuation analysis

NASA Astrophysics Data System (ADS)

Grech, Dariusz; Mazur, Zygmunt

2013-05-01

We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.

The spectra and periodograms of anti-correlated discrete fractional Gaussian noise.

PubMed

Raymond, G M; Percival, D B; Bassingthwaighte, J B

2003-05-01

Discrete fractional Gaussian noise (dFGN) has been proposed as a model for interpreting a wide variety of physiological data. The form of actual spectra of dFGN for frequencies near zero varies as f(1-2H), where 0 < H < 1 is the Hurst coefficient; however, this form for the spectra need not be a good approximation at other frequencies. When H approaches zero, dFGN spectra exhibit the 1 - 2H power-law behavior only over a range of low frequencies that is vanishingly small. When dealing with a time series of finite length drawn from a dFGN process with unknown H, practitioners must deal with estimated spectra in lieu of actual spectra. The most basic spectral estimator is the periodogram. The expected value of the periodogram for dFGN with small H also exhibits non-power-law behavior. At the lowest Fourier frequencies associated with a time series of N values sampled from a dFGN process, the expected value of the periodogram for H approaching zero varies as f(0) rather than f(1-2H). For finite N and small H, the expected value of the periodogram can in fact exhibit a local power-law behavior with a spectral exponent of 1 - 2H at only two distinct frequencies.

The Complexity of Solar and Geomagnetic Indices

NASA Astrophysics Data System (ADS)

Pesnell, W. Dean

2017-08-01

How far in advance can the sunspot number be predicted with any degree of confidence? Solar cycle predictions are needed to plan long-term space missions. Fleets of satellites circle the Earth collecting science data, protecting astronauts, and relaying information. All of these satellites are sensitive at some level to solar cycle effects. Statistical and timeseries analyses of the sunspot number are often used to predict solar activity. These methods have not been completely successful as the solar dynamo changes over time and one cycle's sunspots are not a faithful predictor of the next cycle's activity. In some ways, using these techniques is similar to asking whether the stock market can be predicted. It has been shown that the Dow Jones Industrial Average (DJIA) can be more accurately predicted during periods when it obeys certain statistical properties than at other times. The Hurst exponent is one such way to partition the data. Another measure of the complexity of a timeseries is the fractal dimension. We can use these measures of complexity to compare the sunspot number with other solar and geomagnetic indices. Our concentration is on how trends are removed by the various techniques, either internally or externally. Comparisons of the statistical properties of the various solar indices may guide us in understanding how the dynamo manifests in the various indices and the Sun.

The effects of drought and disturbance on the growth and developmental instability of loblolly pine (Pinus taeda L.)

USGS Publications Warehouse

Graham, John H.; Duda, Jeffrey J.; Brown, Michelle L.; Kitchen, Stanley G.; Emlen, John M.; Malol, Jagadish; Bankstahl, Elizabeth; Krzysik, Anthony J.; Balbach, Harold E.; Freeman, D. Carl

2012-01-01

Ecological indicators provide early warning of adverse environmental change, helping land managers adaptively manage their resources while minimizing costly remediation. In 1999 and 2000, we studied two such indicators, growth and developmental instability, of loblolly pine (Pinus taeda L.) influenced by mechanized infantry training at Fort Benning, Georgia. Disturbed areas were used for military training; tracked and wheeled vehicles damaged vegetation and soils. Highly disturbed sites had fewer trees, diminished ground cover, warmer soils in the summer, and more compacted soils with a shallower A-horizon. We hypothesized that disturbance would decrease the growth of needles, branches, and tree rings, increase the complexity of tree rings, and increase the developmental instability of needles. Contrary to our expectations, however, disturbance enhanced growth in the first year of the study, possibly by reducing competition. In the second year, a drought reduced growth of branches and needles, eliminating the stimulatory effect of disturbance. Growth-ring widths increased with growing-season precipitation, and decreased with growing-season temperature over the last 40 years. Disturbance had no effect on tree-ring complexity, as measured by the Hurst exponent. Within-fascicle variation of current-year needle length, a measure of developmental instability, differed among the study populations, but appeared unrelated to mechanical disturbance or drought.

Effects of surface topography on SERS response: Correlating nanoscopy with spectroscopy

NASA Astrophysics Data System (ADS)

Das, Sumit Kumar; Ghosh, Manash; Chowdhury, Joydeep

2018-05-01

This paper reports for the first time the hidden correlation between the topographical features of the bilayer Langmuir-Blodgett (LB) film substrates of stearic acid (SA) incubated in Au@Ag nanocolloids over various dipping times (DTs) with their corresponding SERS responses. The topographies of the as prepared substrates are investigated from the statistical considerations in terms of lateral correlation length, interface width, Hurst and Lyapnov exponents. The real space of the substrates are mapped directly from the FESEM and AFM images of the bilayer LB film of SA immersed in Au@Ag nanocolloids over various DTs ranging between 6 and 72 h. The SERS spectra of the Rhodamine 6G molecules adsorbed on the as prepared substrates have been reported. The statistical parameters of the substrates that exhibit maximum SERS efficacy have been suggested. The far field distributions in presence and in absence of Raman dipole together with spatial distribution of the near field from the hottest spot of the as prepared substrate have also been reported. To our knowledge, this is the first report that links nanoscopy with SERS spectroscopy from statistical considerations and is expected to open a new window towards the fabrication of more efficient and reproducible SERS active substrates in future endeavours.

Diagnosis of skin cancer by correlation and complexity analyses of damaged DNA

PubMed Central

Namazi, Hamidreza; Kulish, Vladimir V.; Delaviz, Fatemeh; Delaviz, Ali

2015-01-01

Skin cancer is a common, low-grade cancerous (malignant) growth of the skin. It starts from cells that begin as normal skin cells and transform into those with the potential to reproduce in an out-of-control manner. Cancer develops when DNA, the molecule found in cells that encodes genetic information, becomes damaged and the body cannot repair the damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to diagnose the skin cancer, first DNA walk plots of genomes of patients with skin cancer were generated. Then, the data so obtained was checked for complexity by computing the fractal dimension. Furthermore, the Hurst exponent has been employed in order to study the correlation of damaged DNA. By analysing different samples it has been found that the damaged DNA sequences are exhibiting higher degree of complexity and less correlation compared to normal DNA sequences. This investigation confirms that this method can be used for diagnosis of skin cancer. The method discussed in this research is useful not only for diagnosis of skin cancer but can be applied for diagnosis and growth analysis of different types of cancers. PMID:26497203

Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal

PubMed Central

Namazi, Hamidreza; Kulish, Vladimir V.

2016-01-01

One of the major challenges in brain research is to relate the structural features of the auditory stimulus to structural features of Electroencephalogram (EEG) signal. Memory content is an important feature of EEG signal and accordingly the brain. On the other hand, the memory content can also be considered in case of stimulus. Beside all works done on analysis of the effect of stimuli on human EEG and brain memory, no work discussed about the stimulus memory and also the relationship that may exist between the memory content of stimulus and the memory content of EEG signal. For this purpose we consider the Hurst exponent as the measure of memory. This study reveals the plasticity of human EEG signals in relation to the auditory stimuli. For the first time we demonstrated that the memory content of an EEG signal shifts towards the memory content of the auditory stimulus used. The results of this analysis showed that an auditory stimulus with higher memory content causes a larger increment in the memory content of an EEG signal. For the verification of this result, we benefit from approximate entropy as indicator of time series randomness. The capability, observed in this research, can be further investigated in relation to human memory. PMID:27528219

Antarctica: Cooling or Warming?

NASA Astrophysics Data System (ADS)

Bunde, Armin; Ludescher, Josef; Franzke, Christian

2013-04-01

We consider the 14 longest instrumental monthly mean temperature records from the Antarctica and analyse their correlation properties by wavelet and detrended fluctuation analysis. We show that the stations in the western and the eastern part of the Antarctica show significant long-term memory governed by Hurst exponents close to 0.8 and 0.65, respectively. In contrast, the temperature records at the inner part of the continent (South Pole and Vostok), resemble white noise. We use linear regression to estimate the respective temperature differences in the records per decade (i) for the annual data, (ii) for the summer and (iii) for the winter season. Using a recent approach by Lennartz and Bunde [1] we estimate the respective probabilities that these temperature differences can be exceeded naturally without inferring an external (anthropogenic) trend. We find that the warming in the western part of the continent and the cooling at the South Pole is due to a gradually changes in the cold extremes. For the winter months, both cooling and warming are well outside the 95 percent confidence interval, pointing to an anthropogenic origin. In the eastern Antarctica, the temperature increases and decreases are modest and well within the 95 percent confidence interval. [1] S. Lennartz and A. Bunde, Phys. Rev. E 84, 021129 (2011)

Model selection for identifying power-law scaling.

PubMed

Ton, Robert; Daffertshofer, Andreas

2016-08-01

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. Copyright © 2016 Elsevier Inc. All rights reserved.

Intermittency of solar system plasma turbulence near Venus and Earth

NASA Astrophysics Data System (ADS)

Teodorescu, Eliza; Echim, Marius; Chang, Tom

2016-04-01

We analyze magnetic field data from Venus Express (VEX) and CLUSTER to investigate the turbulent properties of the solar wind and the Earth's and Venus' magnetosheaths. A systematic study of the PDFs (Probability Distribution Functions) of the measured magnetic fluctuations and their fourth order moments (kurtosis) reveals numerous intermittent time series. The presence of intermittency is marked by non-Gaussian PDFs with heavy wings and a scale dependent kurtosis. Higher order analyses on the scale dependence of several moment orders of the PDFs, the structure functions, along with the scaling of the kurtosis allow for a selection of scales that pertain to different scaling regimes, governed by different physics. On such sub-ranges of scales we investigate the fractal structure of fluctuations through the Rank Ordered Multifractal Analysis - ROMA (Chang and Wu, 2008). ROMA is applied to a selection of intermittent magnetic field time series in the solar wind and planetary magnetosheaths and helps to quantify the turbulence properties through the estimation of a spectrum of local Hurst exponents. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM, and a grant of the Romanian Ministry of National Education, CNCS - UEFISCDI, project number PN-II-ID-PCE-2012-4-0418.

Definition of (so MIScalled) ``Complexity" as UTTER-SIMPLICITY!!!(sMciUS!!!) Versus Deviations From( sMciUS!!!): ``COMPLICATEDNESS" Definition(s) and MEASURE(S)!!!

NASA Astrophysics Data System (ADS)

Young, F.; Siegel, E.

2010-03-01

(so MIScalled) ``complexity''(sMc) associated BOTH SCALE- INVARIANCE Symmetry-RESTORING(S-I S-R) [vs. S-I S-B!!!], AND X (w) P(w ) 1/w^(1.000...) ``pink''/Zipf/Archimedes-HYPERBOLICITY INEVITABILITY CONNECTION is by simple-calculus SISR's logarithm- function derivative: (d/dw)ln(w)=1/w=1/w^(1.000...), hence: (d/dw) [SISR](w)=1/w=1/w^(1.000...)=(via Noether-theorem relating continuous-(SISR)-symmetries to conservation-laws)=(d/dw)[4-DIV (J(INTER-SCALE)=0](w)=1/w =1/w^(1.000...). Hence sMc is information inter-scale conservation [as Anderson-Mandell, Fractals of Brain; Fractals of Mind(1994)-experimental- psychology!!!], i.e. sMciUS!!!, VERSUS ``COMPLICATEDNESS", is sMcciUS!!!: EITHER: PLUS (Additive: Murphy's-law absence) OR TIMES (Multiplicative: Murphy's-law dominance) various disparate system-specificity ``COMPLICATIONS". ``COMPLICATEDNESS" MEASURES: DEVIATIONS FROM sMciUS!!!: EITHER [S-I S-B] MINUS [S- I S-R] AND/OR [``red"/Pareto X(w) P(w) 1/w^(#=/=1.000...)] MINUS [X(w) P(w) 1/w^(1.000...) ``pink"/Zipf/Archimedes-HYPERBOLICITY INEVITABILITY] = [1/w^(#=/=1.000...)] MINUS [1/w^(1.000...)]; almost but not exactly a fractals Hurst-exponent-like [# - 1.000...]!!!

Long-term memory and volatility clustering in high-frequency price changes

NASA Astrophysics Data System (ADS)

oh, Gabjin; Kim, Seunghwan; Eom, Cheoljun

2008-02-01

We studied the long-term memory in diverse stock market indices and foreign exchange rates using Detrended Fluctuation Analysis (DFA). For all high-frequency market data studied, no significant long-term memory property was detected in the return series, while a strong long-term memory property was found in the volatility time series. The possible causes of the long-term memory property were investigated using the return data filtered by the AR(1) model, reflecting the short-term memory property, the GARCH(1,1) model, reflecting the volatility clustering property, and the FIGARCH model, reflecting the long-term memory property of the volatility time series. The memory effect in the AR(1) filtered return and volatility time series remained unchanged, while the long-term memory property diminished significantly in the volatility series of the GARCH(1,1) filtered data. Notably, there is no long-term memory property, when we eliminate the long-term memory property of volatility by the FIGARCH model. For all data used, although the Hurst exponents of the volatility time series changed considerably over time, those of the time series with the volatility clustering effect removed diminish significantly. Our results imply that the long-term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series.

Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal.

PubMed

Namazi, Hamidreza; Khosrowabadi, Reza; Hussaini, Jamal; Habibi, Shaghayegh; Farid, Ali Akhavan; Kulish, Vladimir V

2016-08-30

One of the major challenges in brain research is to relate the structural features of the auditory stimulus to structural features of Electroencephalogram (EEG) signal. Memory content is an important feature of EEG signal and accordingly the brain. On the other hand, the memory content can also be considered in case of stimulus. Beside all works done on analysis of the effect of stimuli on human EEG and brain memory, no work discussed about the stimulus memory and also the relationship that may exist between the memory content of stimulus and the memory content of EEG signal. For this purpose we consider the Hurst exponent as the measure of memory. This study reveals the plasticity of human EEG signals in relation to the auditory stimuli. For the first time we demonstrated that the memory content of an EEG signal shifts towards the memory content of the auditory stimulus used. The results of this analysis showed that an auditory stimulus with higher memory content causes a larger increment in the memory content of an EEG signal. For the verification of this result, we benefit from approximate entropy as indicator of time series randomness. The capability, observed in this research, can be further investigated in relation to human memory.

Revisiting the Decision of Death in Hurst v. Florida.

PubMed

Cooke, Brian K; Ginory, Almari; Zedalis, Jennifer

2016-12-01

The United States Supreme Court has considered the question of whether a judge or a jury must make the findings necessary to support imposition of the death penalty in several notable cases, including Spaziano v. Florida (1984), Hildwin v. Florida (1989), and Ring v. Arizona (2002). In 2016, the U.S. Supreme Court revisited the subject in Hurst v. Florida Florida Statute § 921.141 allows the judge, after weighing aggravating and mitigating circumstances, to enter a sentence of life imprisonment or death. Before Hurst, Florida's bifurcated sentencing proceedings included an advisory sentence from jurors and a separate judicial hearing without juror involvement. In Hurst, the Court revisited the question of whether Florida's capital sentencing scheme violates the Sixth Amendment, which requires a jury, not a judge, to find each fact necessary to impose a sentence of death in light of Ring In an eight-to-one decision, the Court reversed the judgment of the Florida Supreme Court, holding that the Sixth Amendment requires a jury to find the aggravating factors necessary for imposing the death penalty. The role of Florida juries in capital sentencing proceedings was thereby elevated from advisory to determinative. We examine the Court's decision and offer commentary regarding this shift from judge to jury in the final imposition of the death penalty and the overall effect of this landmark case. © 2016 American Academy of Psychiatry and the Law.

How sensitivity to ongoing interaural temporal disparities is affected by manipulations of temporal features of the envelopes of high-frequency stimuli

PubMed Central

Bernstein, Leslie R.; Trahiotis, Constantine

2009-01-01

This study addressed how manipulating certain aspects of the envelopes of high-frequency stimuli affects sensitivity to envelope-based interaural temporal disparities (ITDs). Listener’s threshold ITDs were measured using an adaptive two-alternative paradigm employing “raised-sine” stimuli [John, M. S., et al. (2002). Ear Hear. 23, 106–117] which permit independent variation in their modulation frequency, modulation depth, and modulation exponent. Threshold ITDs were measured while manipulating modulation exponent for stimuli having modulation frequencies between 32 and 256 Hz. The results indicated that graded increases in the exponent led to graded decreases in envelope-based threshold ITDs. Threshold ITDs were also measured while parametrically varying modulation exponent and modulation depth. Overall, threshold ITDs decreased with increases in the modulation depth. Unexpectedly, increases in the exponent of the raised-sine led to especially large decreases in threshold ITD when the modulation depth was low. An interaural correlation-based model was generally able to capture changes in threshold ITD stemming from changes in the exponent, depth of modulation, and frequency of modulation of the raised-sine stimuli. The model (and several variations of it), however, could not account for the unexpected interaction between the value of raised-sine exponent and its modulation depth. PMID:19425666

Definition of fractal topography to essential understanding of scale-invariance

NASA Astrophysics Data System (ADS)

Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

2017-04-01

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faranda, Davide, E-mail: davide.faranda@cea.fr; Dubrulle, Bérengère; Daviaud, François

We introduce a novel way to extract information from turbulent datasets by applying an Auto Regressive Moving Average (ARMA) statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded time series to a discrete version of a stochastic differential equation which is able to describe the correlation structure in the dataset. We introduce a new index Υ that measures the difference between the resulting analysis and the Obukhov model of turbulence, the simplest stochastic model reproducing both Richardson law and the Kolmogorov spectrum. We test themore » method on datasets measured in a von Kármán swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the Υ is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyze flow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system.« less

Temporal scaling and spatial statistical analyses of groundwater level fluctuations

NASA Astrophysics Data System (ADS)

Sun, H.; Yuan, L., Sr.; Zhang, Y.

2017-12-01

Natural dynamics such as groundwater level fluctuations can exhibit multifractionality and/or multifractality due likely to multi-scale aquifer heterogeneity and controlling factors, whose statistics requires efficient quantification methods. This study explores multifractionality and non-Gaussian properties in groundwater dynamics expressed by time series of daily level fluctuation at three wells located in the lower Mississippi valley, after removing the seasonal cycle in the temporal scaling and spatial statistical analysis. First, using the time-scale multifractional analysis, a systematic statistical method is developed to analyze groundwater level fluctuations quantified by the time-scale local Hurst exponent (TS-LHE). Results show that the TS-LHE does not remain constant, implying the fractal-scaling behavior changing with time and location. Hence, we can distinguish the potentially location-dependent scaling feature, which may characterize the hydrology dynamic system. Second, spatial statistical analysis shows that the increment of groundwater level fluctuations exhibits a heavy tailed, non-Gaussian distribution, which can be better quantified by a Lévy stable distribution. Monte Carlo simulations of the fluctuation process also show that the linear fractional stable motion model can well depict the transient dynamics (i.e., fractal non-Gaussian property) of groundwater level, while fractional Brownian motion is inadequate to describe natural processes with anomalous dynamics. Analysis of temporal scaling and spatial statistics therefore may provide useful information and quantification to understand further the nature of complex dynamics in hydrology.

Insights on Microbial Activity from Reduction Potential: Electrochemical Noise Analysis of a Pristine Aquifer

NASA Astrophysics Data System (ADS)

Enright, A. M.; Shirokova, V.; Ferris, G.

2012-12-01

Reduction potential was measured in a shallow, till-hosted, pristine aquifer. A previous study* characterized the microbial community of the aquifer, and geochemical analysis of water from the aquifer from 2010, 2011, and 2012 indicates persistent localized geochemical gradients of ferrous, ferric, sulphate, and sulphide ions. The chemical plume changes oxidation state from a reduced centre to oxidized outer boundaries, and microbial activity is responsible for the shift in redox state. Analysis of reduction potential as electrochemical noise in both the frequency and time domains provides insight into the manipulation of dissolved ions by the microbial community. Analysis of electrochemical noise is sensitive enough to distinguish the rates and magnitude of influence of the mechanisms which contribute to the redox state of a system. Self-similarity has been suggested to arise in any system where electrochemical noise is the result of a multitude of contributory processes, and this type of noise signature has been reported for many biological and abiotic natural processes. This observed ubiquity is not well understood. Reduction potential data is analyzed using detrended fluctuation analysis in the frequency domain and detrended moving average analysis in the time domain to characterize the Hurst exponent and fractal dimension of this physiological time series. *V.L. Shirokova and F.G. Ferris. (2012). Microbial Diversity and Biogeochemistry of a Pristine Canadian Shield Groundwater System. Geomicrobiology Journal.

Multiscale rescaled range analysis of EEG recordings in sevoflurane anesthesia.

PubMed

Liang, Zhenhu; Li, Duan; Ouyang, Gaoxiang; Wang, Yinghua; Voss, Logan J; Sleigh, Jamie W; Li, Xiaoli

2012-04-01

The Hurst exponent (HE) is a nonlinear method measuring the smoothness of a fractal time series. In this study we applied the HE index, extracted from electroencephalographic (EEG) recordings, as a measure of anesthetic drug effects on brain activity. In 19 adult patients undergoing sevoflurane general anesthesia, we calculated the HE of the raw EEG; comparing the maximal overlap discrete wavelet transform (MODWT) with the traditional rescaled range (R/S) analysis techniques, and with a commercial index of depth of anesthesia - the response entropy (RE). We analyzed each wavelet-decomposed sub-band as well as the combined low frequency bands (HEOLFBs). The methods were compared in regard to pharmacokinetic/pharmacodynamic (PK/PD) modeling, and prediction probability. All the low frequency band HE indices decreased when anesthesia deepened. However the HEOLFB was the best index because: it was less sensitive to artifacts, most closely tracked the exact point of loss of consciousness, showed a better prediction probability in separating the awake and unconscious states, and tracked sevoflurane concentration better - as estimated by the PK/PD models. The HE is a useful measure for estimating the depth of anesthesia. It was noted that HEOLFB showed the best performance for tracking drug effect. The HEOLFB could be used as an index for accurately estimating the effect of anesthesia on brain activity. Copyright © 2011 International Federation of Clinical Neurophysiology. All rights reserved.

Trends in currency’s return

NASA Astrophysics Data System (ADS)

Tan, A.; Shahrill, M.; Daud, S.; Leung, E.

2018-03-01

The purpose of this paper is to show that short-ranged dependence prevailed for Singapore-Malaysia exchange. Although, it is perceived that there is some evidence of long-ranged dependence [1,2], it is still unclear whether Singapore-Malaysia exchange indeed exhibits long-ranged dependence. For this paper, we focus on the currency rate for a sixteen-year period ranging from September 2002 to September 2017. We estimate the Hurst parameter using the famous rescaled R/S statistics technique. From our analysis, we showed that the Hurst parameter is approximately 0.5 which indicates short-ranged dependence. This short memory property is further validated by performing a one-tailed z-test whose alternative hypothesis is that the Hurst parameter is not 0.5 at 1% significance level. We conclude that the alternative hypothesis is rejected. The existence of short memory proves that the behaviour of the exchange rate is unpredictable, supporting the efficient market hypothesis, which states that not only is price movement completely random but also tomorrow’s prices are predicted by all the information in today’s prices.

Mapping lava flow textures using three-dimensional measures of surface roughness

NASA Astrophysics Data System (ADS)

Mallonee, H. C.; Kobs-Nawotniak, S. E.; McGregor, M.; Hughes, S. S.; Neish, C.; Downs, M.; Delparte, D.; Lim, D. S. S.; Heldmann, J. L.

2016-12-01

Lava flow emplacement conditions are reflected in the surface textures of a lava flow; unravelling these conditions is crucial to understanding the eruptive history and characteristics of basaltic volcanoes. Mapping lava flow textures using visual imagery alone is an inherently subjective process, as these images generally lack the resolution needed to make these determinations. Our team has begun mapping lava flow textures using visual spectrum imagery, which is an inherently subjective process involving the challenge of identifying transitional textures such as rubbly and slabby pāhoehoe, as these textures are similar in appearance and defined qualitatively. This is particularly problematic for interpreting planetary lava flow textures, where we have more limited data. We present a tool to objectively classify lava flow textures based on quantitative measures of roughness, including the 2D Hurst exponent, RMS height, and 2D:3D surface area ratio. We collected aerial images at Craters of the Moon National Monument (COTM) using Unmanned Aerial Vehicles (UAVs) in 2015 and 2016 as part of the FINESSE (Field Investigations to Enable Solar System Science and Exploration) and BASALT (Biologic Analog Science Associated with Lava Terrains) research projects. The aerial images were stitched together to create Digital Terrain Models (DTMs) with resolutions on the order of centimeters. The DTMs were evaluated by the classification tool described above, with output compared against field assessment of the texture. Further, the DTMs were downsampled and reevaluated to assess the efficacy of the classification tool at data resolutions similar to current datasets from other planetary bodies. This tool allows objective classification of lava flow texture, which enables more accurate interpretations of flow characteristics. This work also gives context for interpretations of flows with comparatively low data resolutions, such as those on the Moon and Mars. Textural maps based on quantitative measures of roughness are a valuable asset for studies of lava flows on Earth and other planetary bodies.

Effect of fault roughness on aftershock distribution and post co-seismic strain accumulation.

NASA Astrophysics Data System (ADS)

Aslam, K.; Daub, E. G.

2017-12-01

We perform physics-based simulations of earthquake rupture propagation on geometrically complex strike-slip faults. We consider many different realization of the fault roughness and obtain heterogeneous stress fields by performing dynamic rupture simulation of large earthquakes. We calculate the Coulomb failure function (CFF) for all these realizations so that we can quantify zones of stress increase/shadows surrounding the main fault and compare our results to seismic catalogs. To do this comparison, we use relocated earthquake catalogs from Northern and Southern California. We specify the range of fault roughness parameters based on past observational studies. The Hurst exponent (H) varies in range from 0.5 to 1 and RMS height to wavelength ratio ( RMS deviation of a fault profile from planarity) has values between 10-2 to 10-3. For any realization of fault roughness, the Probability density function (PDF) values relative to the mean CFF change show a wider spread near the fault and this spread squeezes into a narrow band as we move away from fault. For lower value of RMS ratio ( 10-3), we see bigger zones of stress change near the hypocenter and for higher value of RMS ratio ( 10-2), we see alternate zones of stress increase/decrease surrounding the fault to have comparable lengths. We also couple short-term dynamic rupture simulation with long-term tectonic modelling. We do this by giving the stress output from one of the dynamic rupture simulation (of a single realization of fault roughness) to long term tectonic model (LTM) as initial condition and then run LTM over duration of seismic cycle. This short term and long term coupling enables us to understand how heterogeneous stresses due to fault geometry influence the dynamics of strain accumulation in the post-seismic and inter-seismic phase of seismic cycle.

Decoding the Margins: What Can the Fractal Geometry of Basaltic Flow Margins Tell Us?

NASA Astrophysics Data System (ADS)

Schaefer, E. I.; Hamilton, C.; Neish, C.; Beard, S. P.; Bramson, A. M.; Sori, M.; Rader, E. L.

2016-12-01

Studying lava flows on other planetary bodies is essential to characterizing eruption styles and constraining the bodies' thermal evolution. Although planetary basaltic flows are common, many key features are not resolvable in orbital imagery. We are thus developing a technique to characterize basaltic flow type, sub-meter roughness, and sediment mantling from these data. We will present the results from upcoming fieldwork at Craters of the Moon National Monument and Preserve with FINESSE (August) and at Hawai'i Volcanoes National Park (September). We build on earlier work that showed that basaltic flow margins are approximately fractal [Bruno et al., 1992; Gaonac'h et al., 1992] and that their fractal dimensions (D) have distinct `a`ā and pāhoehoe ranges under simple conditions [Bruno et al., 1994]. Using a differential GPS rover, we have recently shown that the margin of Iceland's 2014 Holuhraun flow exhibits near-perfect (R2=0.9998) fractality for ≥24 km across dm to km scales [Schaefer et al., 2016]. This finding suggests that a fractal-based technique has significant potential to characterize flows at sub-resolution scales. We are simultaneously seeking to understand how margin fractality can be modified. A preliminary result for an `a'ā flow in Hawaii's Ka'ū Desert suggests that although aeolian mantling obscures the original flow margin, the apparent margin (i.e., sediment-lava interface) remains fractal [Schaefer et al., 2015]. Further, the apparent margin's D is likely significantly modified from that of the original margin. Other factors that we are exploring include erosion, transitional flow types, and topographic confinement. We will also rigorously test the intriguing possibility that margin D correlates with the sub-meter Hurst exponent H of the flow surface, a common metric of roughness scaling [e.g., Shepard et al., 2001]. This hypothesis is based on geometric arguments [Turcotte, 1997] and is qualitatively consistent with all results so far.

Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

PubMed

Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael

2011-02-01

This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.

Chaos in Magnetic Flux Ropes

NASA Astrophysics Data System (ADS)

Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

2013-12-01

Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)

Nanoscale Roughness of Faults Explained by the Scale-Dependent Yield Stress of Geologic Materials

NASA Astrophysics Data System (ADS)

Thom, C.; Brodsky, E. E.; Carpick, R. W.; Goldsby, D. L.; Pharr, G.; Oliver, W.

2017-12-01

Despite significant differences in their lithologies and slip histories, natural fault surfaces exhibit remarkably similar scale-dependent roughness over lateral length scales spanning 7 orders of magnitude, from microns to tens of meters. Recent work has suggested that a scale-dependent yield stress may result in such a characteristic roughness, but experimental evidence in favor of this hypothesis has been lacking. We employ an atomic force microscope (AFM) operating in intermittent-contact mode to map the topography of the Corona Heights fault surface. Our experiments demonstrate that the Corona Heights fault exhibits isotropic self-affine roughness with a Hurst exponent of 0.75 +/- 0.05 at all wavelengths from 60 nm to 10 μm. If yield stress controls roughness, then the roughness data predict that yield strength varies with length scale as λ-0.25 +/ 0.05. To test the relationship between roughness and yield stress, we conducted nanoindentation tests on the same Corona Heights sample and a sample of the Yair Fault, a carbonate fault surface that has been previously characterized by AFM. A diamond Berkovich indenter tip was used to indent the samples at a nominally constant strain rate (defined as the loading rate divided by the load) of 0.2 s-1. The continuous stiffness method (CSM) was used to measure the indentation hardness (which is proportional to yield stress) and the elastic modulus of the sample as a function of depth in each test. For both samples, the yield stress decreases with increasing size of the indents, a behavior consistent with that observed for many engineering materials and recently for other geologic materials such as olivine. The magnitude of this "indentation size effect" is best described by a power-law with exponents of -0.12 +/- 0.06 and -0.18 +/- 0.08 for the Corona Heights and Yair Faults, respectively. These results demonstrate a link between surface roughness and yield stress, and suggest that fault geometry is the physical manifestation of a scale-dependent yield stress.

Map of Pseudo-F-statistics of seismic noise parameters as an indicator of current seismic danger in Japan

NASA Astrophysics Data System (ADS)

Lyubushin, Alexey

2016-04-01

The problem of estimate of current seismic danger based on monitoring of seismic noise properties from broadband seismic network F-net in Japan (84 stations) is considered. Variations of the following seismic noise parameters are analyzed: multifractal singularity spectrum support width, generalized Hurst exponent, minimum Hölder-Lipschitz exponent and minimum normalized entropy of squared orthogonal wavelet coefficients. These parameters are estimated within adjacent time windows of the length 1 day for seismic noise waveforms from each station. Calculating daily median values of these parameters by all stations provides 4-dimensional time series which describes integral properties of the seismic noise in the region covered by the network. Cluster analysis is applied to the sequence of clouds of 4-dimensional vectors within moving time window of the length 365 days with mutual shift 3 days starting from the beginning of 1997 up to the current time. The purpose of the cluster analysis is to find the best number of clusters (BNC) from probe numbers which are varying from 1 up to the maximum value 40. The BNC is found from the maximum of pseudo-F-statistics (PFS). A 2D map could be created which presents dependence of PFS on the tested probe number of clusters and the right-hand end of moving time window which is rather similar to usual spectral time-frequency diagrams. In the paper [1] it was shown that the BNC before Tohoku mega-earthquake on March 11, 2011, has strongly chaotic regime with jumps from minimum up to maximum values in the time interval 1 year before the event and this time intervals was characterized by high PFS values. The PFS-map is proposed as the method for extracting time intervals with high current seismic danger. The next danger time interval after Tohoku mega-EQ began at the end of 2012 and was finished at the middle of 2013. Starting from middle of 2015 the high PFS values and chaotic regime of BNC variations were returned. This could be interpreted as the increasing of the danger of the next mega-EQ in Japan in the region of Nankai Trough [1] at the first half of 2016. References 1. Lyubushin, A., 2013. How soon would the next mega-earthquake occur in Japan? // Natural Science, 5 (8A1), 1-7. http://dx.doi.org/10.4236/ns.2013.58A1001

QSPR modeling: graph connectivity indices versus line graph connectivity indices

PubMed

Basak; Nikolic; Trinajstic; Amic; Beslo

2000-07-01

Five QSPR models of alkanes were reinvestigated. Properties considered were molecular surface-dependent properties (boiling points and gas chromatographic retention indices) and molecular volume-dependent properties (molar volumes and molar refractions). The vertex- and edge-connectivity indices were used as structural parameters. In each studied case we computed connectivity indices of alkane trees and alkane line graphs and searched for the optimum exponent. Models based on indices with an optimum exponent and on the standard value of the exponent were compared. Thus, for each property we generated six QSPR models (four for alkane trees and two for the corresponding line graphs). In all studied cases QSPR models based on connectivity indices with optimum exponents have better statistical characteristics than the models based on connectivity indices with the standard value of the exponent. The comparison between models based on vertex- and edge-connectivity indices gave in two cases (molar volumes and molar refractions) better models based on edge-connectivity indices and in three cases (boiling points for octanes and nonanes and gas chromatographic retention indices) better models based on vertex-connectivity indices. Thus, it appears that the edge-connectivity index is more appropriate to be used in the structure-molecular volume properties modeling and the vertex-connectivity index in the structure-molecular surface properties modeling. The use of line graphs did not improve the predictive power of the connectivity indices. Only in one case (boiling points of nonanes) a better model was obtained with the use of line graphs.

Working memory performance inversely predicts spontaneous delta and theta-band scaling relations.

PubMed

Euler, Matthew J; Wiltshire, Travis J; Niermeyer, Madison A; Butner, Jonathan E

2016-04-15

Electrophysiological studies have strongly implicated theta-band activity in human working memory processes. Concurrently, work on spontaneous, non-task-related oscillations has revealed the presence of long-range temporal correlations (LRTCs) within sub-bands of the ongoing EEG, and has begun to demonstrate their functional significance. However, few studies have yet assessed the relation of LRTCs (also called scaling relations) to individual differences in cognitive abilities. The present study addressed the intersection of these two literatures by investigating the relation of narrow-band EEG scaling relations to individual differences in working memory ability, with a particular focus on the theta band. Fifty-four healthy adults completed standardized assessments of working memory and separate recordings of their spontaneous, non-task-related EEG. Scaling relations were quantified in each of the five classical EEG frequency bands via the estimation of the Hurst exponent obtained from detrended fluctuation analysis. A multilevel modeling framework was used to characterize the relation of working memory performance to scaling relations as a function of general scalp location in Cartesian space. Overall, results indicated an inverse relationship between both delta and theta scaling relations and working memory ability, which was most prominent at posterior sensors, and was independent of either spatial or individual variability in band-specific power. These findings add to the growing literature demonstrating the relevance of neural LRTCs for understanding brain functioning, and support a construct- and state-dependent view of their functional implications. Copyright © 2016 Elsevier B.V. All rights reserved.

Innovative techniques to analyze time series of geomagnetic activity indices

NASA Astrophysics Data System (ADS)

Balasis, Georgios; Papadimitriou, Constantinos; Daglis, Ioannis A.; Potirakis, Stelios M.; Eftaxias, Konstantinos

2016-04-01

Magnetic storms are undoubtedly among the most important phenomena in space physics and also a central subject of space weather. The non-extensive Tsallis entropy has been recently introduced, as an effective complexity measure for the analysis of the geomagnetic activity Dst index. The Tsallis entropy sensitively shows the complexity dissimilarity among different "physiological" (normal) and "pathological" states (intense magnetic storms). More precisely, the Tsallis entropy implies the emergence of two distinct patterns: (i) a pattern associated with the intense magnetic storms, which is characterized by a higher degree of organization, and (ii) a pattern associated with normal periods, which is characterized by a lower degree of organization. Other entropy measures such as Block Entropy, T-Complexity, Approximate Entropy, Sample Entropy and Fuzzy Entropy verify the above mentioned result. Importantly, the wavelet spectral analysis in terms of Hurst exponent, H, also shows the existence of two different patterns: (i) a pattern associated with the intense magnetic storms, which is characterized by a fractional Brownian persistent behavior (ii) a pattern associated with normal periods, which is characterized by a fractional Brownian anti-persistent behavior. Finally, we observe universality in the magnetic storm and earthquake dynamics, on a basis of a modified form of the Gutenberg-Richter law for the Tsallis statistics. This finding suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism. Signatures of discrete scale invariance in Dst time series further supports the aforementioned proposal.

Non-contact measurements of creep properties of niobium at 1985 °C

NASA Astrophysics Data System (ADS)

Lee, J.; Wall, J. J.; Rogers, J. R.; Rathz, T. J.; Choo, H.; Liaw, P. K.; Hyers, R. W.

2015-01-01

The stress exponent in the power-law creep of niobium at 1985 °C was measured by a non-contact technique using an electrostatic levitation facility at NASA MSFC. This method employs a distribution of stress to allow the stress exponent to be determined from each test, rather than from the curve fit through measurements from multiple samples that is required by conventional methods. The sample is deformed by the centripetal acceleration from the rapid rotation, and the deformed shapes are analyzed to determine the strain. Based on a mathematical proof, which revealed that the stress exponent was determined uniquely by the ratio of the polar to equatorial strains, a series of finite-element analyses with the models of different stress exponents were also performed to determine the stress exponent corresponding to the measured strain ratio. The stress exponent from the ESL experiment showed a good agreement with those from the literature and the conventional creep test.

Non-universal critical exponents in earthquake complex networks

NASA Astrophysics Data System (ADS)

Pastén, Denisse; Torres, Felipe; Toledo, Benjamín A.; Muñoz, Víctor; Rogan, José; Valdivia, Juan Alejandro

2018-02-01

The problem of universality of critical exponents in complex networks is studied based on networks built from seismic data sets. Using two data sets corresponding to Chilean seismicity (northern zone, including the 2014 Mw = 8 . 2 earthquake in Iquique; and central zone without major earthquakes), directed networks for each set are constructed. Connectivity and betweenness centrality distributions are calculated and found to be scale-free, with respective exponents γ and δ. The expected relation between both characteristic exponents, δ >(γ + 1) / 2, is verified for both data sets. However, unlike the expectation for certain scale-free analytical complex networks, the value of δ is found to be non-universal.

Validating the operational bias and hypothesis of universal exponent in landslide frequency-area distribution.

PubMed

Huang, Jr-Chuan; Lee, Tsung-Yu; Teng, Tse-Yang; Chen, Yi-Chin; Huang, Cho-Ying; Lee, Cheing-Tung

2014-01-01

The exponent decay in landslide frequency-area distribution is widely used for assessing the consequences of landslides and with some studies arguing that the slope of the exponent decay is universal and independent of mechanisms and environmental settings. However, the documented exponent slopes are diverse and hence data processing is hypothesized for this inconsistency. An elaborated statistical experiment and two actual landslide inventories were used here to demonstrate the influences of the data processing on the determination of the exponent. Seven categories with different landslide numbers were generated from the predefined inverse-gamma distribution and then analyzed by three data processing procedures (logarithmic binning, LB, normalized logarithmic binning, NLB and cumulative distribution function, CDF). Five different bin widths were also considered while applying LB and NLB. Following that, the maximum likelihood estimation was used to estimate the exponent slopes. The results showed that the exponents estimated by CDF were unbiased while LB and NLB performed poorly. Two binning-based methods led to considerable biases that increased with the increase of landslide number and bin width. The standard deviations of the estimated exponents were dependent not just on the landslide number but also on binning method and bin width. Both extremely few and plentiful landslide numbers reduced the confidence of the estimated exponents, which could be attributed to limited landslide numbers and considerable operational bias, respectively. The diverse documented exponents in literature should therefore be adjusted accordingly. Our study strongly suggests that the considerable bias due to data processing and the data quality should be constrained in order to advance the understanding of landslide processes.

Study of polytropic exponent based on high pressure switching expansion reduction

NASA Astrophysics Data System (ADS)

Wang, Xuanyin; Luo, Yuxi; Xu, Zhipeng

2011-10-01

Switching expansion reduction (SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics. The experiments indicate that the simulation model well predicts the actual characteristics. The heat transfers and polytropic exponents of the air in expansion tank and supply tanks of SER have been studied on the basis of the experiments and the simulation model. Through the mathematical reasoning in this paper, the polytropic exponent can be calculated by the air mass, heat, and work exchanges of the pneumatic container. For the air in a constant volume tank, when the heat-absorption is large enough to raise air temperature in discharging process, the polytropic exponent is less than 1; when the air is experiencing a discharging and heat-releasing process, the polytropic exponent exceeds the specific heat ratio (the value of 1.4).

The Angstrom Exponent and Bimodal Aerosol Size Distributions

NASA Technical Reports Server (NTRS)

Schuster, Gregory L.; Dubovik, Oleg; Holben, Brent H.

2005-01-01

Powerlaws have long been used to describe the spectral dependence of aerosol extinction, and the wavelength exponent of the aerosol extinction powerlaw is commonly referred to as the Angstrom exponent. The Angstrom exponent is often used as a qualitative indicator of aerosol particle size, with values greater than two indicating small particles associated with combustion byproducts, and values less than one indicating large particles like sea salt and dust. In this study, we investigate the relationship between the Angstrom exponent and the mode parameters of bimodal aerosol size distributions using Mie theory calculations and Aerosol Robotic Network (AERONET) retrievals. We find that Angstrom exponents based upon seven wavelengths (0.34, 0.38, 0.44, 0.5, 0.67, 0.87, and 1.02 micrometers) are sensitive to the volume fraction of aerosols with radii less then 0.6 micrometers, but not to the fine mode effective radius. The Angstrom exponent is also known to vary with wavelength, which is commonly referred to as curvature; we show how the spectral curvature can provide additional information about aerosol size distributions for intermediate values of the Angstrom exponent. Curvature also has a significant effect on the conclusions that can be drawn about two-wavelength Angstrom exponents; long wavelengths (0.67, 0.87 micrometers) are sensitive to fine mode volume fraction of aerosols but not fine mode effective radius, while short wavelengths (0.38, 0.44 micrometers) are sensitive to the fine mode effective radius but not the fine mode volume fraction.

Validating the Operational Bias and Hypothesis of Universal Exponent in Landslide Frequency-Area Distribution

PubMed Central

Huang, Jr-Chuan; Lee, Tsung-Yu; Teng, Tse-Yang; Chen, Yi-Chin; Huang, Cho-Ying; Lee, Cheing-Tung

2014-01-01

The exponent decay in landslide frequency-area distribution is widely used for assessing the consequences of landslides and with some studies arguing that the slope of the exponent decay is universal and independent of mechanisms and environmental settings. However, the documented exponent slopes are diverse and hence data processing is hypothesized for this inconsistency. An elaborated statistical experiment and two actual landslide inventories were used here to demonstrate the influences of the data processing on the determination of the exponent. Seven categories with different landslide numbers were generated from the predefined inverse-gamma distribution and then analyzed by three data processing procedures (logarithmic binning, LB, normalized logarithmic binning, NLB and cumulative distribution function, CDF). Five different bin widths were also considered while applying LB and NLB. Following that, the maximum likelihood estimation was used to estimate the exponent slopes. The results showed that the exponents estimated by CDF were unbiased while LB and NLB performed poorly. Two binning-based methods led to considerable biases that increased with the increase of landslide number and bin width. The standard deviations of the estimated exponents were dependent not just on the landslide number but also on binning method and bin width. Both extremely few and plentiful landslide numbers reduced the confidence of the estimated exponents, which could be attributed to limited landslide numbers and considerable operational bias, respectively. The diverse documented exponents in literature should therefore be adjusted accordingly. Our study strongly suggests that the considerable bias due to data processing and the data quality should be constrained in order to advance the understanding of landslide processes. PMID:24852019

Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems

NASA Astrophysics Data System (ADS)

He, Jianbin; Yu, Simin; Cai, Jianping

2016-12-01

Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.

Analysis of persistence in fluctuation of the Cauca river through the Hurst coefficient

NASA Astrophysics Data System (ADS)

Prada, D. A.; Sanabria, M. P.; Torres, A. F.; Acevedo, A.; Gómez, J.

2018-04-01

Study the continuous changes in the fluctuations in the levels of watersheds, it is of great importance because it allows you to adjust predictions about behaviors that can lead to floods or droughts. The Cauca River is one of the most important rivers in Colombia due to its 1350km long, its drainage area of 59.074km 2 which represents 5% of the national territory. The Government entity Cormagdalena records daily levels of the Cauca River to the height of La Mojana in the rods. From these data, we developed a series of time on which normal test were applied to calculate the coefficient of Hurst and the fractal dimension to determine the persistence associated with this behavior.

Characterization of bedload transport in steep-slope streams

NASA Astrophysics Data System (ADS)

Mettra, F.; Heyman, J.; Ancey, C.

2012-04-01

Large fluctuations in the sediment transport rate are observed in rivers, particularly in mountain streams at intermediate flow rates. These fluctuations seem to be, to some degree, correlated to the formation and migration of bedforms. Today the central question is still how to understand and account for the strong bedload variability. Recent experimental studies shed new light on the processes. The objective of this presentation is to show some of our results. To understand the behavior and the origins of sediment transport rate fluctuations in the case of steep-slope streams, we conducted laboratory experiments in a 3-m long, 8-cm wide, transparent flume. The experimental parameters are the flume inclination, flow rate and sediment input rate. Well-sorted natural gravel (8.5 mm mean diameter) were used. We focused on two-dimensional flows and incipient bedforms (i.e., for flow rates just above the threshold of incipient motion). A technique based on accelerometers was developed to record every particle passing through the flume outlet (more specifically, we measured the vibrations of a metallic slab, which was impacted by the falling particles). Analysis of bedload transport rates was then possible on all time scales. Moreover, the bed and flow were monitored using 2 cameras. We computed bed elevation, water depth and erosion/deposition at high temporal and spatial rates from camera shots (one image per second during several hours or days). In our laboratory experiments, the fluctuations of the sediment rate were large even for steady flow conditions involving well-sorted particles. Time series exhibited fluctuations at all scales and displayed long range correlations with a Hurst exponent close to 0.8. The results were compared for different input solid discharges. The main bedforms observed in our flume were anti-dunes migrating upstream. Bedform formation and propagation showed intermittency with pulses (high activity) followed by long sequences of low activity. We tried to interpret our results (bedform behavior, bed scouring) in terms of sediment outflow rate.

Scale Effects in the Flow of a Shear-Thinning Fluid in Geological Fractures

NASA Astrophysics Data System (ADS)

Meheust, Y.; Roques, C.; Le Borgne, T.; Selker, J. S.

2017-12-01

Subsurface flow processes involving non-Newtonian fluids play a major role in many engineering applications, from in-situ remediation to enhanced oil recovery. The fluids of interest in such applications (f.e., polymers in remediation) often present shear-thinning properties, i.e., their viscosity decreases as a function of the local shear rate. We investigate how fracture wall roughness impacts the flow of a shear-thinning fluid. Numerical simulations of flow in 3D geological fractures are carried out by solving a modified Navier-Stokes equation incorporating the Carreau viscous-shear model. The numerical fractures consist of two isotropic self-affine surfaces which are correlated with each other above a characteristic scale (thecorrelation length of Méheust et al. PAGEOPH 2003). Perfect plastic closing is assumed when the surfaces are in contact. The statistical parameters describing a fracture are the standard deviation of the wall roughness, the mean aperture, the correlation length, and the fracture length, the Hurst exponent being fixed (equal to 0.8). The objective is to investigate how varying the correlation length impacts the flow behavior, for different degrees of closure, and how this behavior diverges from what is known for Newtonian fluids. The results from the 3D simulations are also compared to 2D simulations based on the lubrication theory, which we have developed as an extension of the Reynolds equation for Newtonian fluids. These 2D simulations run orders of magnitude faster, which allows considering a significant statistics of fractures of identical statistical parameters, and therefore draw general conclusions despite the large stochasticity of the media. We also discuss the implications of our results for solute transport by such flows. References:Méheust, Y., & Schmittbuhl, J. (2003). Scale effects related to flow in rough fractures. Pure and Applied Geophysics, 160(5-6), 1023-1050.

Quantitative assessment of the impacts of climate change and human activities on runoff change in a typical karst watershed, SW China.

PubMed

Wu, Luhua; Wang, Shijie; Bai, Xiaoyong; Luo, Weijun; Tian, Yichao; Zeng, Cheng; Luo, Guangjie; He, Shiyan

2017-12-01

The Yinjiang River watershed is a typical karst watershed in Southwest China. The present study explored runoff change and its responses to different driving factors in the Yinjiang River watershed over the period of 1984 to 2015. The methods of cumulative anomaly, continuous wavelet analysis, Mann-Kendall rank correlation trend test, and Hurst exponent were applied to analyze the impacts of climate change and human activities on runoff change. The contributions of climate change and human activities to runoff change were quantitatively assessed using the comparative method of the slope changing ratio of cumulative quantity (SCRCQ). The following results were obtained: (1) From 1984 to 2015, runoff and precipitation exhibited no-significant increasing trend, whereas evaporation exhibited significant decreasing trend. (2) In the future, runoff, precipitation, and evaporation will exhibit weak anti-persistent feature with different persistent times. This feature indicated that in their persistent times, runoff and precipitation will continuously decline, whereas evaporation will continuously increase. (3) Runoff and precipitation were well-synchronized with abrupt change features and stage characteristics, and exhibited consistent multi-timescale characteristics that were different from that of evaporation. (4) The contribution of precipitation to runoff change was 50%-60% and was considered high and stable. The contribution of evaporation to runoff change was 10%-90% and was variable with a positive or negative effects. The contribution of human activities to runoff change was 20%-60% and exerted a low positive or negative effect. (5) Climatic factors highly contributed to runoff change. By contrast, the contribution of human activities to runoff change was low. The contribution of climatic factors to runoff change was highly variable because of differences among base periods. In conclusion, this paper provides a basic theoretical understanding of the main factors that contribute to runoff change in a karst watershed. Copyright © 2017 Elsevier B.V. All rights reserved.

Statistical analysis of aerosols over the Gangetic-Himalayan region using ARIMA model based on long-term MODIS observations

NASA Astrophysics Data System (ADS)

Soni, Kirti; Kapoor, Sangeeta; Parmar, Kulwinder Singh; Kaskaoutis, Dimitris G.

2014-11-01

Long-term observations and modeling of aerosol loading over the Indo-Gangetic plains (IGP), the Indian desert region and Himalayan slopes are analyzed in the present study. The Box-Jenkins popular ARIMA (AutoRegressive Integrated Moving Average) model was applied to simulate the monthly-mean Terra MODIS (MODerate Resolution Imaging Spectroradiometer) Aerosol Optical Depth (AOD550 nm) over eight sites in the region covering a period of about 13 years (March 2000-May 2012). The autocorrelation structure has been analyzed indicating a deterministic pattern in the time series that it regains its structure every 24 month period. The ARIMA models namely ARIMA(2,0,12), ARIMA(1,0,6), ARIMA(3,0,0), ARIMA(2,0,13) ARIMA(0,0,12), ARIMA(2,0,2), ARIMA(1,0,12) and ARIMA(0,0,1) have been developed as the most suitable for simulating and forecasting the monthly-mean AOD over the eight selected locations. The Stationary R-squared, R-squared, Root Mean Square Error (RMSE) and Normalized BIC (Bayesian Information Criterion) are used to test the validity and applicability of the developed ARIMA models revealing adequate accuracy in the model performance. The values of Hurst Exponent, Fractal Dimension and Predictability Index for AODs are about 0.5, 1.5 and 0, respectively, suggesting that the AODs in all sites follow the Brownian time-series motion (true random walk). High AOD values (> 0.7) are observed over the industrialized and densely-populated IGP sites associated with low ones over the foothills/slopes of the Himalayas. The trends in AOD during the ~ 13-year period differentiates depending on season and site. During post-monsoon and winter accumulation of aerosols and increasing trends are shown over IGP sites, which are neutralized in pre-monsoon and become slightly negative in monsoon. The AOD over the Himalayan sites does not exhibit any significant trend and seems to be practically unaffected by the aerosol built-up over IGP.

Mammographic evidence of microenvironment changes in tumorous breasts.

PubMed

Marin, Zach; Batchelder, Kendra A; Toner, Brian C; Guimond, Lyne; Gerasimova-Chechkina, Evgeniya; Harrow, Amy R; Arneodo, Alain; Khalil, Andre

2017-04-01

The microenvironment of breast tumors plays a critical role in tumorigenesis. As long as the structural integrity of the microenvironment is upheld, the tumor is suppressed. If tissue structure is lost through disruptions in the normal cell cycle, the microenvironment may act as a tumor promoter. Therefore, the properties that distinguish between healthy and tumorous tissues may not be solely in the tumor characteristics but rather in surrounding non-tumor tissue. The goal of this paper was to show preliminary evidence that tissue disruption and loss of homeostasis in breast tissue microenvironment and breast bilateral asymmetry can be quantitatively and objectively assessed from mammography via a localized, wavelet-based analysis of the whole breast. A wavelet-based multifractal formalism called the 2D Wavelet Transform Modulus Maxima (WTMM) method was used to quantitate density fluctuations from mammographic breast tissue via the Hurst exponent (H). Each entire mammogram was cut in hundreds of 360 × 360 pixel subregions in a gridding scheme of overlapping sliding windows, with each window boundary separated by 32 pixels. The 2D WTMM method was applied to each subregion individually. A data mining approach was set up to determine which metrics best discriminated between normal vs. cancer cases. These same metrics were then used, without modification, to discriminate between normal vs. benign and benign vs. cancer cases. The density fluctuations in healthy mammographic breast tissue are either monofractal anti-correlated (H < 1/2) for fatty tissue or monofractal long-range correlated (H>1/2) for dense tissue. However, tissue regions with H~1/2, as well as left vs. right breast asymetries, were found preferably in tumorous (benign or cancer) breasts vs. normal breasts, as quantified via a combination metric yielding a P-value ~ 0.0006. No metric considered showed significant differences between cancer vs. benign breasts. Since mammographic tissue regions associated with uncorrelated (H~1/2) density fluctuations were predominantly in tumorous breasts, and since the underlying physical processes associated with a H~1/2 signature are those of randomness, lack of spatial correlation, and free diffusion, it is hypothesized that this signature is also associated with tissue disruption and loss of tissue homeostasis. © 2017 American Association of Physicists in Medicine.

Fractal Analysis of Brain Blood Oxygenation Level Dependent (BOLD) Signals from Children with Mild Traumatic Brain Injury (mTBI).

PubMed

Dona, Olga; Noseworthy, Michael D; DeMatteo, Carol; Connolly, John F

2017-01-01

Conventional imaging techniques are unable to detect abnormalities in the brain following mild traumatic brain injury (mTBI). Yet patients with mTBI typically show delayed response on neuropsychological evaluation. Because fractal geometry represents complexity, we explored its utility in measuring temporal fluctuations of brain resting state blood oxygen level dependent (rs-BOLD) signal. We hypothesized that there could be a detectable difference in rs-BOLD signal complexity between healthy subjects and mTBI patients based on previous studies that associated reduction in signal complexity with disease. Fifteen subjects (13.4 ± 2.3 y/o) and 56 age-matched (13.5 ± 2.34 y/o) healthy controls were scanned using a GE Discovery MR750 3T MRI and 32-channel RF-coil. Axial FSPGR-3D images were used to prescribe rs-BOLD (TE/TR = 35/2000ms), acquired over 6 minutes. Motion correction was performed and anatomical and functional images were aligned and spatially warped to the N27 standard atlas. Fractal analysis, performed on grey matter, was done by estimating the Hurst exponent using de-trended fluctuation analysis and signal summation conversion methods. Voxel-wise fractal dimension (FD) was calculated for every subject in the control group to generate mean and standard deviation maps for regional Z-score analysis. Voxel-wise validation of FD normality across controls was confirmed, and non-Gaussian voxels (3.05% over the brain) were eliminated from subsequent analysis. For each mTBI patient, regions where Z-score values were at least 2 standard deviations away from the mean (i.e. where |Z| > 2.0) were identified. In individual patients the frequently affected regions were amygdala (p = 0.02), vermis(p = 0.03), caudate head (p = 0.04), hippocampus(p = 0.03), and hypothalamus(p = 0.04), all previously reported as dysfunctional after mTBI, but based on group analysis. It is well known that the brain is best modeled as a complex system. Therefore a measure of complexity using rs-BOLD signal FD could provide an additional method to grade and monitor mTBI. Furthermore, this approach can be personalized thus providing unique patient specific assessment.

The Multiplicative Situation

ERIC Educational Resources Information Center

Hurst, Chris

2015-01-01

The relationships between three critical elements, and the associated mathematical language, to assist students to make the critical transition from additive to multiplicative thinking are examined in this article by Chris Hurst.

Brief communication: Possible explanation of the values of Hack's drainage basin, river length scaling exponent

NASA Astrophysics Data System (ADS)

Hunt, Allen G.

2016-04-01

Percolation theory can be used to find water flow paths of least resistance. Application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

Explanation of the values of Hack's drainage basin, river length scaling exponent

NASA Astrophysics Data System (ADS)

Hunt, A. G.

2015-08-01

Percolation theory can be used to find water flow paths of least resistance. The application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law allows interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement

NASA Astrophysics Data System (ADS)

Sikora, Grzegorz; Teuerle, Marek; Wyłomańska, Agnieszka; Grebenkov, Denis

2017-08-01

The most common way of estimating the anomalous scaling exponent from single-particle trajectories consists of a linear fit of the dependence of the time-averaged mean-square displacement on the lag time at the log-log scale. We investigate the statistical properties of this estimator in the case of fractional Brownian motion (FBM). We determine the mean value, the variance, and the distribution of the estimator. Our theoretical results are confirmed by Monte Carlo simulations. In the limit of long trajectories, the estimator is shown to be asymptotically unbiased, consistent, and with vanishing variance. These properties ensure an accurate estimation of the scaling exponent even from a single (long enough) trajectory. As a consequence, we prove that the usual way to estimate the diffusion exponent of FBM is correct from the statistical point of view. Moreover, the knowledge of the estimator distribution is the first step toward new statistical tests of FBM and toward a more reliable interpretation of the experimental histograms of scaling exponents in microbiology.

Power Law Distributions of Patents as Indicators of Innovation

NASA Astrophysics Data System (ADS)

O'Neale, Dion; Hendy, Shaun

2013-03-01

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.

The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

PubMed Central

Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang

2015-01-01

The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body's standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age. PMID:26064182

Multifractal Analysis for Nutritional Assessment

PubMed Central

Park, Youngja; Lee, Kichun; Ziegler, Thomas R.; Martin, Greg S.; Hebbar, Gautam; Vidakovic, Brani; Jones, Dean P.

2013-01-01

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (1H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on 1H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from 1H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of 1H NMR spectra provides a new approach to characterize nutritional status. PMID:23990878

Statistical regularities of Carbon emission trading market: Evidence from European Union allowances

NASA Astrophysics Data System (ADS)

Zheng, Zeyu; Xiao, Rui; Shi, Haibo; Li, Guihong; Zhou, Xiaofeng

2015-05-01

As an emerging financial market, the trading value of carbon emission trading market has definitely increased. In recent years, the carbon emission allowances have already become a way of investment. They are bought and sold not only by carbon emitters but also by investors. In this paper, we analyzed the price fluctuations of the European Union allowances (EUA) futures in European Climate Exchange (ECX) market from 2007 to 2011. The symmetric and power-law probability density function of return time series was displayed. We found that there are only short-range correlations in price changes (return), while long-range correlations in the absolute of price changes (volatility). Further, detrended fluctuation analysis (DFA) approach was applied with focus on long-range autocorrelations and Hurst exponent. We observed long-range power-law autocorrelations in the volatility that quantify risk, and found that they decay much more slowly than the autocorrelation of return time series. Our analysis also showed that the significant cross correlations exist between return time series of EUA and many other returns. These cross correlations exist in a wide range of fields, including stock markets, energy concerned commodities futures, and financial futures. The significant cross-correlations between energy concerned futures and EUA indicate the physical relationship between carbon emission and energy production process. Additionally, the cross-correlations between financial futures and EUA indicate that the speculation behavior may become an important factor that can affect the price of EUA. Finally we modeled the long-range volatility time series of EUA with a particular version of the GARCH process, and the result also suggests long-range volatility autocorrelations.

Stock market context of the Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that assumes a different constant value between the successive turning points, i.e., the velocity is a piecewise constant function. This model is a kind of Lévy walks where we assume a hierarchical, self-similar in a stochastic sense, spatio-temporal representation of the main quantities such as waiting-time distribution and sojourn probability density (which are principal quantities in the continuous-time random walk formalism). The WW model makes possible to analyze both the structure of the Hurst exponent and the power-law behavior of kurtosis. This structure results from the hierarchical, spatio-temporal coupling between the walker displacement and the corresponding time of the walks. The analysis uses both the fractional diffusion and the super Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic for stationary situations. We thus have a model ready for describing the data presented, e.g., in the form of moving averages; the operation is often used for stochastic time series, especially financial ones. The model was inspired by properties of financial time series and tested for empirical data extracted from the Warsaw stock exchange since it offers an opportunity to study in an unbiased way several features of stock exchange in its early stage.

Mapping Transient Hyperventilation Induced Alterations with Estimates of the Multi-Scale Dynamics of BOLD Signal.

PubMed

Kiviniemi, Vesa; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Haapea, Marianne; Silven, Olli; Tervonen, Osmo

2009-01-01

Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/f(alpha). Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF) after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant alpha, fractal dimension D(f), and, Hurst exponent H) characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The alpha was able to differentiate also blood vessels from grey matter changes. D(f) was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.

Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences

PubMed Central

Fetterhoff, Dustin; Kraft, Robert A.; Sandler, Roman A.; Opris, Ioan; Sexton, Cheryl A.; Marmarelis, Vasilis Z.; Hampson, Robert E.; Deadwyler, Sam A.

2015-01-01

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal neuronal ensembles were recorded from rats before, during and after a spatial working memory task following administration of tetrahydrocannabinol (THC), a memory-impairing component of cannabis. Multifractal detrended fluctuation analysis was performed on hippocampal interspike interval sequences to determine characteristics of monofractal long-range temporal correlations (LRTCs), quantified by the Hurst exponent, and the degree/magnitude of multifractal complexity, quantified by the width of the singularity spectrum. Our results demonstrate that multifractal firing patterns of hippocampal spike trains are a marker of functional memory processing, as they are more complex during the working memory task and significantly reduced following administration of memory impairing THC doses. Conversely, LRTCs are largest during resting state recordings, therefore reflecting different information compared to multifractality. In order to deepen conceptual understanding of multifractal complexity and LRTCs, these measures were compared to classical methods using hippocampal frequency content and firing variability measures. These results showed that LRTCs, multifractality, and theta rhythm represent independent processes, while delta rhythm correlated with multifractality. Taken together, these results provide a novel perspective on memory function by demonstrating that the multifractal nature of spike trains reflects hippocampal microcircuit activity that can be used to detect and quantify cognitive, physiological, and pathological states. PMID:26441562

Fractal scaling analysis of groundwater dynamics in confined aquifers

NASA Astrophysics Data System (ADS)

Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

2017-10-01

Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Reactions of Ions with Ionic Liquid Vapors by Selected-Ion Flow Tube Mass Spectrometry

DTIC Science & Technology

2011-03-29

Emel’yanenko, V. N.; Verevkin, S. P.; Heintz, A.; Corfield, J.-A.; Deyko, A.; Lovelock , K. R. J.; Licence, P.; Jones, R. G. Pyrrolidinium- Based Ionic...112, 11734–11742. (2) Lovelock , K. R. J.; Deyko, A.; Licence, P.; Jones, R. G. Vaporisa- tion of an Ionic Liquid Near Room Temperature. Phys. Chem...Relevance of pKa from Aqueous Solutions. J. Am. Chem. Soc. 2003, 125, 15411–15419. (15) Armstrong, J. P.; Hurst, C.; Jones, R. G.; Licence, P.; Lovelock , K

Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

Genetics Home Reference: Floating-Harbor syndrome

MedlinePlus

... Patton MA, Hurst J, Donnai D, McKeown CM, Cole T, Goodship J. Floating-Harbor syndrome. J Med ... medicine? What is newborn screening? New Pages Lyme disease Fibromyalgia White-Sutton syndrome All New & Updated Pages ...

p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Leonarduzzi, R.; Wendt, H.; Abry, P.; Jaffard, S.; Melot, C.; Roux, S. G.; Torres, M. E.

2016-04-01

Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and image processing tool and is commonly used in numerous applications of different natures. In its common formulation, it relies on the Hölder exponent as a measure of local regularity, which is by nature restricted to positive values and can hence be used for locally bounded functions only. In this contribution, it is proposed to replace the Hölder exponent with a collection of novel exponents for measuring local regularity, the p-exponents. One of the major virtues of p-exponents is that they can potentially take negative values. The corresponding wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit the definition of a new multifractal formalism, yielding an accurate practical estimation of the multifractal properties of real-world data. Moreover, theoretical and practical connections to and comparisons against another multifractal formalism, referred to as multifractal detrended fluctuation analysis, are achieved. The performance of the proposed p-leader multifractal formalism is studied and compared to previous formalisms using synthetic multifractal signals and images, illustrating its theoretical and practical benefits. The present contribution is complemented by a companion article studying in depth the theoretical properties of p-exponents and the rich classification of local singularities it permits.

Towards a unifying basis of auditory thresholds: binaural summation.

PubMed

Heil, Peter

2014-04-01

Absolute auditory threshold decreases with increasing sound duration, a phenomenon explainable by the assumptions that the sound evokes neural events whose probabilities of occurrence are proportional to the sound's amplitude raised to an exponent of about 3 and that a constant number of events are required for threshold (Heil and Neubauer, Proc Natl Acad Sci USA 100:6151-6156, 2003). Based on this probabilistic model and on the assumption of perfect binaural summation, an equation is derived here that provides an explicit expression of the binaural threshold as a function of the two monaural thresholds, irrespective of whether they are equal or unequal, and of the exponent in the model. For exponents >0, the predicted binaural advantage is largest when the two monaural thresholds are equal and decreases towards zero as the monaural threshold difference increases. This equation is tested and the exponent derived by comparing binaural thresholds with those predicted on the basis of the two monaural thresholds for different values of the exponent. The thresholds, measured in a large sample of human subjects with equal and unequal monaural thresholds and for stimuli with different temporal envelopes, are compatible only with an exponent close to 3. An exponent of 3 predicts a binaural advantage of 2 dB when the two ears are equally sensitive. Thus, listening with two (equally sensitive) ears rather than one has the same effect on absolute threshold as doubling duration. The data suggest that perfect binaural summation occurs at threshold and that peripheral neural signals are governed by an exponent close to 3. They might also shed new light on mechanisms underlying binaural summation of loudness.

Modeling Fractal Structure of City-Size Distributions Using Correlation Functions

PubMed Central

Chen, Yanguang

2011-01-01

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences. PMID:21949753

Effects of Annealing Process on the Formability of Friction Stir Welded Al-Li Alloy 2195 Plates

NASA Technical Reports Server (NTRS)

Chen, Po-Shou; Bradford, Vann; Russell, Carolyn

2011-01-01

Large rocket cryogenic tank domes have typically been fabricated using Al-Cu based alloys like Al-Cu alloy 2219. The use of aluminum-lithium based alloys for rocket fuel tank domes can reduce weight because aluminum-lithium alloys have lower density and higher strength than Al-Cu alloy 2219. However, Al-Li alloys have rarely been used to fabricate rocket fuel tank domes because of the inherent low formability characteristic that make them susceptible to cracking during the forming operations. The ability to form metal by stretch forming or spin forming without excessive thinning or necking depends on the strain hardening exponent "n". The stain hardening exponent is a measure of how rapidly a metal becomes stronger and harder. A high strain hardening exponent is beneficial to a material's ability to uniformly distribute the imposed strain. Marshall Space Flight Center has developed a novel annealing process that can achieve a work hardening exponent on the order of 0.27 to 0.29, which is approximately 50% higher than what is typically obtained for Al-Li alloys using the conventional method. The strain hardening exponent of the Al-Li alloy plates or blanks heat treated using the conventional method is typically on the order of 0.17 to 0.19. The effects of this novel annealing process on the formability of friction stir welded Al-Li alloy blanks are being studied at Marshall Space Flight Center. The formability ratings will be generated using the strain hardening exponent, strain rate sensitivity and forming range. The effects of forming temperature on the formability will also be studied. The objective of this work is to study the deformation behavior of the friction stir welded Al-Li alloy 2195 blank and determine the formability enhancement by the new annealing process.

On universality of scaling law describing roughness of triple line.

PubMed

Bormashenko, Edward; Musin, Albina; Whyman, Gene; Barkay, Zahava; Zinigrad, Michael

2015-01-01

The fine structure of the three-phase (triple) line was studied for different liquids, various topographies of micro-rough substrates and various wetting regimes. Wetting of porous and pillar-based micro-scaled polymer surfaces was investigated. The triple line was visualized with the environmental scanning electron microscope and scanning electron microscope for the "frozen" triple lines. The value of the roughness exponent ζ for water (ice)/rough polymer systems was located within 0.55-0.63. For epoxy glue/rough polymer systems somewhat lower values of the exponent, 0.42 < ζ < 0.54, were established. The obtained values of ζ were close for the Cassie and Wenzel wetting regimes, different liquids, and different substrates' topographies. Thus, the above values of the exponent are to a great extent universal. The switch of the exponent, when the roughness size approaches to the correlation length of the defects, is also universal.

Analysis of Mining-Induced Subsidence Prediction by Exponent Knothe Model Combined with Insar and Leveling

NASA Astrophysics Data System (ADS)

Chen, Lei; Zhang, Liguo; Tang, Yixian; Zhang, Hong

2018-04-01

The principle of exponent Knothe model was introduced in detail and the variation process of mining subsidence with time was analysed based on the formulas of subsidence, subsidence velocity and subsidence acceleration in the paper. Five scenes of radar images and six levelling measurements were collected to extract ground deformation characteristics in one coal mining area in this study. Then the unknown parameters of exponent Knothe model were estimated by combined levelling data with deformation information along the line of sight obtained by InSAR technique. By compared the fitting and prediction results obtained by InSAR and levelling with that obtained only by levelling, it was shown that the accuracy of fitting and prediction combined with InSAR and levelling was obviously better than the other that. Therefore, the InSAR measurements can significantly improve the fitting and prediction accuracy of exponent Knothe model.

Adaptation of the Carter-Tracy water influx calculation to groundwater flow simulation

USGS Publications Warehouse

Kipp, Kenneth L.

1986-01-01

The Carter-Tracy calculation for water influx is adapted to groundwater flow simulation with additional clarifying explanation not present in the original papers. The Van Everdingen and Hurst aquifer-influence functions for radial flow from an outer aquifer region are employed. This technique, based on convolution of unit-step response functions, offers a simple but approximate method for embedding an inner region of groundwater flow simulation within a much larger aquifer region where flow can be treated in an approximate fashion. The use of aquifer-influence functions in groundwater flow modeling reduces the size of the computational grid with a corresponding reduction in computer storage and execution time. The Carter-Tracy approximation to the convolution integral enables the aquifer influence function calculation to be made with an additional storage requirement of only two times the number of boundary nodes more than that required for the inner region simulation. It is a good approximation for constant flow rates but is poor for time-varying flow rates where the variation is large relative to the mean. A variety of outer aquifer region geometries, exterior boundary conditions, and flow rate versus potentiometric head relations can be used. The radial, transient-flow case presented is representative. An analytical approximation to the functions of Van Everdingen and Hurst for the dimensionless potentiometric head versus dimensionless time is given.

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Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-15

... K. Hurst, Management Program Analyst, FBI, CJIS Division, Biometric Services Section (BSS), Support... identification record to review it or to obtain a change, correction, or an update to the record. (5) An estimate...

Taylor dispersion in two-dimensional bacterial turbulence

NASA Astrophysics Data System (ADS)

Huang, Yongxiang; Ou, Wenyu; Chen, Ming; Lu, Zhiming; Jiang, Nan; Liu, Yulu; Qiu, Xiang; Zhou, Quan

2017-05-01

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. The two-regime power-law behavior for short and long time evolutions was identified experimentally, which was separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be 0.94 and 0.97 for short and long time evolutions, respectively. For the case without the mean velocity effect, the values were 0.88 and 0.58. Moreover, very weak intermittency correction was detected. All measured Hurst numbers were above 1/2, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rahmani, N.; Dariani, R. S., E-mail: dariani@alzahra.ac.ir

Porous silicon films with porosity ranging from 42% to 77% were fabricated by electrochemical anodization under different current density. We used atomic force microscopy and dynamic scaling theory for deriving the surface roughness profile and processing the topography of the porous silicon layers, respectively. We first compared the topography of bare silicon surface with porous silicon and then studied the effect of the porosity of porous silicon films on their scaling behavior by using their self-affinity nature. Our work demonstrated that silicon compared to the porous silicon films has the highest Hurst parameter, indicating that the formation of porous layermore » due to the anodization etching of silicon surface leads to an increase of its roughness. Fractal analysis revealed that the evolution of the nanocrystallites’ fractal dimension along with porosity. Also, we found that both interface width and Hurst parameter are affected by the increase of porosity.« less

Graded Response Model Based on the Logistic Positive Exponent Family of Models for Dichotomous Responses

ERIC Educational Resources Information Center

Samejima, Fumiko

2008-01-01

Samejima ("Psychometrika "65:319--335, 2000) proposed the logistic positive exponent family of models (LPEF) for dichotomous responses in the unidimensional latent space. The objective of the present paper is to propose and discuss a graded response model that is expanded from the LPEF, in the context of item response theory (IRT). This…

Scaling properties of the aerodynamic noise generated by low-speed fans

NASA Astrophysics Data System (ADS)

Canepa, Edward; Cattanei, Andrea; Mazzocut Zecchin, Fabio

2017-11-01

The spectral decomposition algorithm presented in the paper may be applied to selected parts of the SPL spectrum, i.e. to specific noise generating mechanisms. It yields the propagation and the generation functions, and indeed the Mach number scaling exponent associated with each mechanism as a function of the Strouhal number. The input data are SPL spectra obtained from measurements taken during speed ramps. Firstly, the basic theory and the implemented algorithm are described. Then, the behaviour of the new method is analysed with reference to numerically generated spectral data and the results are compared with the ones of an existing method based on the assumption that the scaling exponent is constant. Guidelines for the employment of both methods are provided. Finally, the method is applied to measurements taken on a cooling fan mounted on a test plenum designed following the ISO 10302 standards. The most common noise generating mechanisms are present and attention is focused on the low-frequency part of the spectrum, where the mechanisms are superposed. Generally, both propagation and generation functions are determined with better accuracy than the scaling exponent, whose values are usually consistent with expectations based on coherence and compactness of the acoustic sources. For periodic noise, the computed exponent is less accurate, as the related SPL data set has usually a limited size. The scaling exponent is very sensitive to the details of the experimental data, e.g. to slight inconsistencies or random errors.

Critical dynamic approach to stationary states in complex systems

NASA Astrophysics Data System (ADS)

Rozenfeld, A. F.; Laneri, K.; Albano, E. V.

2007-04-01

A dynamic scaling Ansatz for the approach to stationary states in complex systems is proposed and tested by means of extensive simulations applied to both the Bak-Sneppen (BS) model, which exhibits robust Self-Organised Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway, whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations such that ρ(t=0) →0, one observes an initial increase of the density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively; ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS and GOL models, respectively. It is also shown that the temporal autocorrelation decays with exponents Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model. By using these dynamically determined critical exponents and suitable scaling relationships, we also obtain the dynamic exponents z = 2.10(5) (z = 2.10(5)) for the BS (GOL) model. Based on this evidence we conclude that the dynamic approach to stationary states of the investigated models can be described by suitable power-law functions of time with well-defined exponents.

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

NASA Astrophysics Data System (ADS)

Poveda, Germán

2011-02-01

Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time and the kind of temporal memory are investigated. Data sets from the Andes of Colombia at different resolutions (15 min and 1-h), and record lengths (21 months and 8-40 years) are used. A mixture of two timescales is found in the autocorrelation and autoinformation functions, with short-term memory holding for time lags less than 15-30 min, and long-term memory onwards. Consistently, rainfall variance exhibits different temporal scaling regimes separated at 15-30 min and 24 h. Tests for the Hurst effect evidence the frailty of the R/ S approach in discerning the kind of memory in high resolution rainfall, whereas rigorous statistical tests for short-memory processes do reject the existence of the Hurst effect. Rainfall information entropy grows as a power law of aggregation time, S( T) ˜ Tβ with < β> = 0.51, up to a timescale, TMaxEnt (70-202 h), at which entropy saturates, with β = 0 onwards. Maximum entropy is reached through a dynamic Generalized Pareto distribution, consistently with the maximum information-entropy principle for heavy-tailed random variables, and with its asymptotically infinitely divisible property. The dynamics towards the limit distribution is quantified. Tsallis q-entropies also exhibit power laws with T, such that Sq( T) ˜ Tβ( q) , with β( q) ⩽ 0 for q ⩽ 0, and β( q) ≃ 0.5 for q ⩾ 1. No clear patterns are found in the geographic distribution within and among the statistical parameters studied, confirming the strong variability of tropical Andean rainfall.

Ensemble Solute Transport in 2-D Operator-Stable Random Fields

NASA Astrophysics Data System (ADS)

Monnig, N. D.; Benson, D. A.

2006-12-01

The heterogeneous velocity field that exists at many scales in an aquifer will typically cause a dissolved solute plume to grow at a rate faster than Fick's Law predicts. Some statistical model must be adopted to account for the aquifer structure that engenders the velocity heterogeneity. A fractional Brownian motion (fBm) model has been shown to create the long-range correlation that can produce continually faster-than-Fickian plume growth. Previous fBm models have assumed isotropic scaling (defined here by a scalar Hurst coefficient). Motivated by field measurements of aquifer hydraulic conductivity, recent techniques were developed to construct random fields with anisotropic scaling with a self-similarity parameter that is defined by a matrix. The growth of ensemble plumes is analyzed for transport through 2-D "operator- stable" fBm hydraulic conductivity (K) fields. Both the longitudinal and transverse Hurst coefficients are important to both plume growth rates and the timing and duration of breakthrough. Smaller Hurst coefficients in the transverse direction lead to more "continuity" or stratification in the direction of transport. The result is continually faster-than-Fickian growth rates, highly non-Gaussian ensemble plumes, and a longer tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rate never exceeds Mercado's [1967] purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-Mercado growth must be the result of other factors, such as larger plumes corresponding to either a larger initial plume size or greater variance of the ln(K) field.

Hurst revisited: Are symptoms and signs of functional motor and sensory disorders "dependent on idea"?

PubMed

Stone, Jon; Mutch, Jennifer; Giannokous, Denis; Hoeritzauer, Ingrid; Carson, Alan

2017-10-15

Symptoms and signs of functional (psychogenic) motor and sensory disorder are often said to be dependent on the patients' idea of what symptoms should be, rather than anatomy and physiology. This hypothesis has however rarely been tested. Inspired by a brief experiment carried out in 1919 by neurologist Arthur Hurst we aimed to assess the views of healthy non-medical adults towards paralysis and numbness and their response to tests for functional disorders when asked to pretend to have motor and sensory symptoms. When subjects were asked to pretend they had a paralysed arm 80% thought there would be sensory loss. Of these 60% thought it would have a circumferential (functional) distribution at the wrist, elbow or shoulder. Hoover's sign of functional weakness was only positive in 75% of patients pretending to have leg paralysis with 23% maintaining weakness of hip extension in the feigned weak leg, a rare finding in neurological practice. 20% of subjects managed to continue having their feigned tremor during the entrainment test. 52% of subjects thought there was asymmetry of a tuning fork across their forehead even when no prior instruction had been given. The study confirmed Hurst's finding that non-medical people generally expect sensory loss to go along with paralysis, especially if the examiner suggests it. When present, it usually conforms to functional patterns of sensory loss. Clinical tests for functional and motor disorders appear to behave somewhat differently in patients asked to pretend to have symptoms suggesting that larger more detailed studies would be worthwhile. Copyright © 2017 Elsevier B.V. All rights reserved.

Interplay between Functional Connectivity and Scale-Free Dynamics in Intrinsic fMRI Networks

PubMed Central

Ciuciu, Philippe; Abry, Patrice; He, Biyu J.

2014-01-01

Studies employing functional connectivity-type analyses have established that spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals are organized within large-scale brain networks. Meanwhile, fMRI signals have been shown to exhibit 1/f-type power spectra – a hallmark of scale-free dynamics. We studied the interplay between functional connectivity and scale-free dynamics in fMRI signals, utilizing the fractal connectivity framework – a multivariate extension of the univariate fractional Gaussian noise model, which relies on a wavelet formulation for robust parameter estimation. We applied this framework to fMRI data acquired from healthy young adults at rest and performing a visual detection task. First, we found that scale-invariance existed beyond univariate dynamics, being present also in bivariate cross-temporal dynamics. Second, we observed that frequencies within the scale-free range do not contribute evenly to inter-regional connectivity, with a systematically stronger contribution of the lowest frequencies, both at rest and during task. Third, in addition to a decrease of the Hurst exponent and inter-regional correlations, task performance modified cross-temporal dynamics, inducing a larger contribution of the highest frequencies within the scale-free range to global correlation. Lastly, we found that across individuals, a weaker task modulation of the frequency contribution to inter-regional connectivity was associated with better task performance manifesting as shorter and less variable reaction times. These findings bring together two related fields that have hitherto been studied separately – resting-state networks and scale-free dynamics, and show that scale-free dynamics of human brain activity manifest in cross-regional interactions as well. PMID:24675649

The time-delayed inverted pendulum: Implications for human balance control

NASA Astrophysics Data System (ADS)

Milton, John; Cabrera, Juan Luis; Ohira, Toru; Tajima, Shigeru; Tonosaki, Yukinori; Eurich, Christian W.; Campbell, Sue Ann

2009-06-01

The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, τn, be greater than a critical delay τc that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when θ exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.

Altered Functional Performance in Patients with Fibromyalgia.

PubMed

Costa, Isis da Silva; Gamundí, Antoni; Miranda, José G Vivas; França, Lucas G Souza; De Santana, Charles Novaes; Montoya, Pedro

2017-01-01

Fibromyalgia is a common chronic pain condition that exerts a considerable impact on patients' daily activities and quality of life. Objectives: The main objective of the present study was to evaluate kinematic parameters of gait, functional performance, and balance in women with fibromyalgia syndrome. Methods: The study included 26 female patients with fibromyalgia (49.2 ± 8.0 years) according to the criteria of the American College of Rheumatology, as well as 16 pain-free women (43.5 ± 8.5 years). Gait and balance parameters were extracted from video recordings of participants performing several motor tasks. Non-linear dynamic of body sway time series was also analyzed by computing the Hurst exponent. In addition, functional performance and clinical pain were obtained by using standardized motor tests (Berg's balance scale, 6-min walking test, timed up and go task, Romberg's balance test) and self-report questionnaires (Fibromyalgia Impact Questionnaire). Results: Walking speed was significantly diminished ( p < 0.001) in FM patients as compared to pain-free controls, probably due to significant reductions in stride length ( p < 0.001) and cycle frequency ( p < 0.001). Analyses of balance also revealed significant differences between fibromyalgia and pain-free controls on body sway in the medial-lateral and anterior-posterior axes (all ps < 0.01). Several parameters of gait and balance were significantly associated with high levels of pain, depression, stiffness, anxiety, and fatigue in fibromyalgia. Conclusion: Our data revealed that both gait and balance were severely impaired in FM, and that subjective complaints associated with FM could contribute to functional disability in these patients. These findings suggest that optimal rehabilitation and fall prevention in fibromyalgia require a comprehensive assessment of both psychological responses to pain and physical impairments during postural control and gait.

Estimation of preterm labor immediacy by nonlinear methods

PubMed Central

Martinez, Luis; Matorras, Roberto; Bringas, Carlos; Aranburu, Larraitz; Fernández-Llebrez, Luis; Gonzalez, Leire; Arana, Itziar; Pérez, Martín-Blas; Martínez de la Fuente, Ildefonso

2017-01-01

Preterm delivery affects about one tenth of human births and is associated with an increased perinatal morbimortality as well as with remarkable costs. Even if there are a number of predictors and markers of preterm delivery, none of them has a high accuracy. In order to find quantitative indicators of the immediacy of labor, 142 cardiotocographies (CTG) recorded from women consulting because of suspected threatened premature delivery with gestational ages comprehended between 24 and 35 weeks were collected and analyzed. These 142 samples were divided into two groups: the delayed labor group (n = 75), formed by the women who delivered more than seven days after the tocography was performed, and the anticipated labor group (n = 67), which corresponded to the women whose labor took place during the seven days following the recording. As a means of finding significant differences between the two groups, some key informational properties were analyzed by applying nonlinear techniques on the tocography recordings. Both the regularity and the persistence levels of the delayed labor group, which were measured by Approximate Entropy (ApEn) and Generalized Hurst Exponent (GHE) respectively, were found to be significantly different from the anticipated labor group. As delivery approached, the values of ApEn tended to increase while the values of GHE tended to decrease, suggesting that these two methods are sensitive to labor immediacy. On this paper, for the first time, we have been able to estimate childbirth immediacy by applying nonlinear methods on tocographies. We propose the use of the techniques herein described as new quantitative diagnosis tools for premature birth that significantly improve the current protocols for preterm labor prediction worldwide. PMID:28570658

Physical modeling of the formation and evolution of seismically active fault zones

USGS Publications Warehouse

Ponomarev, A.V.; Zavyalov, A.D.; Smirnov, V.B.; Lockner, D.A.

1997-01-01

Acoustic emission (AE) in rocks is studied as a model of natural seismicity. A special technique for rock loading has been used to help study the processes that control the development of AE during brittle deformation. This technique allows us to extend to hours fault growth which would normally occur very rapidly. In this way, the period of most intense interaction of acoustic events can be studied in detail. Characteristics of the acoustic regime (AR) include the Gutenberg-Richter b-value, spatial distribution of hypocenters with characteristic fractal (correlation) dimension d, Hurst exponent H, and crack concentration parameter Pc. The fractal structure of AR changes with the onset of the drop in differential stress during sample deformation. The change results from the active interaction of microcracks. This transition of the spatial distribution of AE hypocenters is accompanied by a corresponding change in the temporal correlation of events and in the distribution of event amplitudes as signified by a decrease of b-value. The characteristic structure that develops in the low-energy background AE is similar to the sequence of the strongest microfracture events. When the AR fractal structure develops, the variations of d and b are synchronous and d = 3b. This relation which occurs once the fractal structure is formed only holds for average values of d and b. Time variations of d and b are anticorrelated. The degree of temporal correlation of AR has time variations that are similar to d and b variations. The observed variations in laboratory AE experiments are compared with natural seismicity parameters. The close correspondence between laboratory-scale observations and naturally occurring seismicity suggests a possible new approach for understanding the evolution of complex seismicity patterns in nature. ?? 1997 Elsevier Science B.V. All rights reserved.

Analyzing Crisis in Global Financial Indices

NASA Astrophysics Data System (ADS)

Kumar, Sunil; Deo, Nivedita

We apply the Random Matrix Theory and complex network techniques to 20 global financial indices and study the correlation and network properties before and during the financial crisis of 2008 respectively. We find that the largest eigenvalue deviate significantly from the upper bound which shows a strong correlation between financial indices. By using a sliding window of 25 days we find that largest eigenvalue represent the collective information about the correlation between global financial indices and its trend indicate the market conditions. It is confirmed that eigenvectors corresponding to second largest eigenvalue gives useful information about the sector formation in the global financial indices. We find that these clusters are formed on the basis of the geographical location. The correlation network is constructed using threshold method for different values of threshold θ in the range 0 to 0.9, at θ=0.2 the network is fully connected. At θ=0.6, the Americas, Europe and Asia/Pacific form different clusters before the crisis but during the crisis Americas and Europe are strongly linked. If we further increase the threshold to 0.9 we find that European countries France, Germany and UK consistently constitute the most tightly linked markets before and during the crisis. We find that the structure of Minimum Spanning Tree before the crisis is more star like whereas during the crisis it changes to be more chain like. Using the multifractal analysis, we find that Hurst exponents of financial indices increases during the period of crisis as compared to the period before the crisis. The empirical results verify the validity of measures, and this has led to a better understanding of complex financial markets.

Perturbation theory for fractional Brownian motion in presence of absorbing boundaries.

PubMed

Wiese, Kay Jörg; Majumdar, Satya N; Rosso, Alberto

2011-06-01

Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations (x(t(1))x(t(2)))=D(t(1)(2H)+t(2)(2H)-|t(1)-t(2)|(2H)), where H, with 0

Rupture Dynamics and Ground Motion from Earthquakes in Heterogeneous Media

NASA Astrophysics Data System (ADS)

Bydlon, S.; Dunham, E. M.; Kozdon, J. E.

2012-12-01

Heterogeneities in the material properties of Earth's crust scatter propagating seismic waves. The effects of scattered waves are reflected in the seismic coda and depend on the relative strength of the heterogeneities, spatial arrangement, and distance from source to receiver. In the vicinity of the fault, scattered waves influence the rupture process by introducing fluctuations in the stresses driving propagating ruptures. Further variability in the rupture process is introduced by naturally occurring geometric complexity of fault surfaces, and the stress changes that accompany slip on rough surfaces. We have begun a modeling effort to better understand the origin of complexity in the earthquake source process, and to quantify the relative importance of source complexity and scattering along the propagation path in causing incoherence of high frequency ground motion. To do this we extended our two-dimensional high order finite difference rupture dynamics code to accommodate material heterogeneities. We generate synthetic heterogeneous media using Von Karman correlation functions and their associated power spectral density functions. We then nucleate ruptures on either flat or rough faults, which obey strongly rate-weakening friction laws. Preliminary results for flat faults with uniform frictional properties and initial stresses indicate that off-fault material heterogeneity alone can lead to a complex rupture process. Our simulations reveal the excitation of high frequency bursts of waves, which radiate energy away from the propagating rupture. The average rupture velocity is thus reduced relative to its value in simulations employing homogeneous material properties. In the coming months, we aim to more fully explore parameter space by varying the correlation length, Hurst exponent, and amplitude of medium heterogeneities, as well as the statistical properties characterizing fault roughness.

Altered Functional Performance in Patients with Fibromyalgia

PubMed Central

Costa, Isis da Silva; Gamundí, Antoni; Miranda, José G. Vivas; França, Lucas G. Souza; De Santana, Charles Novaes; Montoya, Pedro

2017-01-01

Fibromyalgia is a common chronic pain condition that exerts a considerable impact on patients' daily activities and quality of life. Objectives: The main objective of the present study was to evaluate kinematic parameters of gait, functional performance, and balance in women with fibromyalgia syndrome. Methods: The study included 26 female patients with fibromyalgia (49.2 ± 8.0 years) according to the criteria of the American College of Rheumatology, as well as 16 pain-free women (43.5 ± 8.5 years). Gait and balance parameters were extracted from video recordings of participants performing several motor tasks. Non-linear dynamic of body sway time series was also analyzed by computing the Hurst exponent. In addition, functional performance and clinical pain were obtained by using standardized motor tests (Berg's balance scale, 6-min walking test, timed up and go task, Romberg's balance test) and self-report questionnaires (Fibromyalgia Impact Questionnaire). Results: Walking speed was significantly diminished (p < 0.001) in FM patients as compared to pain-free controls, probably due to significant reductions in stride length (p < 0.001) and cycle frequency (p < 0.001). Analyses of balance also revealed significant differences between fibromyalgia and pain-free controls on body sway in the medial-lateral and anterior-posterior axes (all ps < 0.01). Several parameters of gait and balance were significantly associated with high levels of pain, depression, stiffness, anxiety, and fatigue in fibromyalgia. Conclusion: Our data revealed that both gait and balance were severely impaired in FM, and that subjective complaints associated with FM could contribute to functional disability in these patients. These findings suggest that optimal rehabilitation and fall prevention in fibromyalgia require a comprehensive assessment of both psychological responses to pain and physical impairments during postural control and gait. PMID:28184193

A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions

NASA Astrophysics Data System (ADS)

Mendes, Eduardo M. A. M.; Nepomuceno, Erivelton G.

2016-12-01

In this letter, a very simple method to calculate the positive Largest Lyapunov Exponent (LLE) based on the concept of interval extensions and using the original equations of motion is presented. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system. It is shown that the algorithm is robust, fast and easy to implement and can be considered as alternative to other algorithms available in the literature. The method has been successfully tested in five well-known systems: Logistic, Hénon, Lorenz and Rössler equations and the Mackey-Glass system.

Dynamics of phase separation of binary fluids

NASA Technical Reports Server (NTRS)

Ma, Wen-Jong; Maritan, Amos; Banavar, Jayanth R.; Koplik, Joel

1992-01-01

The results of molecular-dynamics studies of surface-tension-dominated spinodal decomposition of initially well-mixed binary fluids in the absence and presence of gravity are presented. The growth exponent for the domain size and the decay exponent of the potential energy of interaction between the two species with time are found to be 0.6 +/- 0.1, inconsistent with scaling arguments based on dimensional analysis.

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Sanders, Sören; Holthaus, Martin

2017-10-01

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

75 FR 57329 - Qualification of Drivers; Exemption Applications; Diabetes Mellitus

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-20

..., Tommy S. Boden, Travis D. Bjerk, Scott L. Colson, Dustin G. Cook, Nathan J. Enloe, Stephen J. Faxon, Joseph B. Hall, Mark H. Horne, Michael J. Hurst, Chad W. Lawyer, John R. Little, Roy L. McKinney, Thomas...

Fitting power-laws in empirical data with estimators that work for all exponents

PubMed Central

Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan

2017-01-01

Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249

Structure Function Scaling Exponent and Intermittency in the Wake of a Wind Turbine Array

NASA Astrophysics Data System (ADS)

Aseyev, Aleksandr; Ali, Naseem; Cal, Raul

2015-11-01

Hot-wire measurements obtained in a 3 × 3 wind turbine array boundary layer are utilized to analyze high order structure functions, intermittency effects as well as the probability density functions of velocity increments at different scales within the energy cascade. The intermittency exponent is found to be greater in the far wake region in comparison to the near wake. At hub height, the intermittency exponent is found to be null. ESS scaling exponents of the second, fourth, and fifth order structure functions remain relatively constant as a function of height in the far-wake whereas in the near-wake these highly affected by the passage of the rotor thus showing a dependence on physical location. When comparing with proposed models, these generally over predict the structure functions in the far wake region. The pdf distributions in the far wake region display wider tails compared to the near wake region, and constant skewness hypothesis based on the local isotropy is verified in the wake. CBET-1034581.

Critical exponents of the explosive percolation transition

NASA Astrophysics Data System (ADS)

da Costa, R. A.; Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F.

2014-04-01

In a new type of percolation phase transition, which was observed in a set of nonequilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential merging of small components and delays the emergence of the percolation cluster. First simulations led to a conclusion that a percolation cluster in this irreversible process is born discontinuously, by a discontinuous phase transition, which results in the term "explosive percolation transition." We have shown that this transition is actually continuous (second order) though with an anomalously small critical exponent of the percolation cluster. Here we propose an efficient numerical method enabling us to find the critical exponents and other characteristics of this second-order transition for a representative set of explosive percolation models with different number of choices. The method is based on gluing together the numerical solutions of evolution equations for the cluster size distribution and power-law asymptotics. For each of the models, with high precision, we obtain critical exponents and the critical point.

Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation.

PubMed

Gómez-Extremera, Manuel; Carpena, Pedro; Ivanov, Plamen Ch; Bernaola-Galván, Pedro A

2016-04-01

We systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series, which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations. First, we decompose artificial long-range power-law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series, and we study their correlation properties. We find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series. Such expressions are necessary for modeling surrogate time series with desired scaling properties. Next, we study linear and nonlinear correlation properties of series composed as products of independent magnitude and sign series. These surrogate series can be considered as a zero-order approximation to the analysis of the coupling of magnitude and sign in real data, a problem still open in many fields. We find analytical results for the scaling behavior of the composed series as a function of the correlation exponents of the magnitude and sign series used in the composition, and we determine the ranges of magnitude and sign correlation exponents leading to either single scaling or to crossover behaviors. Finally, we obtain how the linear and nonlinear properties of the composed series depend on the correlation exponents of their magnitude and sign series. Based on this information we propose a method to generate surrogate series with controlled correlation exponent and multifractal spectrum.

The Steep Nekhoroshev's Theorem

NASA Astrophysics Data System (ADS)

Guzzo, M.; Chierchia, L.; Benettin, G.

2016-03-01

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

Improved dual-porosity models for petrophysical analysis of vuggy reservoirs

NASA Astrophysics Data System (ADS)

Wang, Haitao

2017-08-01

A new vug interconnection, isolated vug (IVG), was investigated through resistivity modeling and the dual-porosity model for connected vug (CVG) vuggy reservoirs was tested. The vuggy models were built by pore-scale modeling, and their electrical resistivity was calculated by the finite difference method. For CVG vuggy reservoirs, the CVG reduced formation factors and increased the porosity exponents, and the existing dual-porosity model failed to match these results. Based on the existing dual-porosity model, a conceptual dual-porosity model for CVG was developed by introducing a decoupled term to reduce the resistivity of the model. For IVG vuggy reservoirs, IVG increased the formation factors and porosity exponents. The existing dual-porosity model succeeded due to accurate calculation of the formation factors of the deformed interparticle porous media caused by the insertion of the IVG. Based on the existing dual-porosity model, a new porosity model for IVG vuggy reservoirs was developed by simultaneously recalculating the formation factors of the altered interparticle pore-scale models. The formation factors and porosity exponents from the improved and extended dual-porosity models for CVG and IVG vuggy reservoirs well matched the simulated formation factors and porosity exponents. This work is helpful for understanding the influence of connected and disconnected vugs on resistivity factors—an issue of particular importance in carbonates.

Susceptibility of the Ising Model on a Kagomé Lattice by Using Wang-Landau Sampling

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon; Kwak, Wooseop

2018-03-01

The susceptibility of the Ising model on a kagomé lattice has never been obtained. We investigate the properties of the kagomé-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt, we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.

Studying plastic shear localization in aluminum alloys under dynamic loading

NASA Astrophysics Data System (ADS)

Bilalov, D. A.; Sokovikov, M. A.; Chudinov, V. V.; Oborin, V. A.; Bayandin, Yu. V.; Terekhina, A. I.; Naimark, O. B.

2016-12-01

An experimental and theoretical study of plastic shear localization mechanisms observed under dynamic deformation using the shear-compression scheme on a Hopkinson-Kolsky bar has been carried out using specimens of AMg6 alloy. The mechanisms of plastic shear instability are associated with collective effects in the microshear ensemble in spatially localized areas. The lateral surface of the specimens was photographed in the real-time mode using a CEDIP Silver 450M high-speed infrared camera. The temperature distribution obtained at different times allowed us to trace the evolution of the localization of the plastic strain. Based on the equations that describe the effect of nonequilibrium transitions on the mechanisms of structural relaxation and plastic flow, numerical simulation of plastic shear localization has been performed. A numerical experiment relevant to the specimen-loading scheme was carried out using a system of constitutive equations that reflect the part of the structural relaxation mechanisms caused by the collective behavior of microshears with the autowave modes of the evolution of the localized plastic flow. Upon completion of the experiment, the specimens were subjected to microstructure analysis using a New View-5010 optical microscope-interferometer. After the dynamic deformation, the constancy of the Hurst exponent, which reflects the relationship between the behavior of defects and roughness induced by the defects on the surfaces of the specimens is observed in a wider range of spatial scales. These investigations revealed the distinctive features in the localization of the deformation followed by destruction to the script of the adiabatic shear. These features may be caused by the collective multiscale behavior of defects, which leads to a sharp decrease in the stress-relaxation time and, consequently, a localized plastic flow and generation of fracture nuclei in the form of adiabatic shear. Infrared scanning of the localization zone of the plastic strain in situ and the subsequent study of the defect structure corroborated the hypothesis about the decisive role of non-equilibrium transitions in defect ensembles during the evolution of a localized plastic flow.

Global and Local Approaches Describing Critical Phenomena on the Developing and Developed Financial Markets

NASA Astrophysics Data System (ADS)

Grech, Dariusz

We define and confront global and local methods to analyze the financial crash-like events on the financial markets from the critical phenomena point of view. These methods are based respectively on the analysis of log-periodicity and on the local fractal properties of financial time series in the vicinity of phase transitions (crashes). The log-periodicity analysis is made in a daily time horizon, for the whole history (1991-2008) of Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. We find that crash-like events on the Polish financial market are described better by the log-divergent price model decorated with log-periodic behavior than by the power-law-divergent price model usually discussed in log-periodic scenarios for developed markets. Predictions coming from log-periodicity scenario are verified for all main crashes that took place in WIG history. It is argued that crash predictions within log-periodicity model strongly depend on the amount of data taken to make a fit and therefore are likely to contain huge inaccuracies. Next, this global analysis is confronted with the local fractal description. To do so, we provide calculation of the so-called local (time dependent) Hurst exponent H loc for the WIG time series and for main US stock market indices like DJIA and S&P 500. We point out dependence between the behavior of the local fractal properties of financial time series and the crashes appearance on the financial markets. We conclude that local fractal method seems to work better than the global approach - both for developing and developed markets. The very recent situation on the market, particularly related to the Fed intervention in September 2007 and the situation immediately afterwards is also analyzed within fractal approach. It is shown in this context how the financial market evolves through different phases of fractional Brownian motion. Finally, the current situation on American market is analyzed in fractal language. This is to show how far we still are from the end of recession and from the beginning of a new boom on US financial market or on other world leading stocks.

Dependence of seismic energy on higher wavenumber components

NASA Astrophysics Data System (ADS)

Hirano, S.; Yagi, Y.

2014-12-01

Seismic Energy ESE_S gives a minimum of strain energy drop defined as an inner product of spacial distribution of coseismic slip and stress change on a fault surface (Andrews 1978 JGR). Traditionally, ESE_S has been obtained by multiplying mean stress drop and seismic moment divided by the rigidity by assuming the distribution of stress drop is constant in space, which yields an elliptic slip distribution. It has, however, been pointed out that slip distributions are approximated not as the elliptic distribution but as the kk-squared model (Herrero & Bernard 1994 BSSA), so that the product of mean stress drop and seismic moment does not give proper estimation of ESE_S. For the case of heterogeneous stress drop, the inner product requires shorter wavelength components of slip distribution (Andrews 1980 JGR). Mai & Beroza (2002 JGR) revealed that observed slip distributions in the wavenumber domain are well modeled with the von Karman power spectrum density parameterized by a corner wavenumber kck_c and the Hurst exponent HH, and quantified these two parameters for some inversion results. Although they discussed a condition of convergence of the inner product, they did not consider dependence of ESE_S on kck_c, HH, and a maximum wavenumber kmaxk_{max}. In this study, we analytically obtain the dependence and suggest how we should consider higher wavenumber components of slip distribution for estimation of ESE_S. We show that the relationship ES∝C(kmax/kc,H)μP2k3cE_S propto C(k_{max}/k_c, H) mu P^2 k_c^3 holds, where μmu is the rigidity, and PP is the seismic potency. An analytical solution of C(kmax/kc,H)C(k_{max}/k_c, H) tells us that even components of kmax/kc˜10k_{max}/k_c sim 10 or 100100 are not negligible for ESE_S under kk-squared model while such components do not contribute to ESE_S for the elliptic slip distribution. We discuss this feature quantitatively and show some examples of estimation of ESE_S based on results of slip inversions.

Theme: Focus on Teaching.

ERIC Educational Resources Information Center

Connors, James J.; And Others

1996-01-01

Includes "The More Things Change..." (Connors); "Students--Bored of Education?" (Earle); "Yesterday, Today and Tomorrow" (Wesch et al.); "Attitude and the Value of Environment" (Foster); "Fins, Feathers and Fur" (Crank); "Greenhouse as a Focus for Agriscience" (Hurst); and "Agricultural and Environmental Education at Milton Hershey School"…

Critical short-time dynamics in a system with interacting static and diffusive populations

NASA Astrophysics Data System (ADS)

Argolo, C.; Quintino, Yan; Gleria, Iram; Lyra, M. L.

2012-01-01

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal

NASA Astrophysics Data System (ADS)

Krčmár, Roman; Šamaj, Ladislav

2018-01-01

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ηe and δe which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

NASA Astrophysics Data System (ADS)

Kwapień, Jarosław; Oświecimka, Paweł; Forczek, Marcin; DroŻdŻ, Stanisław

2017-05-01

Based on a recently proposed q -dependent detrended cross-correlation coefficient, ρq [J. Kwapień, P. Oświęcimka, and S. Drożdż, Phys. Rev. E 92, 052815 (2015), 10.1103/PhysRevE.92.052815], we generalize the concept of the minimum spanning tree (MST) by introducing a family of q -dependent minimum spanning trees (q MST s ) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients ρq, which are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. The conventional MST with detrending corresponds in this context to q =2 . In order to illustrate their performance, we apply the q MSTs to sample empirical data from the American stock market and discuss the results. We show that the q MST graphs can complement ρq in disentangling "hidden" correlations that cannot be observed in the MST graphs based on ρDCCA, and therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. As an example, we apply this method to empirical data from the stock market and show that by constructing the q MSTs for a spectrum of q values we obtain more information about the correlation structure of the data than by using q =2 only. More specifically, we show that two sets of signals that differ from each other statistically can give comparable trees for q =2 , while only by using the trees for q ≠2 do we become able to distinguish between these sets. We also show that a family of q MSTs for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different q 's. As regards the correlation structure of the stock market, our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.

Developing Stochastic Models as Inputs for High-Frequency Ground Motion Simulations

NASA Astrophysics Data System (ADS)

Savran, William Harvey

High-frequency ( 10 Hz) deterministic ground motion simulations are challenged by our understanding of the small-scale structure of the earth's crust and the rupture process during an earthquake. We will likely never obtain deterministic models that can accurately describe these processes down to the meter scale length required for broadband wave propagation. Instead, we can attempt to explain the behavior, in a statistical sense, by including stochastic models defined by correlations observed in the natural earth and through physics based simulations of the earthquake rupture process. Toward this goal, we develop stochastic models to address both of the primary considerations for deterministic ground motion simulations: namely, the description of the material properties in the crust, and broadband earthquake source descriptions. Using borehole sonic log data recorded in Los Angeles basin, we estimate the spatial correlation structure of the small-scale fluctuations in P-wave velocities by determining the best-fitting parameters of a von Karman correlation function. We find that Hurst exponents, nu, between 0.0-0.2, vertical correlation lengths, az, of 15-150m, an standard deviation, sigma of about 5% characterize the variability in the borehole data. Usin these parameters, we generated a stochastic model of velocity and density perturbations and combined with leading seismic velocity models to perform a validation exercise for the 2008, Chino Hills, CA using heterogeneous media. We find that models of velocity and density perturbations can have significant effects on the wavefield at frequencies as low as 0.3 Hz, with ensemble median values of various ground motion metrics varying up to +/-50%, at certain stations, compared to those computed solely from the CVM. Finally, we develop a kinematic rupture generator based on dynamic rupture simulations on geometrically complex faults. We analyze 100 dynamic rupture simulations on strike-slip faults ranging from Mw 6.4-7.2. We find that our dynamic simulations follow empirical scaling relationships for inter-plate strike-slip events, and provide source spectra comparable with an o -2 model. Our rupture generator reproduces GMPE medians and intra-event standard deviations spectral accelerations for an ensemble of 10 Hz fully-deterministic ground motion simulations, as compared to NGA West2 GMPE relationships up to 0.2 seconds.

Dependence of long-term persistence properties of precipitation on spatial and regional characteristics

NASA Astrophysics Data System (ADS)

Tyralis, Hristos; Dimitriadis, Panayiotis; Iliopoulou, Theano; Tzouka, Katerina; Koutsoyiannis, Demetris

2017-04-01

The long-term persistence (LTP), else known in hydrological science as the Hurst phenomenon, is a behaviour observed in geophysical processes in which wet years or dry years are clustered to respective long time periods. A common practice for evaluating the presence of the LTP is to model the geophysical time series with the Hurst-Kolmogorov process (HKp) and estimate its Hurst parameter H where high values of H indicate strong LTP. We estimate H of the mean annual precipitation using instrumental data from approximately 1 500 stations which cover a big area of the earth's surface and span from 1916 to 2015. We regress the H estimates of all stations on their spatial and regional characteristics (i.e. their location, elevation and Köppen-Geiger climate class) using a random forest algorithm. Furthermore, we apply the Mann-Kendall test under the LTP assumption (MKt-LTP) to all time series to assess the significance of observed trends of the mean annual precipitation. To summarize the results, the LTP seems to depend mostly on the location of the stations, while the predictive value of the fitted regression model is good. Thus when investigating for LTP properties we recommend that the local characteristics should be considered. Additionally, the application of the MKt-LTP suggests that no significant monotonic trend can characterize the global precipitation. Dominant positive significant trends are observed mostly in main climate type D (snow), while in the other climate types the percentage of stations with positive significant trends was approximately equal to that of negative significant trends. Furthermore, 50% of all stations do not exhibit significant trends at all.

ARC-2010-ACD10-0120-001

NASA Image and Video Library

2010-06-21

Singularity University Staff; Tasha McCauley, Manuel Zaera-Sanz, David Ayotte, Jose Cordeiro, Sarah Russell, Candi Sterling, Marco Chacin, Ola Abraham, Jonathan Badal, Eric Dahlstrom, Susan Fonseca-Klein, Emeline Paat-Dahlstrom, Keith Powers, Bruce Klein, Tracy Nguyen, Kelly Lewis, Ken Hurst, Paul Sieveke, Kathryn Myronuk, Andy Barry.

77 FR 9923 - Agency Information Collection Activities

Federal Register 2010, 2011, 2012, 2013, 2014

2012-02-21

... electronically at http://www.regulations.gov , which is the Federal eRulemaking Portal. Follow the instructions... directly or through the Federal eRulemaking Portal will be available for review, by advance appointment....) FOR FURTHER INFORMATION CONTACT: Veta Hurst, Federal Sector Programs, Office of Federal Operations...

The Muslim Brotherhood in Egypt, Jordan and Syria: A Comparison

DTIC Science & Technology

2009-03-01

Studies in Contemporary History and Security ,ed Kurt Spillman and Andreas Wenger (Bern, Peter Lang Publishing, 1999), 68. 94 Maye Kassem ...Washington Institute for Near East Policy, 972 (2005): 1. Joffe, George. Jordan in transition. New York: Hurst & Co, 2002. Kassem , Maye. Egyptain

Cumulative Effective Hölder Exponent Based Indicator for Real-Time Fetal Heartbeat Analysis during Labour

NASA Astrophysics Data System (ADS)

Struzik, Zbigniew R.; van Wijngaarden, Willem J.

We introduce a special purpose cumulative indicator, capturing in real time the cumulative deviation from the reference level of the exponent h (local roughness, Hölder exponent) of the fetal heartbeat during labour. We verify that the indicator applied to the variability component of the heartbeat coincides with the fetal outcome as determined by blood samples. The variability component is obtained from running real time decomposition of fetal heartbeat into independent components using an adaptation of an oversampled Haar wavelet transform. The particular filters used and resolutions applied are motivated by obstetricial insight/practice. The methodology described has the potential for real-time monitoring of the fetus during labour and for the prediction of the fetal outcome, allerting the attending staff in the case of (threatening) hypoxia.

The effect of 1/f fluctuation in inter-stimulus intervals on auditory evoked mismatch field.

PubMed

Harada, Nobuyoshi; Masuda, Tadashi; Endo, Hiroshi; Nakamura, Yukihiro; Takeda, Tsunehiro; Tonoike, Mitsuo

2005-05-13

This study focused on the effect of regularity of environmental stimuli on the informational order extracting function of human brain. The regularity of environmental stimuli can be described with the exponent n of the fluctuation 1/f(n). We studied the effect of the exponent of the fluctuation in the inter-stimulus interval (ISI) on the elicitation of auditory evoked mismatch fields (MMF) with two sounds with alternating frequency. ISI times were given by three types of fluctuation, 1/f(0), 1/f(1), 1/f(2), and with a fixed interval (1/f(infinity)). The root mean square (RMS) value of the MMF increased significantly (F(3/9)=4.95, p=0.027) with increases in the exponent of the fluctuation. Increments in the regularity of the fluctuation provoked enhancement of the MMF, which reflected the production of a memory trace, based on the anticipation of the stimulus timing. The gradient of the curve, indicating the ratio of increments between the MMF and the exponent of fluctuation, can express a subject's capability to extract regularity from fluctuating stimuli.

Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus

NASA Astrophysics Data System (ADS)

Itto, Yuichi

2018-05-01

In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.

Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the Lifshitz black hole background

NASA Astrophysics Data System (ADS)

Sherkatghanad, Z.; Mirza, B.; Lalehgani Dezaki, F.

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while z is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm-Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, z, and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, z.

Identification of exponent from load-deformation relation for soft materials from impact tests

NASA Astrophysics Data System (ADS)

Ciornei, F. C.; Alaci, S.; Romanu, I. C.; Ciornei, M. C.; Sopon, G.

2018-01-01

When two bodies are brought into contact, the magnitude of occurring reaction forces increase together with the amplitude of deformations. The load-deformation dependency of two contacting bodies is described by a function having the form F = Cxα . An accurate illustration of this relationship assumes finding the precise coefficient C and exponent α. This representation proved to be very useful in hardness tests, in dynamic systems modelling or in considerations upon the elastic-plastic ratio concerning a Hertzian contact. The classical method for identification of the exponent consists in finding it from quasi-static tests. The drawback of the method is the fact that the accurate estimation of the exponent supposes precise identification of the instant of contact initiation. To overcome this aspect, the following observation is exploited: during an impact process, the dissipated energy is converted into heat released by internal friction in the materials and energy for plastic deformations. The paper is based on the remark that for soft materials the hysteresis curves obtained for a static case are similar to the ones obtained for medium velocities. Furthermore, utilizing the fact that for the restitution phase the load-deformation dependency is elastic, a method for finding the α exponent for compression phase is proposed. The maximum depth of the plastic deformations obtained for a series of collisions, by launching, from different heights, a steel ball in free falling on an immobile prism made of soft material, is evaluated by laser profilometry method. The condition that the area of the hysteresis loop equals the variation of kinetical energy of the ball is imposed and two tests are required for finding the exponent. Five collisions from different launching heights of the ball were taken into account. For all the possible impact-pair cases, the values of the exponent were found and close values were obtained.

The isentropic exponent in plasmas

NASA Astrophysics Data System (ADS)

Burm, K. T. A. L.; Goedheer, W. J.; Schram, D. C.

1999-06-01

The isentropic exponent for gases is a physical quantity that can ease significantly the hydrodynamic modeling effort. In gas dynamics the isentropic exponent depends only on the number of degrees of freedom of the considered gas. The isentropic exponent for a plasma is lower due to an extra degree of freedom caused by ionization. In this paper it will be shown that, like for gases, the isentropic exponent for atomic plasmas is also constant, as long as the ionization degree is between 5%-80%. Only a very weak dependence on the electron temperature and the two nonequilibrium parameters remain. An argon plasma is used to demonstrate the behavior of the isentropic exponent on the plasma conditions, and to make an estimation of the value of the isentropic exponent of a customary plasma. For atmospheric plasmas, which usually have an electron temperature of about 1 eV, a sufficiently accurate estimate for the isentropic exponent of plasmas is 1.16.

On identifying relationships between the flood scaling exponent and basin attributes.

PubMed

Medhi, Hemanta; Tripathi, Shivam

2015-07-01

Floods are known to exhibit self-similarity and follow scaling laws that form the basis of regional flood frequency analysis. However, the relationship between basin attributes and the scaling behavior of floods is still not fully understood. Identifying these relationships is essential for drawing connections between hydrological processes in a basin and the flood response of the basin. The existing studies mostly rely on simulation models to draw these connections. This paper proposes a new methodology that draws connections between basin attributes and the flood scaling exponents by using observed data. In the proposed methodology, region-of-influence approach is used to delineate homogeneous regions for each gaging station. Ordinary least squares regression is then applied to estimate flood scaling exponents for each homogeneous region, and finally stepwise regression is used to identify basin attributes that affect flood scaling exponents. The effectiveness of the proposed methodology is tested by applying it to data from river basins in the United States. The results suggest that flood scaling exponent is small for regions having (i) large abstractions from precipitation in the form of large soil moisture storages and high evapotranspiration losses, and (ii) large fractions of overland flow compared to base flow, i.e., regions having fast-responding basins. Analysis of simple scaling and multiscaling of floods showed evidence of simple scaling for regions in which the snowfall dominates the total precipitation.

Genetics Home Reference: 17q12 duplication

MedlinePlus

... books/NBK344340/ Citation on PubMed Mefford HC, Clauin S, Sharp AJ, Moller RS, Ullmann R, Kapur R, Pinkel D, Cooper GM, ... 10.1002/ajmg.a.37848. Citation on PubMed Sharp AJ, Hansen S, Selzer RR, Cheng Z, Regan R, Hurst JA, Stewart H, Price SM, Blair E, ...

Security Implications of ISAF Exit from Afghanistan on South Asia

DTIC Science & Technology

2014-12-12

Afghanistan for their security interests. Cindy A. Hurst and Robert Mathers , discussed the implications of US withdrawal with reference to the presence...... Mathers , “Strategic Implications of the Afghan Mother Lode.” 42 CHAPTER 5 ANALYSIS OF EXTERNAL FACTORS Afghanistan’s future will be determined by

Interest-Driven Model for Human Dynamics

NASA Astrophysics Data System (ADS)

Shang, Ming-Sheng; Chen, Guan-Xiong; Dai, Shuang-Xing; Wang, Bing-Hong; Zhou, Tao

2010-04-01

Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin of such heavy tails, however, it cannot explain all the temporal statistics of human behavior especially for the daily entertainments. We propose an interest-driven model, which can reproduce the power-law distribution of interevent time. The exponent can be analytically obtained and is in good accordance with the simulations. This model well explains the observed relationship between activities and power-law exponents, as reported recently for web-based behavior and the instant message communications.

Effects of film growth kinetics on grain coarsening and grain shape.

PubMed

Reis, F D A Aarão

2017-04-01

We study models of grain nucleation and coarsening during the deposition of a thin film using numerical simulations and scaling approaches. The incorporation of new particles in the film is determined by lattice growth models in three different universality classes, with no effect of the grain structure. The first model of grain coarsening is similar to that proposed by Saito and Omura [Phys. Rev. E 84, 021601 (2011)PLEEE81539-375510.1103/PhysRevE.84.021601], in which nucleation occurs only at the substrate, and the grain boundary evolution at the film surface is determined by a probabilistic competition of neighboring grains. The surface grain density has a power-law decay, with an exponent related to the dynamical exponent of the underlying growth kinetics, and the average radius of gyration scales with the film thickness with the same exponent. This model is extended by allowing nucleation of new grains during the deposition, with constant but small rates. The surface grain density crosses over from the initial power law decay to a saturation; at the crossover, the time, grain mass, and surface grain density are estimated as a function of the nucleation rate. The distributions of grain mass, height, and radius of gyration show remarkable power law decays, similar to other systems with coarsening and particle injection, with exponents also related to the dynamical exponent. The scaling of the radius of gyration with the height h relative to the base of the grain show clearly different exponents in growth dominated by surface tension and growth dominated by surface diffusion; thus it may be interesting for investigating the effects of kinetic roughening on grain morphology. In growth dominated by surface diffusion, the increase of grain size with temperature is observed.

Gravity-darkening exponents in semi-detached binary systems from their photometric observations. II.

NASA Astrophysics Data System (ADS)

Djurašević, G.; Rovithis-Livaniou, H.; Rovithis, P.; Georgiades, N.; Erkapić, S.; Pavlović, R.

2006-01-01

This second part of our study concerning gravity-darkening presents the results for 8 semi-detached close binary systems. From the light-curve analysis of these systems the exponent of the gravity-darkening (GDE) for the Roche lobe filling components has been empirically derived. The method used for the light-curve analysis is based on Roche geometry, and enables simultaneous estimation of the systems' parameters and the gravity-darkening exponents. Our analysis is restricted to the black-body approximation which can influence in some degree the parameter estimation. The results of our analysis are: 1) For four of the systems, namely: TX UMa, β Per, AW Cam and TW Cas, there is a very good agreement between empirically estimated and theoretically predicted values for purely convective envelopes. 2) For the AI Dra system, the estimated value of gravity-darkening exponent is greater, and for UX Her, TW And and XZ Pup lesser than corresponding theoretical predictions, but for all mentioned systems the obtained values of the gravity-darkening exponent are quite close to the theoretically expected values. 3) Our analysis has proved generally that with the correction of the previously estimated mass ratios of the components within some of the analysed systems, the theoretical predictions of the gravity-darkening exponents for stars with convective envelopes are highly reliable. The anomalous values of the GDE found in some earlier studies of these systems can be considered as the consequence of the inappropriate method used to estimate the GDE. 4) The empirical estimations of GDE given in Paper I and in the present study indicate that in the light-curve analysis one can apply the recent theoretical predictions of GDE with high confidence for stars with both convective and radiative envelopes.

Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

PubMed Central

Tredennick, Andrew T.; Bentley, Lisa Patrick; Hanan, Niall P.

2013-01-01

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those predicted by ideal models such as MST. PMID:23484003

On the characteristic exponents of the general three-body problem

NASA Technical Reports Server (NTRS)

Broucke, R.

1976-01-01

A description is given of some properties of the characteristic exponents of the general three-body problem. The variational equations on which the analysis is based are obtained by linearizing the Lagrangian equations of motion in the neighborhood of a given known solution. Attention is given to the fundamental matrix of solutions, the characteristic equation, the three trivial solutions of the variational equations of the three-body problem, symmetric periodic orbits, and the half-period properties of symmetric periodic orbits.

Poincaré recurrences of DNA sequences

NASA Astrophysics Data System (ADS)

Frahm, K. M.; Shepelyansky, D. L.

2012-01-01

We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β≈4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent ν≈0.6 that leads to an anomalous superdiffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than one million base pairs. We argue that the approach based on Poncaré recurrences determines new proximity features between different species and sheds a new light on their evolution history.

A finite-time exponent for random Ehrenfest gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moudgalya, Sanjay; Chandra, Sarthak; Jain, Sudhir R., E-mail: srjain@barc.gov.in

2015-10-15

We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in amore » way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.« less

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

PubMed Central

Dziarmaga, Jacek; Zurek, Wojciech H.

2014-01-01

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

Dynamics of social contagions with limited contact capacity.

PubMed

Wang, Wei; Shu, Panpan; Zhu, Yu-Xiao; Tang, Ming; Zhang, Yi-Cheng

2015-10-01

Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacities. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each adopted individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. There is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.