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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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

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.

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.

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

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.

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

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.

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

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.

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

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.

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

Probe-Independent EEG Assessment of Mental Workload in Pilots

DTIC Science & Technology

2015-05-18

Teager Energy Operator - Frequency Modulated Component - z- score 10.94 17.46 10 Hurst Exponent - Discrete Second Order Derivative 7.02 17.06 D. Best...Teager Energy Operator– Frequency Modulated Component – Z-score 45. Line Length – Time Series 46. Line Length – Time Series – Z-score 47. Hurst Exponent ...Discrete Second Order Derivative 48. Hurst Exponent – Wavelet Based Adaptation 49. Hurst Exponent – Rescaled Range 50. Hurst Exponent – Discrete

Influence of Progressive Central Hypovolemia on Multifractal Dimension of Cardiac Interbeat Intervals

DTIC Science & Technology

2010-05-07

by an exponent that he called H in honor of Hurst . 4 Consequently, if X(t) is a fractal process with Hurst exponent H and c is a constant, then X (t...1−2H ≈ f−1−2h0 , (1) where f is the frequency, H is the Hurst exponent and h0 is the average of the Hölder exponent distribution among the...infinitely long monofractal time series. Figure 2 shows a computer generated realization of fGn with Hurst exponent H = 1 or Hölder exponent h0 ≈ 0

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.

Robust Multimodal Cognitive Load Measurement

DTIC Science & Technology

2014-03-26

dimension, Hurst exponent ) of electroencephalogram (EEG) signals to evaluate changes in working memory load during the performance of a cognitive task...dimension, Hurst exponent ) of electroencephalogram (EEG) signals to evaluate changes in working memory load during the performance of a cognitive task with...approximate entropies, wavelet-based complexity measures, correlation dimension, Hurst exponent ) of electroencephalogram (EEG) signals to evaluate changes

Cyberspace Math Models

DTIC Science & Technology

2013-06-01

or indicators are used as long range memory measurements. Hurst and Holder exponents are the most important and popular parameters. Traditionally...the relation between two important parameters, the Hurst exponent (measurement of global long range memory) and the Entropy (measurement of...empirical results and future study. II. BACKGROUND We recall briey the mathematical and statistical definitions and properties of the Hurst exponents

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.

Physiological Signals and Their Fractal Response to Stress Conditions, Environmental Changes and Neurodegenerative Diseases

DTIC Science & Technology

2006-11-01

exponent H=(β+1)/2 and from the fractal dimension D=2- H. The algorithms used to estimate the Hurst exponent directly are usually quite simple and...yields a curve of the type D(τ)=cτH, where c is an opportune constant and H is the Hurst exponent [Scafetta and Grigolini, 2002]. 1 Report Documentation...memory of past events. It is largely expected that the Hurst exponent , which measures the strength of this memory, evolves as a response

The Effects of a Lower Body Exoskeleton Load Carriage Assistive Device on Limits of Stability and Postural Sway

DTIC Science & Technology

2006-11-01

can be determined (Collins and De Luca, 1993). The parameter of interest in this study was the Hurst scaling exponent (0 < H < 1), a dimensionless...LOS measures, the traditional postural sway measures (COPBX, COPBY COPB, COPLX, COPLY, COPLR), and on the six Hurst 5 exponents . In analyses in...included in Tables 2 and 3, respectively. The summary data for each of the Hurst exponents are in Table 4. Table 2. Means (and Standard

Application of an Entropic Approach to Assessing Systems Integration

DTIC Science & Technology

2012-03-01

two econometrical measures of information efficiency – Shannon entropy and Hurst exponent . Shannon entropy (which is explained in Chapter III) can be...applied to evaluate long-term correlation of time series, while Hurst exponent can be applied to classify the time series in accordance to existence...of trend. Hurst exponent is the statistical measure of time series long-range dependence, and its value falls in the interval [0, 1] – a value in

Multiscale Modeling of Stiffness, Friction and Adhesion in Mechanical Contacts

DTIC Science & Technology

2012-02-29

over a lateral length l scales as a power law: h  lH, where H is called the Hurst exponent . For typical experimental surfaces, H ranges from 0.5 to 0.8...surfaces with a wide range of Hurst exponents using fully atomistic calculations and the Green’s function method. A simple relation like Eq. (2...described above to explore a full range of parameter space with different rms roughness h0, rms slope h’0, Hurst exponent H, adhesion energy

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

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.

32 CFR 516.62 - PFD and HQ USACIDC coordination.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 32 National Defense 3 2010-07-01 2010-07-01 true PFD and HQ USACIDC coordination. 516.62 Section 516.62 National Defense Department of Defense (Continued) DEPARTMENT OF THE ARMY AID OF CIVIL AUTHORITIES AND PUBLIC RELATIONS LITIGATION Remedies in Procurement Fraud and Corruption § 516.62 PFD and HQ...

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.

[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.

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

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

Modeling Complex Phenomena Using Multiscale Time Sequences

DTIC Science & Technology

2009-08-24

measures based on Hurst and Holder exponents , auto-regressive methods and Fourier and wavelet decomposition methods. The applications for this technology...relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and Holder exponents , auto-regressive...different scales and how these scales relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and

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.

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

Analysis of field errors for LARP Nb 3Sn HQ03 quadrupole magnet

DOE PAGES

Wang, Xiaorong; Ambrosio, Giorgio; Chlachidze, Guram; ...

2016-12-01

The U.S. LHC Accelerator Research Program, in close collaboration with CERN, has developed three generations of high-gradient quadrupole (HQ) Nb 3Sn model magnets, to support the development of the 150 mm aperture Nb 3Sn quadrupole magnets for the High-Luminosity LHC. The latest generation, HQ03, featured coils with better uniformity of coil dimensions and properties than the earlier generations. We tested the HQ03 magnet at FNAL, including the field quality study. The profiles of low-order harmonics along the magnet aperture observed at 15 kA, 1.9 K can be traced back to the assembled coil pack before the magnet assembly. Based onmore » the measured harmonics in the magnet center region, the coil block positioning tolerance was analyzed and compared with earlier HQ01 and HQ02 magnets to correlate with coil and magnet fabrication. Our study the capability of correcting the low-order non-allowed field errors, magnetic shims were installed in HQ03. Furthermore, the expected shim contribution agreed well with the calculation. For the persistent-current effect, the measured a4 can be related to 4% higher in the strand magnetization of one coil with respect to the other three coils. Lastly, we compare the field errors due to the inter-strand coupling currents between HQ03 and HQ02.« less

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

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.

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.

Test results of the LARP Nb$$_3$$Sn quadrupole HQ03a

DOE PAGES

DiMarco, J.; G. Ambrosio; Chlachidze, G.; ...

2016-03-09

The US LHC Accelerator Research Program (LARP) has been developingmore » $$Nb_3Sn$$ quadrupoles of progressively increasing performance for the high luminosity upgrade of the Large Hadron Collider. The 120 mm aperture High-field Quadrupole (HQ) models are the last step in the R&D phase supporting the development of the new IR Quadrupoles (MQXF). Three series of HQ coils were fabricated and assembled in a shell-based support structure, progressively optimizing the design and fabrication process. The final set of coils consistently applied the optimized design solutions, and was assembled in the HQ03a model. Furthermore, this paper reports a summary of the HQ03a test results, including training, mechanical performance, field quality and quench studies.« less

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.

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.

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.

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

32 CFR 842.12 - HQ USAF claims responsibility.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Administrative Management Program (CAMP) reviews. (2) Implements claims and tort litigation policies, issues... LITIGATION ADMINISTRATIVE CLAIMS Functions and Responsibilities § 842.12 HQ USAF claims responsibility. (a...

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.

The long memory and the transaction cost in financial markets

NASA Astrophysics Data System (ADS)

Li, Daye; Nishimura, Yusaku; Men, Ming

2016-01-01

In the present work, we investigate the fractal dimensions of 30 important stock markets from 2006 to 2013; the analysis indicates that the Hurst exponent of emerging markets shifts significantly away from the standard Brownian motion. We propose a model based on the Hurst exponent to explore the considerable profits from the predictable long-term memory. We take the transaction cost into account to justify why the market inefficiency has not been arbitraged away in the majority of cases. The empirical evidence indicates that the majority of the markets are efficient with a certain transaction cost under the no-arbitrage assumption. Furthermore, we use the Monte Carlo simulation to display "the efficient frontier" of the Hurst exponent with different transaction costs.

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.

Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Lim, S. C.; Murugan, R.

2001-12-01

In this paper, we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to Malaysian currency, Ringgit Malaysia. These time series are examined piecewise before and after the currency control imposed in 1st September 1998 using the monofractal model based on fractional Brownian motion. The global Hurst exponents are determined using the R/ S analysis, the detrended fluctuation analysis and the method of second moment using the correlation coefficients. The limitation of these monofractal analyses is discussed. The usual multifractal analysis reveals that there exists a wide range of Hurst exponents in each of the time series. A new method of modelling the multifractal time series based on multifractional Brownian motion with time-varying Hurst exponents is studied.

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.

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.

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.

Application of wavelet based MFDFA on Mueller matrix images for cervical pre-cancer detection

NASA Astrophysics Data System (ADS)

Zaffar, Mohammad; Pradhan, Asima

2018-02-01

A systematic study has been conducted on application of wavelet based multifractal de-trended fluctuation analysis (MFDFA) on Mueller matrix (MM) images of cervical tissue sections for early cancer detection. Changes in multiple scattering and orientation of fibers are observed by utilizing a discrete wavelet transform (Daubechies) which identifies fluctuations over polynomial trends. Fluctuation profiles, after 9th level decomposition, for all elements of MM qualitatively establish a demarcation of different grades of cancer from normal tissue. Moreover, applying MFDFA on MM images, Hurst exponent profiles for images of MM qualitatively are seen to display differences. In addition, the values of Hurst exponent increase for the diagonal elements of MM with increasing grades of the cervical cancer, while the value for the elements which correspond to linear polarizance decrease. However, for circular polarizance the value increases with increasing grades. These fluctuation profiles reveal the trend of local variation of refractive -indices and along with Hurst exponent profile, may serve as a useful biological metric in the early detection of cervical cancer. The quantitative measurements of Hurst exponent for diagonal and first column (polarizance governing elements) elements which reflect changes in multiple scattering and structural anisotropy in stroma, may be sensitive indicators of pre-cancer.

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.

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.

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.

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

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

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.

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

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.

Field Quality and Fabrication Analysis of HQ02 Reconstructed Nb3Sn Coil Cross Sections

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

Holik, Eddie Frank; Ambrosio, Giorgio; Carbonara, Andrea

2017-01-23

The US LHC Accelerator Research Program (LARP) quadrupole HQ02 was designed and fully tested as part of the low-beta quad development for Hi-Lumi LHC. HQ02’s design is well documented with full fabrication accounting along with full field analysis at low and high current. With this history, HQ02 is an excellent test bed for developing a methodology for measuring turn locations from magnet cross sections and comparing with CAD models and measured field. All 4 coils of HQ02 were cut in identical locations along the magnetic length corresponding to magnetic field measurement and coil metrology. A real-time camera and coordinate measuringmore » equipment was used to plot turn corners. Measurements include systematic and random displacements of winding blocks and individual turns along the magnetic length. The range of cable shifts and the field harmonic range along the length are in agreement, although correlating turn locations and measured harmonics in each cross section is challenging.« less

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.

32 CFR 516.62 - PFD and HQ USACIDC coordination.

Code of Federal Regulations, 2011 CFR

2011-07-01

... AUTHORITIES AND PUBLIC RELATIONS LITIGATION Remedies in Procurement Fraud and Corruption § 516.62 PFD and HQ... procurement fraud or corruption investigations being conducted by USACIDC and possible remedies. These... affected by a significant investigation of fraud or corruption that relates to DOD procurement activities...

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.

Short-Exponent RSA

NASA Astrophysics Data System (ADS)

Sun, Hung-Min; Yang, Cheng-Ta; Wu, Mu-En

In some applications, a short private exponent d is chosen to improve the decryption or signing process for RSA public key cryptosystem. However, in a typical RSA, if the private exponent d is selected first, the public exponent e should be of the same order of magnitude as φ(N). Sun et al. devised three RSA variants using unbalanced prime factors p and q to lower the computational cost. Unfortunately, Durfee & Nguyen broke the illustrated instances of the first and third variants by solving small roots to trivariate modular polynomial equations. They also indicated that the instances with unbalanced primes p and q are more insecure than the instances with balanced p and q. This investigation focuses on designing a new RSA variant with balanced p and q, and short exponents d and e, to improve the security of an RSA variant against the Durfee & Nguyen's attack, and the other existing attacks. Furthermore, the proposed variant (Scheme A) is also extended to another RSA variant (Scheme B) in which p and q are balanced, and a trade-off between the lengths of d and e is enable. In addition, we provide the security analysis and feasibility analysis of the proposed schemes.

85. Command HQ. SAC control center (MOD) new work cross ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

85. Command HQ. SAC control center (MOD) new work cross section, drawing number AW-30-02-07, dated 7 February, 1962 - Offutt Air Force Base, Strategic Air Command Headquarters & Command Center, Headquarters Building, 901 SAC Boulevard, Bellevue, Sarpy County, NE

Evaluation of the highly sensitive chemiluminescent enzyme immunoassay "Lumipulse HBsAg-HQ" for hepatitis B virus screening.

PubMed

Deguchi, Matsuo; Kagita, Masanori; Yoshioka, Nori; Tsukamoto, Hiroko; Takao, Miyuki; Tahara, Kazuko; Maeda, Ikuhiro; Hidaka, Yoh; Yamauchi, Satoshi; Kaneko, Atsushi; Miyakoshi, Hideo; Isomura, Mitsuo

2017-10-06

Ongoing efforts in the development of HBsAg detection kits are focused on improving sensitivity and specificity. The purpose of this study was to evaluate an improved, highly sensitive quantitative assay, "Lumipulse HBsAg-HQ", a chemiluminescent enzyme immunoassay designed for a fully automated instrument, the "Lumipulse G1200". Serum samples for reproducibility, dilution, correlation, sensitivity, and specificity studies were obtained from patients at the Osaka University Hospital. Seroconversion and sensitivity panels were purchased from a commercial vender. Subtype, sensitivity panels, and HBsAg recombinant proteins with one or two amino acid substitutions were prepared in-house. The coefficients of variation for the low, medium, and high concentration samples ranged from 1.93 to 2.55%. The HBsAg-HQ reagent for dilution testing showed good linearity in the 0.005-150 HBsAg IU/mL range and no prozone phenomenon. All 102 HBV carrier samples were positive by HBsAg-HQ, while other commercial reagents showed one or more to be negative. In the seroconversion panel, the 14-day blood sample was positive. The sensitivity against HBsAg-HQ "ad" and "ay" subtypes was 0.025 ng/mL. Comparisons among the HBsAg-HQ, HISCL, and Architect HBsAg reagents were performed using the Bland-Altman plot. Specificity for 1000 seronegative individuals was 99.7%. HBsAg-HQ detected 29 positive serum among 12 231 routinely obtained serum samples, which showed concentrations of 0.005-0.05 HBsAg IU/mL. According to these results, the Lumipulse HBsAg-HQ assay, with a highly sensitive limit of detection of 0.005 IU/mL, may facilitate the development of a better management strategy for a considerable proportion of infected patients. © 2017 Wiley Periodicals, Inc.

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.

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).

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

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.

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

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.

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

23. H.Q. Morton photograph #47 'South Light, Fog Horn from ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

23. H.Q. Morton photograph #47 'South Light, Fog Horn from Bluff', (view looking NE) ca. 1880. (H. Q. Morton, Photographer, 75 Westminster Street, Providence, RI. - Block Island Southeast Light, Spring Street & Mohegan Trail at Mohegan Bluffs, New Shoreham, Washington County, RI

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.

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

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.

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.

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

Apex Exponents for Polymer-Probe Interactions

NASA Astrophysics Data System (ADS)

Zandi, Roya; Slutsky, Michael; Kantor, Yacov

2005-03-01

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents γ1 and γ2, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip's angle. These apex exponents are calculated analytically by ɛ-expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.

Apex Exponents for Polymer-Probe Interactions

NASA Astrophysics Data System (ADS)

Slutsky, Michael; Zandi, Roya; Kantor, Yacov; Kardar, Mehran

2005-05-01

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents γ1 and γ2, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip’s angle. These apex exponents are calculated analytically by ɛ expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.

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

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 0.5Hurst exponents, and make a physical interpretation of the results. An application is made to the time evolution of seismicity in the Betic Cordillera (Southern Spain), and in the Marmara Region (Turkey).

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.

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

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.

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.

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

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

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.

Sample and population exponents of generalized Taylor's law.

PubMed

Giometto, Andrea; Formentin, Marco; Rinaldo, Andrea; Cohen, Joel E; Maritan, Amos

2015-06-23

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.

Choosing the Allometric Exponent in Covariate Model Building.

PubMed

Sinha, Jaydeep; Al-Sallami, Hesham S; Duffull, Stephen B

2018-04-27

Allometric scaling is often used to describe the covariate model linking total body weight (WT) to clearance (CL); however, there is no consensus on how to select its value. The aims of this study were to assess the influence of between-subject variability (BSV) and study design on (1) the power to correctly select the exponent from a priori choices, and (2) the power to obtain unbiased exponent estimates. The influence of WT distribution range (randomly sampled from the Third National Health and Nutrition Examination Survey, 1988-1994 [NHANES III] database), sample size (N = 10, 20, 50, 100, 200, 500, 1000 subjects), and BSV on CL (low 20%, normal 40%, high 60%) were assessed using stochastic simulation estimation. A priori exponent values used for the simulations were 0.67, 0.75, and 1, respectively. For normal to high BSV drugs, it is almost impossible to correctly select the exponent from an a priori set of exponents, i.e. 1 vs. 0.75, 1 vs. 0.67, or 0.75 vs. 0.67 in regular studies involving < 200 adult participants. On the other hand, such regular study designs are sufficient to appropriately estimate the exponent. However, regular studies with < 100 patients risk potential bias in estimating the exponent. Those study designs with limited sample size and narrow range of WT (e.g. < 100 adult participants) potentially risk either selection of a false value or yielding a biased estimate of the allometric exponent; however, such bias is only relevant in cases of extrapolating the value of CL outside the studied population, e.g. analysis of a study of adults that is used to extrapolate to children.

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.

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.

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.

Measurements and analysis of dynamic effects in the LARP model quadrupole HQ02b during rapid discharge

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

Sorbi, Massimo; Ambrosio, Giorgio; Bajas, Hugo

This paper presents the analysis of some quench tests addressed to study the dynamic effects in the 1-m-long 120-mm-aperture Nb 3Sn quadrupole magnet, i.e., HQ02b, designed, fabricated, and tested by the LHC Accelerator Research Program. The magnet has a short sample gradient of 205 T/m at 1.9 K and a peak field of 14.2 T. The test campaign has been performed at CERN in April 2014. In the specific tests, which were dedicated to the measurements of the dynamic inductance of the magnet during the rapid current discharge for a quench, the protection heaters were activated only in some windings,more » in order to obtain the measure of the resistive and inductive voltages separately. The analysis of the results confirms a very low value of the dynamic inductance at the beginning of the discharge, which later approaches the nominal value. Indications of dynamic inductance variation were already found from the analysis of current decay during quenches in the previous magnets HQ02a and HQ02a2; however, with this dedicated test of HQ02b, a quantitative measurement and assessment has been possible. An analytical model using interfilament coupling current influence for the inductance lowering has been implemented in the quench calculation code QLASA, and the comparison with experimental data is given. In conclusion, the agreement of the model with the experimental results is very good and allows predicting more accurately the critical parameters in quench analysis (MIITs, hot spot temperature) for the MQXF Nb3Sn quadrupoles, which will be installed in the High Luminosity LHC.« less

Measurements and analysis of dynamic effects in the LARP model quadrupole HQ02b during rapid discharge

DOE PAGES

Sorbi, Massimo; Ambrosio, Giorgio; Bajas, Hugo; ...

2016-06-01

This paper presents the analysis of some quench tests addressed to study the dynamic effects in the 1-m-long 120-mm-aperture Nb 3Sn quadrupole magnet, i.e., HQ02b, designed, fabricated, and tested by the LHC Accelerator Research Program. The magnet has a short sample gradient of 205 T/m at 1.9 K and a peak field of 14.2 T. The test campaign has been performed at CERN in April 2014. In the specific tests, which were dedicated to the measurements of the dynamic inductance of the magnet during the rapid current discharge for a quench, the protection heaters were activated only in some windings,more » in order to obtain the measure of the resistive and inductive voltages separately. The analysis of the results confirms a very low value of the dynamic inductance at the beginning of the discharge, which later approaches the nominal value. Indications of dynamic inductance variation were already found from the analysis of current decay during quenches in the previous magnets HQ02a and HQ02a2; however, with this dedicated test of HQ02b, a quantitative measurement and assessment has been possible. An analytical model using interfilament coupling current influence for the inductance lowering has been implemented in the quench calculation code QLASA, and the comparison with experimental data is given. In conclusion, the agreement of the model with the experimental results is very good and allows predicting more accurately the critical parameters in quench analysis (MIITs, hot spot temperature) for the MQXF Nb3Sn quadrupoles, which will be installed in the High Luminosity LHC.« less

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.

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.

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

Lyapunov exponent for aging process in induction motor

NASA Astrophysics Data System (ADS)

Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat

2012-09-01

Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly

Recent UAS Developments: VTOL HQ-series Shipboard Recovery and Autonomous Monitoring with MicroQuads

NASA Astrophysics Data System (ADS)

Wardell, L. J.; Farber, A. M.; Douglas, J.

2017-12-01

Ocean research would benefit from reliable shipboard launch and recovery of small class UAS. The vertical take-off and landing (VTOL) system reduces equipment footprint without the need for launchers or recovery systems. The HQ-60 (Latitude Engineering) has demonstrated reliable ship take-off and recovery on a 10x10' area on the R/V Falkor (Schmidt Ocean Institute) and other research vessels. The HQ-60 recently set a record for longest time aloft for a VTOL aircraft, flying nearly 22.5 hours non-stop. To support close-range research, autonomous MicroQuads that "perch" in a protective box that also recharges the aircraft and transmits the data is in development. Recent MicroQuad work with developing high-resolution (<1cm) DEMs using on-board cameras has yielded promising results for the use of surface change detection. Recent USDA development targeted erosion monitoring with this system. The latest updates and testing results for both systems will be presented.

Development and initial cohort validation of the Arthritis Research UK Musculoskeletal Health Questionnaire (MSK-HQ) for use across musculoskeletal care pathways

PubMed Central

Hill, Jonathan C; Kang, Sujin; Benedetto, Elena; Myers, Helen; Blackburn, Steven; Smith, Stephanie; Hay, Elaine; Rees, Jonathan; Beard, David; Glyn-Jones, Sion; Barker, Karen; Ellis, Benjamin; Fitzpatrick, Ray; Price, Andrew

2016-01-01

Objectives Current musculoskeletal outcome tools are fragmented across different healthcare settings and conditions. Our objectives were to develop and validate a single musculoskeletal outcome measure for use throughout the pathway and patients with different musculoskeletal conditions: the Arthritis Research UK Musculoskeletal Health Questionnaire (MSK-HQ). Setting A consensus workshop with stakeholders from across the musculoskeletal community, workshops and individual interviews with a broad mix of musculoskeletal patients identified and prioritised outcomes for MSK-HQ inclusion. Initial psychometric validation was conducted in four cohorts from community physiotherapy, and secondary care orthopaedic hip, knee and shoulder clinics. Participants Stakeholders (n=29) included primary care, physiotherapy, orthopaedic and rheumatology patients (n=8); general practitioners, physiotherapists, orthopaedists, rheumatologists and pain specialists (n=7), patient and professional national body representatives (n=10), and researchers (n=4). The four validation cohorts included 570 participants (n=210 physiotherapy, n=150 hip, n=150 knee, n=60 shoulder patients). Outcome measures Outcomes included the MSK-HQ's acceptability, feasibility, comprehension, readability and responder burden. The validation cohort outcomes were the MSK-HQ's completion rate, test–retest reliability and convergent validity with reference standards (EQ-5D-5L, Oxford Hip, Knee, Shoulder Scores, and the Keele MSK-PROM). Results Musculoskeletal domains prioritised were pain severity, physical function, work interference, social interference, sleep, fatigue, emotional health, physical activity, independence, understanding, confidence to self-manage and overall impact. Patients reported MSK-HQ items to be ‘highly relevant’ and ‘easy to understand’. Completion rates were high (94.2%), with scores normally distributed, and no floor/ceiling effects. Test–retest reliability was excellent, and

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

Estimation of Renyi exponents in random cascades

USGS Publications Warehouse

Troutman, Brent M.; Vecchia, Aldo V.

1999-01-01

We consider statistical estimation of the Re??nyi exponent ??(h), which characterizes the scaling behaviour of a singular measure ?? defined on a subset of Rd. The Re??nyi exponent is defined to be lim?????0 [{log M??(h)}/(-log ??)], assuming that this limit exists, where M??(h) = ??i??h(??i) and, for ??>0, {??i} are the cubes of a ??-coordinate mesh that intersect the support of ??. In particular, we demonstrate asymptotic normality of the least-squares estimator of ??(h) when the measure ?? is generated by a particular class of multiplicative random cascades, a result which allows construction of interval estimates and application of hypothesis tests for this scaling exponent. Simulation results illustrating this asymptotic normality are presented. ?? 1999 ISI/BS.

A novel methodology for radiative transfer in a planetary atmosphere. I - The functions a exponent m and b exponent m of anisotropic scattering

NASA Technical Reports Server (NTRS)

Fymat, A. L.; Kalaba, R. E.

1977-01-01

The original problem of anisotropic scattering in an atmosphere illuminated by a unidirectional source is replaced by an analogous formulation where the incident light is omnidirectional. A radiative-transfer equation for the omnidirectional case is obtained in which the direction of illumination plays no role and the source-function analog, Sobolev's (1972) source function Phi exponent m, contains only a single integral term. For radiation incident on the top or the bottom of the atmosphere, this equation involves the functions b exponent m and h exponent m, respectively, with m corresponding to the order of the harmonic component of the scattered radiation field; these two functions are shown to be only one through some simple reciprocity relations. The transfer problem is then reformulated for the function a exponent m, in which case the source-function analog (Sobolev's function D exponent m) involves incident direction.

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

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

Hazardous Waste Cleanup: HQ 10th MTN Division & Fort Drum in Fort Drum, New York

EPA Pesticide Factsheets

HQ 10th MTN Division & Fort Drum facility is located at Jones Street and Off North Memorial Drive, in Fort Drum, in the northern portion of New York State approximately 10 miles northeast of Watertown. Fort Drum is the largest Army installation in the nort

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.

Development and initial cohort validation of the Arthritis Research UK Musculoskeletal Health Questionnaire (MSK-HQ) for use across musculoskeletal care pathways.

PubMed

Hill, Jonathan C; Kang, Sujin; Benedetto, Elena; Myers, Helen; Blackburn, Steven; Smith, Stephanie; Dunn, Kate M; Hay, Elaine; Rees, Jonathan; Beard, David; Glyn-Jones, Sion; Barker, Karen; Ellis, Benjamin; Fitzpatrick, Ray; Price, Andrew

2016-08-05

Current musculoskeletal outcome tools are fragmented across different healthcare settings and conditions. Our objectives were to develop and validate a single musculoskeletal outcome measure for use throughout the pathway and patients with different musculoskeletal conditions: the Arthritis Research UK Musculoskeletal Health Questionnaire (MSK-HQ). A consensus workshop with stakeholders from across the musculoskeletal community, workshops and individual interviews with a broad mix of musculoskeletal patients identified and prioritised outcomes for MSK-HQ inclusion. Initial psychometric validation was conducted in four cohorts from community physiotherapy, and secondary care orthopaedic hip, knee and shoulder clinics. Stakeholders (n=29) included primary care, physiotherapy, orthopaedic and rheumatology patients (n=8); general practitioners, physiotherapists, orthopaedists, rheumatologists and pain specialists (n=7), patient and professional national body representatives (n=10), and researchers (n=4). The four validation cohorts included 570 participants (n=210 physiotherapy, n=150 hip, n=150 knee, n=60 shoulder patients). Outcomes included the MSK-HQ's acceptability, feasibility, comprehension, readability and responder burden. The validation cohort outcomes were the MSK-HQ's completion rate, test-retest reliability and convergent validity with reference standards (EQ-5D-5L, Oxford Hip, Knee, Shoulder Scores, and the Keele MSK-PROM). Musculoskeletal domains prioritised were pain severity, physical function, work interference, social interference, sleep, fatigue, emotional health, physical activity, independence, understanding, confidence to self-manage and overall impact. Patients reported MSK-HQ items to be 'highly relevant' and 'easy to understand'. Completion rates were high (94.2%), with scores normally distributed, and no floor/ceiling effects. Test-retest reliability was excellent, and convergent validity was strong (correlations 0.81-0.88). A new

Quilamine HQ1-44, an iron chelator vectorized toward tumor cells by the polyamine transport system, inhibits HCT116 tumor growth without adverse effect.

PubMed

Renaud, Stéphanie; Corcé, Vincent; Cannie, Isabelle; Ropert, Martine; Lepage, Sylvie; Loréal, Olivier; Deniaud, David; Gaboriau, François

2015-08-01

Tumor cell growth requires large iron quantities and the deprivation of this metal induced by synthetic metal chelators is therefore an attractive method for limiting the cancer cell proliferation. The antiproliferative effect of the Quilamine HQ1-44, a new iron chelator vectorized toward tumor cells by a polyamine chain, is related to its high selectivity for the Polyamine Transport System (PTS), allowing its preferential uptake by tumoral cells. The difference in PTS activation between healthy cells and tumor cells enables tumor cells to be targeted, whereas the strong dependence of these cells on iron ensures a secondary targeting. Here, we demonstrated in vitro that HQ1-44 inhibits DNA synthesis and cell proliferation of HCT116 cells by modulating the intracellular metabolism of both iron and polyamines. Moreover, in vivo, in xenografted athymic nude mice, we found that HQ1-44 was as effective as cis-platin in reducing HCT116 tumor growth, without its side effects. Furthermore, as suggested by in vitro data, the depletion in exogenous or endogenous polyamines, known to activate the PTS, dramatically enhanced the antitumor efficiency of HQ1-44. These data support the need for further studies to assess the value of HQ1-44 as an adjuvant treatment in cancer. Copyright © 2015 Elsevier Inc. All rights reserved.

The Evolution of the Exponent of Zipf's Law in Language Ontogeny

PubMed Central

Baixeries, Jaume; Elvevåg, Brita; Ferrer-i-Cancho, Ramon

2013-01-01

It is well-known that word frequencies arrange themselves according to Zipf's law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf's law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf's law and linguistic complexity are inter-related. The assumption that Zipf's law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised. PMID:23516390

Calculating Lyapunov Exponents: Applying Products and Evaluating Integrals

ERIC Educational Resources Information Center

McCartney, Mark

2010-01-01

Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…

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

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

75 FR 33610 - Application To Export Electric Energy; H.Q. Energy Services (U.S.) Inc.

Federal Register 2010, 2011, 2012, 2013, 2014

2010-06-14

... DEPARTMENT OF ENERGY [OE Docket No. EA-182-C] Application To Export Electric Energy; H.Q. Energy... electric energy from the United States to Canada pursuant to section 202(e) of the Federal Power Act (FPA... transmit electric energy from the United States to Canada as a power marketer using existing international...

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.

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.

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.

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

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.

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.

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.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Lyapunov exponents for infinite dimensional dynamical systems

NASA Technical Reports Server (NTRS)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Large N critical exponents for the chiral Heisenberg Gross-Neveu universality class

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2018-05-01

We compute the large N critical exponents η , ηϕ and 1 /ν in d dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of 1 /N . For instance, the large N conformal bootstrap method is used to determine η at O (1 /N3) while the other exponents are computed to O (1 /N2). Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behavior of the exponents in 2 exponent near four dimensions is in exact agreement with recent four loop perturbation theory.

Quantitative determination of a synthetic amide derivative of gallic acid, SG-HQ2, using liquid chromatography tandem mass spectrometry, and its pharmacokinetics in rats.

PubMed

Seo, Seung-Yong; Kang, Wonku

2016-11-30

An amide derivative of gallic acid (GA), 3,4,5-trihydroxy-N-(8-hydroxyquinolin-2-yl)benzamide) (SG-HQ2) was recently synthesized, and its inhibitory actions were previously shown on histamine release and pro-inflammatory cytokine expression. In this study, a simultaneous quantification method was developed for the determination of SG-HQ2 and its possible metabolite, GA, in rat plasma using liquid chromatography with a tandem mass spectrometry (LC-MS/MS). After simple protein precipitation with acetonitrile including diclofenac (internal standard, IS), the analytes were chromatographed on a reversed phased column with a mobile phase of acetonitrile and water (60:40, v/v, including 0.1% formic acid). The ion transitions of the precursor to the product ion were principally protonated ion [M+H] + at m/z 313.2→160.6 for SG-HQ2, and deprotonated ions [M-H] - at m/z 168.7→124.9 for GA and 296.0→251.6 for the IS. The accuracy and precision of the assay were in accordance with FDA regulations for the validation of bioanalytical methods. This method was successfully applied to a pharmacokinetic study of SG-HQ2 after intravenous administration in rats. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

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.

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.

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

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

Condensation and critical exponents of an ideal non-Abelian gas

NASA Astrophysics Data System (ADS)

Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein

2017-11-01

We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.

Meteoroid stream flux densities and the zenith exponent

NASA Astrophysics Data System (ADS)

Molau, Sirko; Barentsen, Geert

2013-01-01

The MetRec software was recently extended to measure the limiting magnitude in real-time, and to determine meteoroid stream flux densities. This paper gives a short overview of the applied algorithms. We introduce the MetRec Flux Viewer, a web tool to visualize activity profiles on- line. Starting from the Lyrids 2011, high-quality flux density profiles were derived from IMO Video Network observations for every major meteor shower. They are often in good agreement with visual data. Analyzing the 2011 Perseids, we found systematic daily variations in the flux density profile, which can be attributed to a zenith exponent gamma > 1.0. We analyzed a number of meteor showers in detail and found zenith exponent variations from shower to shower in the range between 1.55 and 2.0. The average value over all analyzed showers is gamma = 1.75. In order to determine the zenith exponent precisely, the observations must cover a large altitude range (at least 45 degrees).

Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures

NASA Astrophysics Data System (ADS)

Kissel, Glen J.

2011-10-01

Existing in the "gray area" between perfectly periodic and purely randomized photonic bandgap structures are the socalled aperoidic structures whose layers are chosen according to some deterministic rule. We consider here a onedimensional photonic bandgap structure, a quarter-wave stack, with the layer thickness of one of the bilayers subject to being either thin or thick according to five deterministic sequence rules and binary random selection. To produce these aperiodic structures we examine the following sequences: Fibonacci, Thue-Morse, Period doubling, Rudin-Shapiro, as well as the triadic Cantor sequence. We model these structures numerically with a long chain (approximately 5,000,000) of transfer matrices, and then use the reliable algorithm of Wolf to calculate the (upper) Lyapunov exponent for the long product of matrices. The Lyapunov exponent is the statistically well-behaved variable used to characterize the Anderson localization effect (exponential confinement) when the layers are randomized, so its calculation allows us to more precisely compare the purely randomized structure with its aperiodic counterparts. It is found that the aperiodic photonic systems show much fine structure in their Lyapunov exponents as a function of frequency, and, in a number of cases, the exponents are quite obviously fractal.

The Morphosyntax of Discontinuous Exponence

ERIC Educational Resources Information Center

Campbell, Amy Melissa

2012-01-01

This thesis offers a systematic treatment of discontinuous exponence, a pattern of inflection in which a single feature or a set of features bundled in syntax is expressed by multiple, distinct morphemes. This pattern is interesting and theoretically relevant because it represents a deviation from the expected one-to-one relationship between…

Lyapunov exponents of stochastic systems—from micro to macro

NASA Astrophysics Data System (ADS)

Laffargue, Tanguy; Tailleur, Julien; van Wijland, Frédéric

2016-03-01

Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the ‘same noise realization’. The purpose of this work is to critically examine what this expression means. For Brownian particles, we consider two natural interpretations of the noise: intrinsic to the particles or stemming from the fluctuations of the environment. We show how they lead to different distributions of the largest Lyapunov exponent as well as different fluctuating hydrodynamics for the collective density field. We discuss, both at microscopic and macroscopic levels, the limits in which these noise prescriptions become equivalent. We close this paper by providing an estimate of the largest Lyapunov exponent and of its fluctuations for interacting particles evolving with Dean-Kawasaki dynamics.

Scaling exponents for ordered maxima

DOE PAGES

Ben-Naim, E.; Krapivsky, P. L.; Lemons, N. W.

2015-12-22

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S N that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S N is universal: it does not depend on themore » distribution from which the random variables are drawn. For two sequences, S N~N –1/2, and in general, the decay is algebraic, S N~N –σm, for large N. We analytically obtain the exponent σ 3≅1.302931 as root of a transcendental equation. Moreover, the exponents σ m grow with m, and we show that σ m~m for large m.« less

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.

Laminar Flame Velocity and Temperature Exponent of Diluted DME-Air Mixture

NASA Astrophysics Data System (ADS)

Naseer Mohammed, Abdul; Anwar, Muzammil; Juhany, Khalid A.; Mohammad, Akram

2017-03-01

In this paper, the laminar flame velocity and temperature exponent diluted dimethyl ether (DME) air mixtures are reported. Laminar premixed mixture of DME-air with volumetric dilutions of carbon dioxides (CO2) and nitrogen (N2) are considered. Experiments were conducted using a preheated mesoscale high aspect-ratio diverging channel with inlet dimensions of 25 mm × 2 mm. In this method, flame velocities are extracted from planar flames that were stabilized near adiabatic conditions inside the channel. The flame velocities are then plotted against the ratio of mixture temperature and the initial reference temperature. A non-linear power law regression is observed suitable. This regression analysis gives the laminar flame velocity at the initial reference temperature and temperature exponent. Decrease in the laminar flame velocity and increase in temperature exponent is observed for CO2 and N2 diluted mixtures. The addition of CO2 has profound influence when compared to N2 addition on both flame velocity and temperature exponent. Numerical prediction of the similar mixture using a detailed reaction mechanism is obtained. The computational mechanism predicts higher magnitudes for laminar flame velocity and smaller magnitudes of temperature exponent compared to experimental data.

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

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).

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.

Maniac talk - Dr. Richard R. Fisher, Director, Heliophysics Division (Emeritus), NASA HQ

NASA Image and Video Library

2016-05-25

Dr. Richard R. Fisher: "As in the case of learning how to perform in any specialized context, I found there were a number of issues I was neither taught nor did I learn from life experience. Over the course of a 50-year career that transitioned from ground-based to space-based, I came to understand that there are specific tools and values that proved vital. Using my own journey, I shall summarize a few of the more useful, to identify and make available things and ideas that helped me with my time with NASA." Dr. Richard R. Fisher, Director, Heliophysics Division (Emeritus), NASA HQ

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.

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.

Critical decay exponent of the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2014-11-01

We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent δ . To obtain an accurate estimate of δ , we first find the strength of corrections to scaling using the recently introduced method [S.-C. Park. J. Korean Phys. Soc. 62, 469 (2013), 10.3938/jkps.62.469]. For small diffusion rate (d ≤0.5 ), the leading corrections-to-scaling term is found to be ˜t-0.15, whereas for large diffusion rate (d =0.95 ) it is found to be ˜t-0.5. After finding the strength of corrections to scaling, effective exponents are systematically analyzed to conclude that the value of critical decay exponent δ is 0.173 (3 ) irrespective of d . This value should be compared with the critical decay exponent of the directed percolation, 0.1595. In addition, we study two types of crossover. At d =0 , the phase boundary is discontinuous and the crossover from the pair contact process to the PCPD is found to be described by the crossover exponent ϕ =2.6 (1 ) . We claim that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP. At d =1 , the crossover from the mean field PCPD to the PCPD is described by ϕ =2 which is argued to be exact.

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.

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

77 FR 72846 - H.Q. Energy Services (U.S.) Inc. v. ISO New England Inc.; Notice of Complaint

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-06

... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission [Docket No. EL13-25-000] H.Q. Energy Services (U.S.) Inc. v. ISO New England Inc.; Notice of Complaint Take notice that on November 28, 2012... ISO New England Inc. (Respondent), requesting the Commission to issue an order requiring the...

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

Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Vastano, John A.; Moser, Robert D.

1991-01-01

The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.

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.

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.

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

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.

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.

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.

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

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.

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

NASA Astrophysics Data System (ADS)

Pompe, B.; Leven, R. W.

1988-11-01

We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.

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.

Lyapunov exponent and criticality in the Hamiltonian mean field model

NASA Astrophysics Data System (ADS)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

Does the Q - H index show a stronger relationship than the H:Q ratio in regard to knee pain during daily activities in patients with knee osteoarthritis?

PubMed

Fujita, Remi; Matsui, Yasumoto; Harada, Atsushi; Takemura, Marie; Kondo, Izumi; Nemoto, Tetsuya; Sakai, Tadahiro; Hiraiwa, Hideki; Ota, Susumu

2016-12-01

[Purpose] The purpose of this study was to elucidate the relationship between knee muscle strength and knee pain in activities of daily living, based on consideration of the difference between extension and flexion strength (Q - H) and the hamstring:quadriceps (H:Q) ratio in patients with knee osteoarthritis. [Subjects and Methods] The participants were 78 females with knee osteoarthritis, and a total of 133 knees that had not been treated surgically were the targets of this research. The legs were divided according to dominance. Isometric knee extension and flexion muscle strength and knee pain during activities of daily living were measured. The H:Q ratio (flexion/extension muscle strength) and the difference between extension and flexion strength, (extension muscle strength/weight) minus (flexion muscle strength/weight), that is, Q - H, were calculated. The correlation between these indices and the knee pain score during activities of daily living was investigated. [Results] Greater knee pain during activities of daily living was related to lower knee extension muscle strength and Q - H in both the dominant and nondominant legs. Knee flexion muscle strength and the H:Q ratio were not significantly correlated with knee pain during any activities of daily living. [Conclusion] Knee extension muscle strength and Q - H were found to be significantly correlated with knee pain during activities of daily living, whereas the H:Q ratio was not.

5-D Choptuik critical exponent and holography

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

Bland, J.; Kunstatter, G.

2007-05-15

Recently, a holographic argument was used to relate the saturation exponent, {gamma}{sub BFKL}, of 4-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, {gamma}{sub 5d}, in 5-dimensional black hole formation via scalar field collapse [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.]. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of {gamma}{sub 5d} with substantially decreased numerical error. Our current result is {gamma}{sub 5d}=0.4131{+-}0.0001, which is close to, but not in strict agreement with, the value of {gamma}{sub BFKL}=0.409more » 552 quoted in [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.].« less

Anomalous charge storage exponents of organic bulk heterojunction solar cells.

NASA Astrophysics Data System (ADS)

Nair, Pradeep; Dwivedi, Raaz; Kumar, Goutam; Dept of Electrical Engineering, IIT Bombay Team

2013-03-01

Organic bulk heterojunction (BHJ) devices are increasingly being researched for low cost solar energy conversion. The efficiency of such solar cells is dictated by various recombination processes involved. While it is well known that the ideality factor and hence the charge storage exponents of conventional PN junction diodes are influenced by the recombination processes, the same aspects are not so well understood for organic solar cells. While dark currents of such devices typically show an ideality factor of 1 (after correcting for shunt resistance effects, if any), surprisingly, a wide range of charge storage exponents for such devices are reported in literature alluding to apparent concentration dependence for bi-molecular recombination rates. In this manuscript we critically analyze the role of bi-molecular recombination processes on charge storage exponents of organic solar cells. Our results indicate that the charge storage exponents are fundamentally influenced by the electrostatics and recombination processes and can be correlated to the dark current ideality factors. We believe that our findings are novel, and advance the state-of the art understanding on various recombination processes that dictate the performance limits of organic solar cells. The authors would like to thank the Centre of Excellence in Nanoelectronics (CEN) and the National Centre for Photovoltaic Research and Education (NCPRE), IIT Bombay for computational and financial support

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.

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.

Power-law exponent of the Bouchaud-Mézard model on regular random networks

NASA Astrophysics Data System (ADS)

Ichinomiya, Takashi

2013-07-01

We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as x→∞. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.

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

H:q ratios and bilateral leg strength in college field and court sports players.

PubMed

Cheung, Roy T H; Smith, Andrew W; Wong, Del P

2012-06-01

One of the key components in sports injury prevention is the identification of imbalances in leg muscle strength. However, different leg muscle characteristics may occur in large playing area (field) sports and small playing area (court) sports, which should be considered in regular injury prevention assessment. This study examined the isokinetic hamstrings-to-quadriceps (H:Q) ratio and bilateral leg strength balance in 40 male college (age: 23.4 ± 2.5 yrs) team sport players (field sport = 23, soccer players; court sport = 17, volleyball and basketball players). Five repetitions of maximal knee concentric flexion and concentric extension were performed on an isokinetic dynamometer at two speeds (slow: 60°·s(-1) and fast: 300°·s(-1)) with 3 minutes rest between tests. Both legs were measured in counterbalanced order with the dominant leg being determined as the leg used to kick a ball. The highest concentric peak torque values (Nm) of the hamstrings and quadriceps of each leg were analyzed after body mass normalization (Nm·kg(-1)). Court sport players showed significantly weaker dominant leg hamstrings muscles at both contraction speeds (P < 0.05). The H:Q ratio was significantly larger in field players in their dominant leg at 60°·s(-1) (P < 0.001), and their non-dominant leg at 300°·s(-1) (P < 0.001) respectively. Sport-specific leg muscle strength was evident in college players from field and court sports. These results suggest the need for different muscle strength training and rehabilitation protocols for college players according to the musculature requirements in their respective sports.

Effect of diamond-like carbon coating on corrosion rate of machinery steel HQ 805

NASA Astrophysics Data System (ADS)

Slat, Winda Sanni; Malau, Viktor; Iswanto, Priyo Tri; Sujitno, Tjipto; Suprapto

2018-04-01

HQ 805 is known as a super strength alloys steel and widely applied in military equipment and, aircraft components, drilling device and so on. It is due to its excellent behavior in wear, fatigue, high temperature and high speed operating conditions. The weakness of this material is the vulnerablality to corrosion when employed in sour environments where hydrogen sulfide and chlorides are present. To overcome the problems, an effort should be made to improve or enhance the surface properties for a longer service life. There are varieties of coatings developed and used to improve surface material properties. There are several kinds of coating methods; chemical vapour deposition (CVD), physical vapour deposition (PVD), thermochemical treatment, oxidation, or plasma spraying. This paper presents the research result of the influence of Diamond-Like Carbon (DLC) coating deposited using DC plasma enhanced chemical vapor deposition (DC-PECVD) on corrosion rate (by potentiodynamic polarization method) of HQ 805 machinery steel. As a carbon sources, a mixture of argon (Ar) and methane (CH4) with ratio 76% : 24% was used in this experiment. The conditions of experiment were 400 °C of temperature, 1.2 mbar, 1.4 mbar, 1.6 mbar and 1.8 mbar of pressure of process. Investigated surface properties were hardness (microhardness tester), roughness (roughness test), chemical composition (Spectrometer), microstructure (SEM) and corrosion rate (potentiodynamic polarization). It has been found that the optimum condition with the lowest corrosion rate is at a pressure of 1.4 mbar with a deposition duration of 4 hours at a constant temperature of 400 °C. In this condition, the corrosion rate decreases from 12.326 mpy to 4.487 mpy.

Finite-time braiding exponents

NASA Astrophysics Data System (ADS)

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Finite-time braiding exponents.

PubMed

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity

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

Friedland, Gerald; Metere, Alfredo

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can bemore » employed at the core of physics simulations.« less

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

NASA Astrophysics Data System (ADS)

Odavić, Jovan; Mali, Petar; Tekić, Jasmina; Pantić, Milan; Pavkov-Hrvojević, Milica

2017-06-01

Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middleton's no passing rule.

Inter-relationship between scaling exponents for describing self-similar river networks

NASA Astrophysics Data System (ADS)

Yang, Soohyun; Paik, Kyungrock

2015-04-01

Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent ɛ) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between ɛ and h. In this study, we expand this to a more general ɛ-η-h relationship. We approach ɛ-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.

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.

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.

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.

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

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.

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.

Fermat's Last Theorem for Factional and Irrational Exponents

ERIC Educational Resources Information Center

Morgan, Frank

2010-01-01

Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.

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.

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

Variation of Zipf's exponent in one hundred live languages: A study of the Holy Bible translations

NASA Astrophysics Data System (ADS)

Mehri, Ali; Jamaati, Maryam

2017-08-01

Zipf's law, as a power-law regularity, confirms long-range correlations between the elements in natural and artificial systems. In this article, this law is evaluated for one hundred live languages. We calculate Zipf's exponent for translations of the holy Bible to several languages, for this purpose. The results show that, the average of Zipf's exponent in studied texts is slightly above unity. All studied languages in some families have Zipf's exponent lower/higher than unity. It seems that geographical distribution impresses the communication between speakers of different languages in a language family, and affect similarity between their Zipf's exponent. The Bible has unique concept regardless of its language, but the discrepancy in grammatical rules and syntactic regularities in applying stop words to make sentences and imply a certain concept, lead to difference in Zipf's exponent for various languages.

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.

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

Primitive graphs with small exponent and small scrambling index

NASA Astrophysics Data System (ADS)

Surbakti, Ita Y.; Suwilo, Saib; Butar-butar, Ericha A.; Oktaviani, Helda

2018-01-01

A connected graph G is primitive provide there is a positive integer k such that for each pair of vertices u and v there is a uv-walk of length k. The smallest of such positive integer k is the exponent of G and is denoted by exp(G). The scrambling index of a primitive graph G, denoted by k(G), is the smallest positive integer k such that for each pair of vertices u and v there is a vertex w such that there is a uw-walk and a vw-walk of length k. By an n-chainring CR(n) we mean a graph obtained from an n-cycle by replacing each edge of the n-cycle by a triangle. By a (q,p)-dory, D(q,p), we mean a graph with vertex set V(D(q,p)) = V(P q × P p ) ∪ {w 1, w 2} and edge set E(D(q,p)) = E(P q × Pp ) ∪ {w 1 - (u i ,v 1) : i = 1, 2,…, q}∪{w 2 -(u i ,vp ) : i = 1, 2,…, q}, where Pn is a path on n vertices. We discus the exponent and scrambling index of an n- chainring and (q, p)-dory. We present formulae for exponent and scrambling index in terms of their diameter.

Prediction of the external work of the native heart from the dynamic H-Q curves of the rotary blood pumps during left heart bypass.

PubMed

Yokoyama, Yoshimasa; Kawaguchi, Osamu; Kitao, Takashi; Kimura, Taro; Steinseifer, Ulrich; Takatani, Setsuo

2010-09-01

The ventricular performance is dependent on the drainage effect of rotary blood pumps (RBPs) and the performance of RBPs is affected by the ventricular pulsation. In this study, the interaction between the ventricle and RBPs was examined using the pressure-volume (P-V) diagram of the ventricle and dynamic head pressure-bypass flow (H-Q) curves (H, head pressure: arterial pressure minus ventricular pressure vs. Q, bypass flow) of the RBPs. We first investigated the relationships in a mock loop with a passive fill ventricle, followed by validation in ex vivo animal experiments. An apical drainage cannula with a micro-pressure sensor was especially fabricated to obtain ventricular pressure, while three pairs of ultrasonic crystals placed on the heart wall were used to derive ventricular volume. The mock loop-configured ventricular apical-descending aorta bypass revealed that the external work of the ventricle expressed by the area inside the P-V diagrams (EW(Heart) ) correlated strongly with the area inside dynamic H-Q curves (EW(VAD)), with the coefficients of correlation being R² = 0.869 ∼ 0.961. The results in the mock loop were verified in the ex vivo studies using three Shiba goats (10-25 kg in body weight), showing the correlation coefficients of R² = 0.802 ∼ 0.817. The linear regression analysis indicated that the increase in the bypass flow reduced pulsatility in the ventricle expressed in EW(Heart) as well as in EW(VAD) . Experimental results, both mock loop and animal studies, showed that the interaction between cardiac external work and H-Q performance of RBPs can be expressed by the relationships "EW(Heart) versus EW(VAD) ." The pulsatile nature of the native heart can be expressed in the area underneath the H-Q curves of RBPs EW(VAD) during left heart bypass indicating the status of the level of assistance by RBPs and the native heart function. © 2010, Copyright the Authors. Artificial Organs © 2010, International Center for Artificial Organs and

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

NASA Astrophysics Data System (ADS)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

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.

Critical exponents of extremal Kerr perturbations

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.; Zimmerman, Peter

2018-05-01

We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero.

Scaling exponent and dispersity of polymers in solution by diffusion NMR.

PubMed

Williamson, Nathan H; Röding, Magnus; Miklavcic, Stanley J; Nydén, Magnus

2017-05-01

Molecular mass distribution measurements by pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) spectroscopy currently require prior knowledge of scaling parameters to convert from polymer self-diffusion coefficient to molecular mass. Reversing the problem, we utilize the scaling relation as prior knowledge to uncover the scaling exponent from within the PGSE data. Thus, the scaling exponent-a measure of polymer conformation and solvent quality-and the dispersity (M w /M n ) are obtainable from one simple PGSE experiment. The method utilizes constraints and parametric distribution models in a two-step fitting routine involving first the mass-weighted signal and second the number-weighted signal. The method is developed using lognormal and gamma distribution models and tested on experimental PGSE attenuation of the terminal methylene signal and on the sum of all methylene signals of polyethylene glycol in D 2 O. Scaling exponent and dispersity estimates agree with known values in the majority of instances, leading to the potential application of the method to polymers for which characterization is not possible with alternative techniques. Copyright © 2017 Elsevier Inc. All rights reserved.

Universality of modulation length and time exponents.

PubMed

Chakrabarty, Saurish; Dobrosavljević, Vladimir; Seidel, Alexander; Nussinov, Zohar

2012-10-01

We study systems with a crossover parameter λ, such as the temperature T, which has a threshold value λ(*) across which the correlation function changes from exhibiting fixed wavelength (or time period) modulations to continuously varying modulation lengths (or times). We introduce a hitherto unknown exponent ν(L) characterizing the universal nature of this crossover and compute its value in general instances. This exponent, similar to standard correlation length exponents, is obtained from motion of the poles of the momentum (or frequency) space correlation functions in the complex k-plane (or ω-plane) as the parameter λ is varied. Near the crossover (i.e., for λ→λ(*)), the characteristic modulation wave vector K(R) in the variable modulation length "phase" is related to that in the fixed modulation length "phase" q via |K(R)-q|[proportionality]|T-T(*)|(νL). We find, in general, that ν(L)=1/2. In some special instances, ν(L) may attain other rational values. We extend this result to general problems in which the eigenvalue of an operator or a pole characterizing general response functions may attain a constant real (or imaginary) part beyond a particular threshold value λ(*). We discuss extensions of this result to multiple other arenas. These include the axial next-nearest-neighbor Ising (ANNNI) model. By extending our considerations, we comment on relations pertaining not only to the modulation lengths (or times), but also to the standard correlation lengths (or times). We introduce the notion of a Josephson time scale. We comment on the presence of aperiodic "chaotic" modulations in "soft-spin" and other systems. These relate to glass-type features. We discuss applications to Fermi systems, with particular application to metal to band insulator transitions, change of Fermi surface topology, divergent effective masses, Dirac systems, and topological insulators. Both regular periodic and glassy (and spatially chaotic behavior) may be found in

Statistics of Lyapunov exponents of quasi-one-dimensional disordered systems

NASA Astrophysics Data System (ADS)

Zhang, Yan-Yang; Xiong, Shi-Jie

2005-10-01

Statistical properties of Lyapunov exponents (LE) are numerically calculated in a quasi-one-dimensional (1D) Anderson model, which is in a 2D or 3D lattice with a finite cross section. The single-parameter scaling (SPS) variable τ relating the Lyapunov exponents γ and their variances σ by τ≡σ2L/⟨γ⟩ is calculated for different lateral coupling t and disorder strength W . In a wide range of t , τ is approximately independent of W , but it has different values for LEs in different channels. For small t , the distribution of the smallest LE is non-Gaussian and τ strongly depends on W , remarkably different from the 1D SPS hypothesis.

Beyond Critical Exponents in Neuronal Avalanches

NASA Astrophysics Data System (ADS)

Friedman, Nir; Butler, Tom; Deville, Robert; Beggs, John; Dahmen, Karin

2011-03-01

Neurons form a complex network in the brain, where they interact with one another by firing electrical signals. Neurons firing can trigger other neurons to fire, potentially causing avalanches of activity in the network. In many cases these avalanches have been found to be scale independent, similar to critical phenomena in diverse systems such as magnets and earthquakes. We discuss models for neuronal activity that allow for the extraction of testable, statistical predictions. We compare these models to experimental results, and go beyond critical exponents.

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.

Improved estimation of anomalous diffusion exponents in single-particle tracking experiments

NASA Astrophysics Data System (ADS)

Kepten, Eldad; Bronshtein, Irena; Garini, Yuval

2013-05-01

The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.

Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi

The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

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

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.

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.

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.

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.

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.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

NASA Astrophysics Data System (ADS)

Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2017-12-01

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.

On the history of the quantum. Introduction to the HQ4 special issue

NASA Astrophysics Data System (ADS)

Navarro, Jaume; Blum, Alexander; Lehner, Christoph

2017-11-01

Eight years ago, a special issue in this journal published a dozen papers with new studies on the history of quantum physics. That issue was an output of a conference in Utrecht one year earlier, the second in a series organized by the then existing large-scale project coordinated by the Max Planck Institute for the History of Science and the Fritz Haber Institute. Since then, that project has produced a number of publications, workshops and other academic outcomes, but more importantly, it triggered the consolidation of an international community of historians and philosophers of science producing novel work on the history of quantum physics. Five years after the third meeting, which took place in Berlin in 2010, many of the scholars from that group and some new ones met for four days in Donostia/San Sebastian for the HQ4 meeting. The time was ripe for new results to be shared and discussed, and this issue collects some of the papers presented at that gathering.

Critical field-exponents for secure message-passing in modular networks

NASA Astrophysics Data System (ADS)

Shekhtman, Louis M.; Danziger, Michael M.; Bonamassa, Ivan; Buldyrev, Sergey V.; Caldarelli, Guido; Zlatić, Vinko; Havlin, Shlomo

2018-05-01

We study secure message-passing in the presence of multiple adversaries in modular networks. We assume a dominant fraction of nodes in each module have the same vulnerability, i.e., the same entity spying on them. We find both analytically and via simulations that the links between the modules (interlinks) have effects analogous to a magnetic field in a spin-system in that for any amount of interlinks the system no longer undergoes a phase transition. We then define the exponents δ, which relates the order parameter (the size of the giant secure component) at the critical point to the field strength (average number of interlinks per node), and γ, which describes the susceptibility near criticality. These are found to be δ = 2 and γ = 1 (with the scaling of the order parameter near the critical point given by β = 1). When two or more vulnerabilities are equally present in a module we find δ = 1 and γ = 0 (with β ≥ 2). Apart from defining a previously unidentified universality class, these exponents show that increasing connections between modules is more beneficial for security than increasing connections within modules. We also measure the correlation critical exponent ν, and the upper critical dimension d c , finding that ν {d}c=3 as for ordinary percolation, suggesting that for secure message-passing d c = 6. These results provide an interesting analogy between secure message-passing in modular networks and the physics of magnetic spin-systems.

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.

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

Bayesian Estimation of the Logistic Positive Exponent IRT Model

ERIC Educational Resources Information Center

Bolfarine, Heleno; Bazan, Jorge Luis

2010-01-01

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

Scaling functions and scaling exponents in turbulence

NASA Astrophysics Data System (ADS)

Stolovitzky, G.; Sreenivasan, K. R.; Juneja, A.

1993-11-01

We extend the recent work of Sirovich, Smith, and Yakhot (unpublished) and obtain for structure functions of arbitrary order an expression that is uniformly valid for the dissipation as well as the inertial range of scales. We compare the expression with experimental data obtained in a moderate-Reynolds-number turbulent boundary layer and find good agreement. This enables a more definitive determination of the scaling exponents and intermittency corrections than has been possible in the past. The results are substantiated by several consistency checks.

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

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).

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 Exponent of High-frequency Source Spectral Falloff and Contribution to Source Parameter Estimates

NASA Astrophysics Data System (ADS)

Kiuchi, R.; Mori, J. J.

2015-12-01

As a way to understand the characteristics of the earthquake source, studies of source parameters (such as radiated energy and stress drop) and their scaling are important. In order to estimate source parameters reliably, often we must use appropriate source spectrum models and the omega-square model is most frequently used. In this model, the spectrum is flat in lower frequencies and the falloff is proportional to the angular frequency squared. However, Some studies (e.g. Allmann and Shearer, 2009; Yagi et al., 2012) reported that the exponent of the high frequency falloff is other than -2. Therefore, in this study we estimate the source parameters using a spectral model for which the falloff exponent is not fixed. We analyze the mainshock and larger aftershocks of the 2008 Iwate-Miyagi Nairiku earthquake. Firstly, we calculate the P wave and SH wave spectra using empirical Green functions (EGF) to remove the path effect (such as attenuation) and site effect. For the EGF event, we select a smaller earthquake that is highly-correlated with the target event. In order to obtain the stable results, we calculate the spectral ratios using a multitaper spectrum analysis (Prieto et al., 2009). Then we take a geometric mean from multiple stations. Finally, using the obtained spectra ratios, we perform a grid search to determine the high frequency falloffs, as well as corner frequency of both of events. Our results indicate the high frequency falloff exponent is often less than 2.0. We do not observe any regional, focal mechanism, or depth dependencies for the falloff exponent. In addition, our estimated corner frequencies and falloff exponents are consistent between the P wave and SH wave analysis. In our presentation, we show differences in estimated source parameters using a fixed omega-square model and a model allowing variable high-frequency falloff.

On the approximation of Lyapunov exponents and a question suggested by Anatole Katok

NASA Astrophysics Data System (ADS)

Dai, Xiongping

2010-03-01

Let \\mathcal {F}\\colon X\\times\\mathbb{Z}_+\\rightarrow \\rm{GL}(n,\\mathbb{R}) be a Hölder-continuous linear cocycle whose driving semiflow f\\colon X\\times\\mathbb{Z}_+\\rightarrow X preserves a probability μ on a compact metric space X. Using the concept of two-sided quasi-Pesin orbits introduced in this paper, we show that the Lyapunov characteristic spectrum of μ can be approached arbitrarily by that of periodic points of f. So, if all periodic points of f have only positive Lyapunov exponents and such exponents are uniformly bounded away from zero, then μ also has only positive exponents. In our arguments, the exponential closing property of the driving semiflow is a basic condition, and it is easy to check that every C1-expanding map of a closed manifold obeys this closing property. Consequently, if f is a C1+Hölder local diffeomorphism of a closed manifold and if it is Hölder conjugated to some C1-expanding map, then f is itself expanding. This gives a positive answer to a question suggested by Anatole Katok.

Investigating textural controls on Archie's porosity exponent using process-based, pore-scale modelling

NASA Astrophysics Data System (ADS)

Niu, Q.; Zhang, C.

2017-12-01

Archie's law is an important empirical relationship linking the electrical resistivity of geological materials to their porosity. It has been found experimentally that the porosity exponent m in Archie's law in sedimentary rocks might be related to the degree of cementation, and therefore m is termed as "cementation factor" in most literatures. Despite it has been known for many years, there is lack of well-accepted physical interpretations of the porosity exponent. Some theoretical and experimental evidences have also shown that m may be controlled by the particle and/or pore shape. In this study, we conduct a pore-scale modeling of the porosity exponent that incorporates different geological processes. The evolution of m of eight synthetic samples with different particle sizes and shapes are calculated during two geological processes, i.e., compaction and cementation. The numerical results show that in dilute conditions, m is controlled by the particle shape. As the samples deviate from dilute conditions, m increases gradually due to the strong interaction between particles. When the samples are at static equilibrium, m is noticeably larger than its values at dilution condition. The numerical simulation results also show that both geological compaction and cementation induce a significant increase in m. In addition, the geometric characteristics of these samples (e.g., pore space/throat size, and their distributions) during compaction and cementation are also calculated. Preliminary analysis shows a unique correlation between the pore size broadness and porosity exponent for all eight samples. However, such a correlation is not found between m and other geometric characteristics.

Signal detection in power-law noise: effect of spectrum exponents.

PubMed

Burgess, Arthur E; Judy, Philip F

2007-12-01

Many natural backgrounds have approximately isotropic power spectra of the power-law form, P(f)=K/f(beta), where f is radial frequency. For natural scenes and mammograms, the values of the exponent, beta, range from 1.5 to 3.5. The ideal observer model predicts that for signals with certain properties and backgrounds that can be treated as random noise, a plot of log (contrast threshold) versus log (signal size) will be linear with slope, m, given by: m=(beta-2)/2. This plot is referred to as a contrast-detail (CD) diagram. It is interesting that this predicts a detection threshold that is independent of signal size for beta equal to 2. We present two-alternative forced-choice (2AFC) detection results for human and channelized model observers of a simple signal in filtered noise with exponents from 1.5 to 3.5. The CD diagram results are in good agreement with the prediction of this equation.

Power-law decay exponents: A dynamical criterion for predicting thermalization

NASA Astrophysics Data System (ADS)

Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.

2017-01-01

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

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.

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

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.

Turbidity determination of the critical exponent eta in the liquid-liquid mixture methanol and cyclohexane.

PubMed

Lytle, Amy; Jacobs, D T

2004-03-22

The turbidity of the liquid-liquid mixture methanol-cyclohexane has been measured very near its critical point and used to test competing theoretical predictions and to determine the critical correlation-correction exponent eta. By measuring the ratio of the transmitted to incident light intensities over five decades in reduced temperature, we are able to determine that Ferrell's theoretical prediction for the turbidity explains the data with the correlation length amplitude xi0=0.330+/-0.003 nm and critical exponents eta=0.041+/-0.005 and nu=0.632+/-0.002. These values are consistent with the values measured before for xi0 in this system and with the exponents predicted by theory. The data allow five different theoretical expressions to be tested and to select two as being equivalent when very close to the critical point. (c) 2004 American Institute of Physics

The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Heydenreich, Markus; Kolesnikov, Leonid

2018-04-01

We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

NASA Technical Reports Server (NTRS)

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-01-01

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

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.

Fractal dimension, walk dimension and conductivity exponent of karst networks around Tulum.

NASA Astrophysics Data System (ADS)

Hendrick, Martin; Renard, Philippe

2016-06-01

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension d_f, conductivity exponent ˜{μ} and walk dimension d_w are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: d_f≈ 1.5, d_w≈ 2.4, ˜{μ}≈ 0.9. We observe that the Einstein relation holds for these structures ˜{μ} ≈ -d_f + d_w. These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

PubMed

Salceanu, Paul L

2011-07-01

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.

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.

Exponent and scrambling index of double alternate circular snake graphs

NASA Astrophysics Data System (ADS)

Rahmayanti, Sri; Pasaribu, Valdo E.; Nasution, Sawaluddin; Liani Salnaz, Sishi

2018-01-01

A graph is primitive if it contains a cycle of odd length. The exponent of a primitive graph G, denoted by exp(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk length k. The scrambling index of a primitive graph G, denoted by k(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk of length 2k. For an even positive integer n and an odd positive integer r, a (n,r)-double alternate circular snake graph, denoted by DA(C r,n ), is a graph obtained from a path u 1 u 2 ... u n by replacing each edge of the form u 2i u 2i+1 by two different r-cycles. We study the exponent and scrambling index of DA(C r,n ) and show that exp(DA(C r,n )) = n + r - 4 and k(DA(C r,n )) = (n + r - 3)/2.

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.

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.

Privacy-Preserving RFID Authentication Using Public Exponent Three RSA Algorithm

NASA Astrophysics Data System (ADS)

Kim, Yoonjeong; Ohm, Seongyong; Yi, Kang

In this letter, we propose a privacy-preserving authentication protocol with RSA cryptosystem in an RFID environment. For both overcoming the resource restriction and strengthening security, our protocol uses only modular exponentiation with exponent three at RFID tag side, with the padded random message whose length is greater than one-sixth of the whole message length.

Autocorrelation analysis for the unbiased determination of power-law exponents in single-quantum-dot blinking.

PubMed

Houel, Julien; Doan, Quang T; Cajgfinger, Thomas; Ledoux, Gilles; Amans, David; Aubret, Antoine; Dominjon, Agnès; Ferriol, Sylvain; Barbier, Rémi; Nasilowski, Michel; Lhuillier, Emmanuel; Dubertret, Benoît; Dujardin, Christophe; Kulzer, Florian

2015-01-27

We present an unbiased and robust analysis method for power-law blinking statistics in the photoluminescence of single nanoemitters, allowing us to extract both the bright- and dark-state power-law exponents from the emitters' intensity autocorrelation functions. As opposed to the widely used threshold method, our technique therefore does not require discriminating the emission levels of bright and dark states in the experimental intensity timetraces. We rely on the simultaneous recording of 450 emission timetraces of single CdSe/CdS core/shell quantum dots at a frame rate of 250 Hz with single photon sensitivity. Under these conditions, our approach can determine ON and OFF power-law exponents with a precision of 3% from a comparison to numerical simulations, even for shot-noise-dominated emission signals with an average intensity below 1 photon per frame and per quantum dot. These capabilities pave the way for the unbiased, threshold-free determination of blinking power-law exponents at the microsecond time scale.

The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point

NASA Technical Reports Server (NTRS)

Zhang, Kai C.; Briggs, Matthew E.; Gammon, Robert W.; Levelt Sengers, J. M. H.

1992-01-01

We report turbidity measurements of a nonaqueous ionic solution of triethyl n-hexylammonium triethyl n-hexylboride in diphenyl ether. A classical susceptibility critical exponent gamma = 1.01 +/- 0.01 is obtained over the reduced temperature range t between values of 0.1 and 0.0001. The best fits of the sample transmission had a standard deviation of 0.39 percent over this range. Ising and spherical model critical exponents are firmly excluded. The correlation length amplitude xi sub 0 from fitting is 1.0 +/- 0.2 nm which is much larger than values found in neutral fluids and some aqueous binary mixtures.

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

NASA Astrophysics Data System (ADS)

Li, Liang-Sheng

2016-12-01

We explore the tricritical points and the critical lines of both Blume-Emery-Grifnths and Ising model within long-range interactions in the microcanonical ensemble. For K = K MTP , the tricritical exponents take the values β = 1/4, 1 = γ- ≠ γ+ = 1/2 and 0 = α- ≠ α+ = -1/2, which disagree with classical (mean held) values. When K > K MTP , the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K CTP ), where the values of the critical expoents become β = 1/2, 1 = γ- ≠ γ+ = 2 and 0 = α- ≠ α+ = 1. Supported by the National Natural Science Foundation of China under Grant No. 11104032

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

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

Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments.

PubMed

Charbonneau, Patrick; Li, Yue Cathy; Pfister, Henry D; Yaida, Sho

2017-09-01

Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical ζ function for one-dimensional systems. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the ζ function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance and is tested against Monte Carlo simulations.

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.

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.

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.

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.

Critical exponents for diluted resistor networks

NASA Astrophysics Data System (ADS)

Stenull, O.; Janssen, H. K.; Oerding, K.

1999-05-01

An approach by Stephen [Phys. Rev. B 17, 4444 (1978)] is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky [Phys. Rev. B 35, 6964 (1987)]. By a decomposition of the principal Feynman diagrams, we obtain diagrams which again can be interpreted as resistor networks. This interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent φ up to second order in ɛ=6-d, where d is the spatial dimension. Our result φ=1+ɛ/42+4ɛ2/3087 verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts-model formulation of the random resistor network.

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

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

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.

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.

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.

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

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.

Implications of Grain Size Evolution for the Effective Stress Exponent in Ice

NASA Astrophysics Data System (ADS)

Behn, M. D.; Goldsby, D. L.; Hirth, G.

2016-12-01

Viscous flow in ice has typically been described by the Glen law—a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice is strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding [1], which explicitly incorporates the grain-size dependence of ice rheology. Yet, neither dislocation creep (n 4), nor grain boundary sliding (n 1.8), have stress exponents that match the value of n 3 for the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form cannot be explained by a single deformation mechanism. Here we seek to understand the origin of the n 3 dependence of the Glen law through a new model for grain-size evolution in ice. In our model, grain size evolves in response to the balance between dynamic recrystallization and grain growth. To simulate these processes we adapt the "wattmeter" [2], originally developed within the solid-Earth community to quantify grain size in crustal and mantle rocks. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. The evolution of grain size in turn controls the relative contributions of dislocation creep and grain boundary sliding, and thus the effective stress exponent for ice flow. Using this approach, we first benchmark our grain size evolution model on experimental data and then calculate grain size in two end-member scenarios: (1) as a function of depth within an ice-sheet, and (2) across an ice-stream margin. We show that the calculated grain sizes match ice core observations for the interior of ice sheets. Furthermore, owing to the influence of grain size on strain rate, the

No ISCOs in Charged Myers Perry Spacetimes by Measuring Lyapunov Exponent

NASA Astrophysics Data System (ADS)

Pradhan, Parthapratim

2015-01-01

By computing coordinate time Lyapunov exponent, we prove that for more than four spacetime dimensions (N ≥ 3), there are no Innermost Stable Circular Orbit (ISCO) in charged Myers Perry blackhole spacetime.Using it, we show that the instability of equatorial circular geodesics, both massive and massless particles for such types of blackhole space-times.

Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type.

PubMed

Zhou, Douglas; Sun, Yi; Rangan, Aaditya V; Cai, David

2010-04-01

We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.

The allometric exponent for scaling clearance varies with age: a study on seven propofol datasets ranging from preterm neonates to adults.

PubMed

Wang, Chenguang; Allegaert, Karel; Peeters, Mariska Y M; Tibboel, Dick; Danhof, Meindert; Knibbe, Catherijne A J

2014-01-01

For scaling clearance between adults and children, allometric scaling with a fixed exponent of 0.75 is often applied. In this analysis, we performed a systematic study on the allometric exponent for scaling propofol clearance between two subpopulations selected from neonates, infants, toddlers, children, adolescents and adults. Seven propofol studies were included in the analysis (neonates, infants, toddlers, children, adolescents, adults1 and adults2). In a systematic manner, two out of the six study populations were selected resulting in 15 combined datasets. In addition, the data of the seven studies were regrouped into five age groups (FDA Guidance 1998), from which four combined datasets were prepared consisting of one paediatric age group and the adult group. In each of these 19 combined datasets, the allometric scaling exponent for clearance was estimated using population pharmacokinetic modelling (nonmem 7.2). The allometric exponent for propofol clearance varied between 1.11 and 2.01 in cases where the neonate dataset was included. When two paediatric datasets were analyzed, the exponent varied between 0.2 and 2.01, while it varied between 0.56 and 0.81 when the adult population and a paediatric dataset except for neonates were selected. Scaling from adults to adolescents, children, infants and neonates resulted in exponents of 0.74, 0.70, 0.60 and 1.11 respectively. For scaling clearance, ¾ allometric scaling may be of value for scaling between adults and adolescents or children, while it can neither be used for neonates nor for two paediatric populations. For scaling to neonates an exponent between 1 and 2 was identified. © 2013 The British Pharmacological Society.

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.

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.

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.

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 use of relative velocity exponents for jet engine exhaust noise

NASA Technical Reports Server (NTRS)

Stone, J. R.

1978-01-01

The effect of flight on jet engine exhaust noise has often been presented in terms of a relative velocity exponent, n, as a function of radiation angle. The value of n is given by the OASPL reduction due to relative velocity divided by 10 times the logarithm of the ratio of relative jet velocity to absolute jet velocity. In such terms, classical subsonic jet noise theory would result in a value of n being approximately 7 at 90 degree angle to the jet axis with n decreasing, but remaining positive, as the inlet axis is approached and increasing as the jet axis is approached. However, flight tests have shown a wide range of results, including negative values of n in some cases. In this paper it is shown that the exponent n is positive for pure subsonic jet mixing noise and varies, in a systematic manner, as a function of flight conditions and jet velocity.

Nonuniversality of the Archie exponent due to multifractality of resistivity well logs

NASA Astrophysics Data System (ADS)

Dashtian, Hassan; Yang, Yafan; Sahimi, Muhammad

2015-12-01

Archie's law expresses a relation between the formation factor F of porous media and their porosity ϕ, F∝ϕ-m, where m is the Archie or the cementation exponent. Despite widespread use of Archie's law, the value of m and whether it is universal and independent of the type of reservoir have remained controversial. We analyze various porosity and resistivity logs along 36 wells in six Iranian oil and gas reservoirs using wavelet transform coherence and multifractal detrended fluctuation analysis. m is estimated for two sets of data: one set contains the resistivity data that include those segments of the well that contain significant clay content and one without. The analysis indicates that the well logs are multifractal and that due to the multifractality the exponent m is nonuniversal. Thus, analysis of the resistivity of laboratory or outcrop samples that are not multifractal yields estimates of m that are not applicable to well logs in oil or gas reservoirs.

Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2012-04-01

By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated Legendre functions (ALF) by recursion without underflow problem. The new method enables us to evaluate ALFs of extremely high degree as 232 = 4,294,967,296, which corresponds to around 1 cm resolution on the Earth's surface. By limiting the application of exponent extension to a few working variables in the recursion, choosing a suitable large power of 2 as the radix, and embedding the contents of the basic arithmetic procedure of floating point numbers with the exponent extension directly in the program computing the recurrence formulas, we achieve the evaluation of ALFs in the double-precision environment at the cost of around 10% increase in computational time per single ALF. This formulation realizes meaningful execution of the spherical harmonic synthesis and/or analysis of arbitrary degree and order.

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 nonlinear properties of epileptic activity using largest Lyapunov exponent

NASA Astrophysics Data System (ADS)

Medvedeva, Tatiana M.; Lüttjohann, Annika; van Luijtelaar, Gilles; Sysoev, Ilya V.

2016-04-01

Absence seizures are known to be highly non-linear large amplitude oscillations with a well pronounced main time scale. Whilst the appearance of the main frequency is usually considered as a transition from noisy complex dynamics of baseline EEG to more regular absence activity, the dynamical properties of this type of epileptiformic activity in genetic absence models was not studied precisely. Here, the estimation of the largest Lyapunov exponent from intracranial EEGs of 10 WAG/Rij rats (genetic model of absence epilepsy) was performed. Fragments of 10 seizures and 10 episodes of on-going EEG each of 4 s length were used for each animal, 3 cortical and 2 thalamic channels were analysed. The method adapted for short noisy data was implemented. The positive values of the largest Lyapunov exponent were found as for baseline as for spike wave discharges (SWDs), with values for SWDs being significantly less than for on-going activity. Current findings may indicate that SWD is a chaotic process with a well pronounced main timescale rather than a periodic regime. Also, the absence activity was shown to be less chaotic than the baseline one.

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Review-Research on the physical training model of human body based on HQ.

PubMed

Junjie, Liu

2016-11-01

Health quotient (HQ) is the newest health culture and concept in the 21st century, and the analysis of the human body sports model is not enough mature at present, what's more, the purpose of this paper is to study the integration of the two subjects the health quotient and the sport model. This paper draws the conclusion that physical training and education in colleges and universities can improve the health quotient, and it will make students possess a more healthy body and mind. Then through a new rigid body model of sports to simulate the human physical exercise. After that this paper has an in-depth study on the dynamic model of the human body movement on the basis of establishing the matrix and equation. The simulation results of the human body bicycle riding and pole throwing show that the human body joint movement simulation can be realized and it has a certain operability as well. By means of such simulated calculation, we can come to a conclusion that the movement of the ankle joint, knee joint and hip joint's motion law and real motion are basically the same. So it further verify the accuracy of the motion model, which lay the foundation of other research movement model, also, the study of the movement model is an important method in the study of human health in the future.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

NASA Astrophysics Data System (ADS)

Benhaiem, David; Joyce, Michael; Sicard, François

2013-03-01

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two-point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the `stable clustering' region from the `universal' region is very well approximated by a `critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of `universality' of non-linear clustering in this context.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

PubMed

Leibovich, N; Dechant, A; Lutz, E; Barkai, E

2016-11-01

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

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.

"A Body Shape Index" in middle-age and older Indonesian population: scaling exponents and association with incident hypertension.

PubMed

Cheung, Yin Bun

2014-01-01

"A Body Shape Index" (ABSI) is a recently proposed index that standardizes waist circumference for body mass index (BMI) and height. This study aims to: (a) examine if the ABSI scaling exponents for standardizing waist circumference for BMI and height are valid in middle-aged and older Indonesian population, and (b) compare the association between incident hypertension and ABSI and other anthropometric measures. The Indonesian Family Life Survey Wave 3 measured anthropometric variables and blood pressure of 8255 adults aged between 40 to 85 years in 2000. The relationship between two anthropometric quantities, e.g. weight (w) and height (h), can be expressed as the power law-equivalent [Formula: see text], where p = 2 is the scaling exponent in the derivation of the BMI and can be estimated by linear regression analysis. This was extended to the regression analysis of the log-transformed waist circumference, weight and height to establish the scaling exponents in the ABSI. The values for men were similar to those developed by the previous American study, which were 2/3 (BMI) and 1/2 (height). Those for women were somewhat smaller, at 3/5 (BMI) and 1/5 (height). The original (American) ABSI leads to mild negative correlation with BMI (-0.14) and height (-0.12) in the female population. Analysis of the development of hypertension between Waves 3 and 4 (average interval 7.5 years) in relation to ABSI measured at Wave 3 showed stronger association if the locally derived (Indonesian) scaling exponents were used. However, both versions of the ABSI were less associated with incident hypertension than waist circumference and BMI. The values for the scaling exponents for ABSI are roughly similar between the American population and the middle-aged and older Indonesian population, although larger discrepancy was found in women. The ABSI is less associated with incident hypertension than waist circumference and BMI.

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.

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

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.

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.

The emergence of different tail exponents in the distributions of firm size variables

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Watanabe, Tsutomu; Mizuno, Takayuki

2013-05-01

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed assets K, the number of workers L, and sales Y, we confirm that these variables have power-law tails with different exponents, and that inversion symmetry and Gibrat’s law hold. Based on these findings, we argue that there exists a plane in the three dimensional space (logK,logL,logY), with respect to which the joint probability density function for the three variables is invariant under the exchange of variables. We provide empirical evidence suggesting that this plane fits the data well, and argue that the plane can be interpreted as the Cobb-Douglas production function, which has been extensively used in various areas of economics since it was first introduced almost a century ago.

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling.

PubMed

Graham, Jonathan Pietarila; Mininni, Pablo D; Pouquet, Annick

2005-10-01

We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.

Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice

NASA Astrophysics Data System (ADS)

Tarkhov, Andrei E.; Wimberger, Sandro; Fine, Boris V.

2017-08-01

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.

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.

Roughness exponent in two-dimensional percolation, Potts model, and clock model

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

Redinz, Jose Arnaldo; Martins, Marcelo Lobato

We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3, and 7) and p=10 clock models as well as from the occupation states for site percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent {alpha} characterizing those profiles. The low temperature phase of the Potts model corresponds to flat ({alpha}{approx_equal}1) profiles, whereas its high temperature phase is associated with rough ({alpha}{approx_equal}0.5) ones. For the p=10 clock model, in addition to themore » flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough (0.5{lt}{alpha}{lt}1) phase{emdash}associated with a soft spin-wave one{emdash}is observed. Our results for the transition temperatures in the Potts and clock models are in agreement with the static values, showing that this approach is able to detect the phase transitions in these models directly from the spin configurations, without any reference to thermodynamical potentials, order parameters, or response functions. Finally, we show that the roughness exponent {alpha} is insensitive to geometric critical phenomena.« less

Numerical investigation on the Ångström exponent of black carbon aerosol

NASA Astrophysics Data System (ADS)

Li, Ji; Liu, Chao; Yin, Yan; Kumar, K. Raghavendra

2016-04-01

Black carbon (BC) plays an important role on the global and regional climate, whereas there are significant uncertainties on its optical properties. Among various optical properties, the Ångström exponent (AE) indicates the spectral variation of the particle-optic interaction and is widely used to understand the aerosol properties. We consider the influence of BC geometry on its optical properties and assess the sensitivity of the AE to particle geometry and size distribution. The fractal aggregates with different fractal dimensions are used to represent realistic BC particles, and popular equivalent volume spherical and spheroidal models are also considered for comparison. Even if the fractal aggregates become highly compact and spherical, their optical properties are still significantly different from those of equivalent volume spheres or spheroids. Meanwhile, the Rayleigh-Debye-Gans approximation can hardly provide accurate results for all optical quantities of aggregates with different dimensions. The extinction Ångström exponent (EAE) and absorption Ångström exponent (AAE) are sensitive to both particle geometry and size distribution. With BC becoming more compact (from fractal aggregate to spheroid and to sphere), the AE becomes more sensitive to particle size distribution. The EAE and AAE of aggregates with different size distributions vary between 1.10-1.63 and 0.87-1.50, respectively, whereas those of the spheres or spheroids have wider ranges. Furthermore, the AE at smaller wavelengths (between 0.35 µm and 0.55 µm) is more sensitive to geometry and size distribution than that given by optical properties at larger wavelengths (between 0.55 µm and 0.88 µm).

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.

Understanding the absorption Angstrom exponent provided in the AERONET database

NASA Astrophysics Data System (ADS)

Schuster, G. L.; Dubovik, O.; Arola, A. T.

2014-12-01

Recently, some authors have suggested that the absorption Angstrom exponent (AAE) can be used to deduce the component aerosol absorption optical depths (AAOD) of dust, brown carbon, and soot carbon in the atmosphere. The premise behind this AAE approach is that AAE is a species-dependent aerosol property that does not depend upon particle size or mass, that absorbing aerosol species are externally mixed with one another, and that AAE is much less than 1 for black carbon. Other authors have found that AAE does not contain enough information to unambiguously speciate the absorbing aerosols. Thus, we explore this topic here, and point out some theoretical inconsistencies associated with using the AAE approach to deduce component AAODs from the AERONET retrievals. For instance, Level 2.0 retrievals at 15 West African sites subsampled for AAE < 1.0 indicate that 86% of the fine volume fractions are less than 0.2, 56% of the depolarization ratios are greater than 0.2, and 94% of the Angstrom exponents are less than 1.0. This indicates that most of the West African data with AAE < 1 are dominated by coarse mode dust, and that low AAE does not indicate pure BC, and that therefore AAE can not be used to separate carbonaceous aerosols from dust. We obtained similar results at five Middle East dust sites subsampled for AAE < 1.0, with 59% of the fine volume fractions less than 0.2, 88% of the depolarization ratios greater than 0.2, and 73% of the Angstrom exponents less than 1.0.Additionally, we find that AAE << 1 is very unlikely to occur for size distributions with fine volume fractions greater than 0.5 at nine southern Africa and South America sites, unless the imaginary refractive index at the 440 nm wavelength is less than the imaginary refractive index at the red and near infrared wavelengths (i.e., k(440) < k(rnir)). Since black carbon has a spectrally invariant imaginary refractive index at these wavelengths, it is unlikely to be the cause of k(440) < k(rnir) and AAE

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.

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

NASA Astrophysics Data System (ADS)

Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis

2018-03-01

This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

Characterization of fish sauce aroma-impact compounds using GC-MS, SPME-Osme-GCO, and Stevens' power law exponents.

PubMed

Pham, A J; Schilling, M W; Yoon, Y; Kamadia, V V; Marshall, D L

2008-05-01

The objectives of this study were to characterize volatile compounds and to determine the characteristic aromas associated with impact compounds in 4 fish sauces using solid-phase micro-extraction, gas chromatography-mass spectrometry, Osme, and gas chromatography olfactometry (SPME-Osme-GCO) coupled with Stevens' Power Law. Compounds were separated using GCMS and GCO and were identified with the mass spectral database, aroma perceived at the sniffing port, retention indices, and verification of compounds by authentic standards in the GCMS and GCO. Aromas that were isolated and present in all 4 fish sauce samples at all concentrations included fishy (trimethylamine), pungent and dirty socks (combination of butanoic, pentanoic, hexanoic, and heptanoic acids), cooked rice and buttery popcorn (2,6-dimethyl pyrazine), and sweet and cotton candy (benzaldehyde). All fish sauces contained the same aromas as determined by GCO and GCMS (verified using authentic standard compounds), but the odor intensity associated with each compound or group of compounds was variable for different fish sauce samples. Stevens' Power Law exponents were also determined using this analytical technique, but exponents were not consistent for the same compounds that were found in all fish sauces. Stevens' Power Law exponents ranged from 0.14 to 0.37, 0.24 to 0.34, 0.09 to 0.21, and 0.10 to 0.35 for dirty socks, fishy, buttery popcorn, and sweet aromas, respectively. This demonstrates that there is variability in Stevens' Power Law exponents for odorants within fish sauce samples.

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

Predicting the long tail of book sales: Unearthing the power-law exponent

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2010-06-01

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.

Dependence of exponents on text length versus finite-size scaling for word-frequency distributions

NASA Astrophysics Data System (ADS)

Corral, Álvaro; Font-Clos, Francesc

2017-08-01

Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of this scaling law, using both careful statistical tests and analytical arguments based on the generalized central-limit theorem applied to the moments of the distribution (and obtaining a novel derivation of Heaps' law as a by-product). We also find that the picture of word-frequency distributions with power-law exponents that decrease with text length [X. Yan and P. Minnhagen, Physica A 444, 828 (2016), 10.1016/j.physa.2015.10.082] does not stand with rigorous statistical analysis. Instead, we show that the distributions are perfectly described by power-law tails with stable exponents, whose values are close to 2, in agreement with the classical Zipf's law. Some misconceptions about scaling are also clarified.

THE COMPUTATION OF CHARACTERISTIC EXPONENTS IN THE PLANAR RESTRICTED PROBLEM OF THREE BODIES

DTIC Science & Technology

methods are applied to evaluate the characteristic exponents of Rabe’s Trojan Orbits; they are found to be of the stable type for the ovals, and of...the unstable type for the horse -shoe shaped orbit. When the periodic orbit is symmetric with respect to the axis of syzygies, four independent

Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

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

Hramov, Alexander E.; Saratov State Technical University, Politechnicheskaja str., 77, Saratov 410054; Koronovskii, Alexey A.

2012-08-15

The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamics, a number of the numerical techniques have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods cannot be applied directly to analysis of complex spatio-temporal dynamics of plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper, we propose the method for the calculation of the spectrum ofmore » the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between the system dynamics and the behavior of the spectrum of the spatial Lyapunov exponents. Along with the proposed method, the possible problems of SLEs calculation are also discussed. It is shown that for the wide class of the spatially extended systems, the set of quantities included in the system state for SLEs calculation can be reduced using the appropriate feature of the plasma systems.« less

Benford's law gives better scaling exponents in phase transitions of quantum XY models.

PubMed

Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; Sen De, Aditi; Sen, Ujjwal

2014-08-01

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.

Lagrangian Coherent Structures, Hyperbolicity, and Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Haller, George

2010-05-01

We review the fundamental physical motivation behind the definition of Lagrangian Coherent Structures (LCS) and show how it leads to the concept of finite-time hyperbolicity in non-autonomous dynamical systems. Using this concept of hyperbolicity, we obtain a self-consistent criterion for the existence of attracting and repelling material surfaces in unsteady fluid flows, such as those in the atmosphere and the ocean. The existence of LCS is often postulated in terms of features of the Finite-Time Lyapunov Exponent (FTLE) field associated with the system. As simple examples show, however, the FTLE field does not necessarily highlight LCS, or may ighlight structures that are not LCS. Under appropriate nondegeneracy conditions, we show that ridges of the FTLE field indeed coincide with LCS in volume-preserving flows. For general flows, we obtain a more general scalar field whose ridges correspond to LCS. We finally review recent applications of LCS techniques to flight safety analysis at Hong Kong International Airport.

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.

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.

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.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

NASA Technical Reports Server (NTRS)

Gonzalez, J. Jesus; Espinosa, Ismael E.; Fuentes, Alberto M.

1995-01-01

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis

PubMed Central

Aldridge, Bree B; Gaudet, Suzanne; Lauffenburger, Douglas A; Sorger, Peter K

2011-01-01

Receptor-mediated apoptosis proceeds via two pathways: one requiring only a cascade of initiator and effector caspases (type I behavior) and the second requiring an initiator–effector caspase cascade and mitochondrial outer membrane permeabilization (type II behavior). Here, we investigate factors controlling type I versus II phenotypes by performing Lyapunov exponent analysis of an ODE-based model of cell death. The resulting phase diagrams predict that the ratio of XIAP to pro-caspase-3 concentrations plays a key regulatory role: type I behavior predominates when the ratio is low and type II behavior when the ratio is high. Cell-to-cell variability in phenotype is observed when the ratio is close to the type I versus II boundary. By positioning multiple tumor cell lines on the phase diagram we confirm these predictions. We also extend phase space analysis to mutations affecting the rate of caspase-3 ubiquitylation by XIAP, predicting and showing that such mutations abolish all-or-none control over activation of effector caspases. Thus, phase diagrams derived from Lyapunov exponent analysis represent a means to study multi-factorial control over a complex biochemical pathway. PMID:22108795

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.

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.

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.

Microscopic processes controlling the Herschel-Bulkley exponent

NASA Astrophysics Data System (ADS)

Lin, Jie; Wyart, Matthieu

2018-01-01

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.

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.

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

Intraspecific variation in the metabolic scaling exponent in ectotherms: testing the effect of latitudinal cline, ontogeny and transgenerational change in the land snail Cornu aspersum.

PubMed

Gaitán-Espitia, Juan Diego; Bruning, Andrea; Mondaca, Fredy; Nespolo, Roberto F

2013-06-01

The strong dependence of metabolic rates on body mass has attracted the interest of ecological physiologists, as it has important implications to many aspects of biology including species variations in body size, the evolution of life history, and the structure and function of biological communities. The great diversity of observed scaling exponents has led some authors to conclude that there is no single universal scaling exponent, but instead it ranges from 2/3 to 1. Most of the telling evidence against the universality of power scaling exponents comes from ontogenetic changes. Nevertheless, there could be other sources of phenotypic variation that influence this allometric relationship at least at the intraspecific level. In order to explore the general concept of the metabolic scaling in terrestrial molluscs we tested the role of several biological and methodological sources of variation on the empirically estimated scaling exponent. Specifically, we measured a proxy of metabolic rate (CO(2) production) in 421 individuals, during three generations, in three different populations. Additionally, we measured this scaling relationship in 208 individuals at five developmental stages. Our results suggest that the metabolic scaling exponent at the intraspecific level does not have a single stationary value, but instead it shows some degree of variation across geographic distribution, transgenerational change and ontogenetic stages. The major differences in the metabolic scaling exponent that we found were at different developmental stages of snails, because ontogeny involves increases in size at different rates, which in turn, generate differential energy demands. Copyright © 2013 Elsevier Inc. All rights reserved.

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

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

Josiński, Henryk; Świtoński, Adam; Silesian University of Technology, Akademicka 16, 44-100 Gliwice

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

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.

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

Computation of entropy and Lyapunov exponent by a shift transform.

PubMed

Matsuoka, Chihiro; Hiraide, Koichi

2015-10-01

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown that the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.

Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains

NASA Astrophysics Data System (ADS)

Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro

1997-12-01

In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.

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…

Automatic detection of ischemic stroke based on scaling exponent electroencephalogram using extreme learning machine

NASA Astrophysics Data System (ADS)

Adhi, H. A.; Wijaya, S. K.; Prawito; Badri, C.; Rezal, M.

2017-03-01

Stroke is one of cerebrovascular diseases caused by the obstruction of blood flow to the brain. Stroke becomes the leading cause of death in Indonesia and the second in the world. Stroke also causes of the disability. Ischemic stroke accounts for most of all stroke cases. Obstruction of blood flow can cause tissue damage which results the electrical changes in the brain that can be observed through the electroencephalogram (EEG). In this study, we presented the results of automatic detection of ischemic stroke and normal subjects based on the scaling exponent EEG obtained through detrended fluctuation analysis (DFA) using extreme learning machine (ELM) as the classifier. The signal processing was performed with 18 channels of EEG in the range of 0-30 Hz. Scaling exponents of the subjects were used as the input for ELM to classify the ischemic stroke. The performance of detection was observed by the value of accuracy, sensitivity and specificity. The result showed, performance of the proposed method to classify the ischemic stroke was 84 % for accuracy, 82 % for sensitivity and 87 % for specificity with 120 hidden neurons and sine as the activation function of ELM.

Two-exponent Lavalette function: a generalization for the case of adherents to a religious movement.

PubMed

Ausloos, Marcel

2014-06-01

The Lavalette function is generalized to a two-exponent function in order to represent data looking like a sigmoid on semilogarithmic plots. A Mandelbrot trick is suggested for further investigations, if more fit parameters are needed. The analyzed data is that of the number of adherents to the main religions in the 20th century.

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

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

Computation of entropy and Lyapunov exponent by a shift transform

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

Matsuoka, Chihiro, E-mail: matsuoka.chihiro.mm@ehime-u.ac.jp; Hiraide, Koichi

2015-10-15

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown thatmore » the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.« less

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.

Relation Between Hertz Stress-Life Exponent, Ball-Race Conformity, and Ball Bearing Life

NASA Technical Reports Server (NTRS)

Zaretsky, Erwin V.; Poplawski, Joseph V.; Root, Lawrence E.

2008-01-01

ANSI/ABMA and ISO standards based on Lundberg-Palmgren bearing life theory are normalized for ball bearings having inner- and outerrace conformities of 52 percent (0.52) and made from pre-1940 bearing steel. The Lundberg-Palmgren theory incorporates an inverse 9th power relation between Hertz stress and fatigue life for ball bearings. The effect of race conformity on ball set life independent of race life is not incorporated into the Lundberg-Palmgren theory. In addition, post-1960 vacuum-processed bearing steel exhibits a 12th power relation between Hertz stress and life. The work reported extends the previous work of Zaretsky, Poplawski, and Root to calculate changes in bearing life--that includes the life of the ball set--caused by race conformity, Hertz stress-life exponent, ball bearing type and bearing series. The bearing fatigue life in actual application will usually be equal to or greater than that calculated using the ANSI/ABMA and ISO standards that incorporate the Lundberg-Palmgren theory. The relative fatigue life of an individual race is more sensitive to changes in race conformity for Hertz stress-life exponent n of 12 than where n = 9. However, when the effects are combined to predict actual bearing life for a specified set of conditions and bearing geometry, the predicted life of the bearing will be greater for a value of n = 12 than n = 9.

Relation between Hertz Stress-Life Exponent, Ball-Race Conformity, and Ball Bearing Life

NASA Technical Reports Server (NTRS)

Zaretsky, Erwin V.; Poplawski, Joseph V.; Root, Lawrence E.

2006-01-01

ANSI/ABMA and ISO standards based on Lundberg-Palmgren bearing life theory are normalized for ball bearings having inner- and outer-race conformities of 52 percent (0.52) and made from pre-1940 bearing steel. The Lundberg-Palmgren theory incorporates an inverse 9th power relation between Hertz stress and fatigue life for ball bearings. The effect of race conformity on ball set life independent of race life is not incorporated into the Lundberg-Palmgren theory. In addition, post-1960 vacuum-processed bearing steel exhibits a 12th power relation between Hertz stress and life. The work reported extends the previous work of Zaretsky, Poplawski, and Root to calculate changes in bearing life, that includes the life of the ball set, caused by race conformity, Hertz stress-life exponent, ball bearing type and bearing series. The bearing fatigue life in actual application will usually be equal to or greater than that calculated using the ANSI/ABMA and ISO standards that incorporate the Lundberg-Palmgren theory. The relative fatigue life of an individual race is more sensitive to changes in race conformity for Hertz stress-life exponent n of 12 than where n = 9. However, when the effects are combined to predict actual bearing life for a specified set of conditions and bearing geometry, the predicted life of the bearing will be greater for a value of n = 12 than n = 9.

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

NASA Astrophysics Data System (ADS)

Hu, D. L.; Liu, X. B.

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

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.

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.

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.

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.

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

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.

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.

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.

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.

Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

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

Hohenadler, M.; Aichhorn, M.; Schmidt, S.

2011-10-15

An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott-insulator transition of lattice polaritons. From mean-field and strong-coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid densitymore » and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the three-dimensional XY universality class, analogous to the Bose-Hubbard model.« less

GPU and APU computations of Finite Time Lyapunov Exponent fields

NASA Astrophysics Data System (ADS)

Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros

2012-03-01

We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Singular Behavior of the Leading Lyapunov Exponent of a Product of Random {2 × 2} Matrices

NASA Astrophysics Data System (ADS)

Genovese, Giuseppe; Giacomin, Giambattista; Greenblatt, Rafael Leon

2017-05-01

We consider a certain infinite product of random {2 × 2} matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter ɛ > 0 and on a real random variable with distribution {μ}. For a large class of {μ}, we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like {C ɛ^{2 α}} in the limit {ɛ \\searrow 0}, where {α \\in (0,1)} and {C > 0} are determined by {μ}. Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small {ɛ}. We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.

The first experimental confirmation of the fractional kinetics containing the complex-power-law exponents: Dielectric measurements of polymerization reactions

NASA Astrophysics Data System (ADS)

Nigmatullin, R. R.; Arbuzov, A. A.; Salehli, F.; Giz, A.; Bayrak, I.; Catalgil-Giz, H.

2007-01-01

For the first time we achieved incontestable evidence that the real process of dielectric relaxation during the polymerization reaction of polyvinylpyrrolidone (PVP) is described in terms of the fractional kinetic equations containing complex-power-law exponents. The possibility of the existence of the fractional kinetics containing non-integer complex-power-law exponents follows from the general theory of dielectric relaxation that has been suggested recently by one of the authors (R.R.N). Based on the physical/geometrical meaning of the fractional integral with complex exponents there is a possibility to develop a general theory of dielectric relaxation based on the self-similar (fractal) character of the reduced (averaged) microprocesses that take place in the mesoscale region. This theory contains some essential predictions related to existence of the non-integer power-law kinetics and the results of this paper can be considered as the first confirmation of existence of the kinetic phenomena that are described by fractional derivatives with complex-power-law exponents. We want to stress here that with the help of a new complex fitting function for the complex permittivity it becomes possible to describe the whole process for real and imaginary parts simultaneously throughout the admissible frequency range (30 Hz-13 MHz). The fitting parameters obtained for the complex permittivity function for three temperatures (70, 90 and 110 °C) confirm in general the picture of reaction that was known qualitatively before. They also reveal some new features, which improve the interpretation of the whole polymerization process. We hope that these first results obtained in the paper will serve as a good stimulus for other researches to find the traces of the existence of new fractional kinetics in other relaxation processes unrelated to the dielectric relaxation. These results should lead to the reconsideration and generalization of irreversibility and kinetic phenomena that

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

Maximum Lyapunov exponents as predictors of global gait stability: a modelling approach.

PubMed

Bruijn, Sjoerd M; Bregman, Daan J J; Meijer, Onno G; Beek, Peter J; van Dieën, Jaap H

2012-05-01

To examine the stability of human walking, methods such as local dynamic stability have been adopted from dynamical systems theory. Local dynamic stability is calculated by estimating maximal finite time Lyapunov exponents (λ(S) and λ(L)), which quantify how a system responds continuously to very small (i.e. "local") perturbations. However, it is unknown if, and to what extent, these measures are correlated to global stability, defined operationally as the probability of falling. We studied whether changes in probability of falling of a simple model of human walking (a so-called dynamic walker) could be predicted from maximum finite time Lyapunov exponents. We used an extended version of the simplest walking model with arced feet and a hip spring. This allowed us to change the probability of falling of the model by changing either the foot radius, the slope at which the model walks, the stiffness of the hip spring, or a combination of these factors. Results showed that λ(S) correlated fairly well with global stability, although this relationship was dependent upon differences in the distance between initial nearest neighbours on the divergence curve. A measure independent of such changes (the log(distance between initially nearest neighbours after 50 samples)) correlated better with global stability, and, more importantly, showed a more consistent relationship across conditions. In contrast, λ(L) showed either weak correlations, or correlations opposite to expected, thus casting doubt on the use of this measure as a predictor of global gait stability. Our findings support the use of λ(S), but not of λ(L), as measure of human gait stability. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

NASA Astrophysics Data System (ADS)

Cho, Y. S.; Lee, J. S.; Herrmann, H. J.; Kahng, B.

2016-01-01

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2 <τ (g )≤2.5 . This pattern reveals a necessary condition for a hybrid transition in cluster aggregation processes, which is comparable to the power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.

Quantification of scaling exponent with Crossover type phenomena for different types of forcing in DC glow discharge plasma

NASA Astrophysics Data System (ADS)

Saha, Debajyoti; Shaw, Pankaj Kumar; Ghosh, Sabuj; Janaki, M. S.; Sekar Iyengar, A. N.

2018-01-01

We have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise, sinusoidal, square on the floating potential fluctuations acquired under different pressures in a DC glow discharge plasma. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics. The complexity of the nonlinear fluctuation has been revealed with the help of recurrence quantification analysis which is a suitable tool for investigating recurrence, an ubiquitous feature providing a deep insight into the dynamics of real dynamical system. An informal test for stationarity which checks for the compatibility of nonlinear approximations to the dynamics made in different segments in a time series has been proposed. In case of sinusoidal, noise, square forcing applied on fluctuation acquired at P = 0.12 mbar only one dominant scaling region is observed whereas the forcing applied on fluctuation (P = 0.04 mbar) two prominent scaling regions have been explored reliably using different forcing amplitudes indicating the signature of crossover phenomena. Furthermore a persistence long range behavior has been observed in one of these scaling regions. A comprehensive study of the quantification of scaling exponents has been carried out with the increase in amplitude and frequency of sinusoidal, square type of forcings. The scalings exponent is envisaged to be the roughness of the time series. The method provides a single quantitative idea of the scaling exponent to quantify the correlation properties of a signal.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

True and apparent scaling: The proximity of the Markov-switching multifractal model to long-range dependence

NASA Astrophysics Data System (ADS)

Liu, Ruipeng; Di Matteo, T.; Lux, Thomas

2007-09-01

In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifractal (MSM) model. In order to see how well the estimated model captures the temporal dependence of the data, we estimate and compare the scaling exponents H(q) (for q=1,2) for both empirical data and simulated data of the MSM model. In most cases the multifractal model appears to generate ‘apparent’ long memory in agreement with the empirical scaling laws.

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

NASA Astrophysics Data System (ADS)

Bera, Anindita; Mishra, Utkarsh; Singha Roy, Sudipto; Biswas, Anindya; Sen(De), Aditi; Sen, Ujjwal

2018-06-01

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.

Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

NASA Astrophysics Data System (ADS)

Linkmann, Moritz; McComb, W. David; Yoffe, Samuel; Berera, Arjun

2014-11-01

The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents ζn from the structure functions Sn (r) , is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio | Sn (r) /S3 (r) | against the separation r in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots the generalized structure functions Gn (r) against G3 (r) , where G3 (r) ~ r . Using our method for the particular case of S2 (r) we obtain the new result that the exponent ζ2 decreases as the Taylor-Reynolds number increases, with ζ2 --> 0 . 679 +/- 0 . 013 as Rλ --> ∞ . This supports the idea of finite-viscosity corrections to the K41 prediction for S2, and is the opposite of the result obtained by ESS. The pseudospectral method permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces. The combination of the viscous and the forcing corrections as calculated by the pseudospectral method is shown to account for the deviation of S3 from Kolmogorov's ``four-fifths''-law at all scales. This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A. B. is supported by STFC, S. R. Y. and M. F. L. are funded by EPSRC.

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.

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.

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.

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.

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

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

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales

NASA Technical Reports Server (NTRS)

Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.

2006-01-01

The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.

Fractal dimensions of graph of Weierstrass-type function and local Hölder exponent spectra

NASA Astrophysics Data System (ADS)

Otani, Atsuya

2018-01-01

We study several fractal properties of the Weierstrass-type function where τ :[0, 1)\\to[0, 1) is a cookie cutter map with possibly fractal repeller, and λ and g are functions with proper regularity. In the first part, we determine the box dimension of the graph of W and Hausdorff dimension of its randomised version. In the second part, the Hausdorff spectrum of the local Hölder exponent is characterised in terms of thermodynamic formalism. Furthermore, in the randomised case, a novel formula for the lifted Hausdorff spectrum on the graph is provided.

201007270004HQ

NASA Image and Video Library

2010-07-26

NASA Astrophycist Dr. John Mather speaks, Tuesday, July 27, 2010, at the Smithsonian National Air and Space Museum in Washington. Mather was speaking as part of a ceremony with STS-132 astronaut Piers Sellers who returned a replica of the Nobel Prize that is in the museum's collection and was flown aboard STS-132 Atlantis. The prize was won by Mather and University of California, Berkeley researcher George Smoot in 2006 for their work using the Cosmic Background Explorer Satellite to understand the big-bang theory of the universe.Photo Credit: (NASA/Paul E. Alers)

Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = -0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.

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.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

PubMed

Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing

2017-12-01

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing

2017-12-01

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N >1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N =1 up to the thermodynamic limit.

Lyapunov exponents, covariant vectors and shadowing sensitivity analysis of 3D wakes: from laminar to chaotic regimes

NASA Astrophysics Data System (ADS)

Wang, Qiqi; Rigas, Georgios; Esclapez, Lucas; Magri, Luca; Blonigan, Patrick

2016-11-01

Bluff body flows are of fundamental importance to many engineering applications involving massive flow separation and in particular the transport industry. Coherent flow structures emanating in the wake of three-dimensional bluff bodies, such as cars, trucks and lorries, are directly linked to increased aerodynamic drag, noise and structural fatigue. For low Reynolds laminar and transitional regimes, hydrodynamic stability theory has aided the understanding and prediction of the unstable dynamics. In the same framework, sensitivity analysis provides the means for efficient and optimal control, provided the unstable modes can be accurately predicted. However, these methodologies are limited to laminar regimes where only a few unstable modes manifest. Here we extend the stability analysis to low-dimensional chaotic regimes by computing the Lyapunov covariant vectors and their associated Lyapunov exponents. We compare them to eigenvectors and eigenvalues computed in traditional hydrodynamic stability analysis. Computing Lyapunov covariant vectors and Lyapunov exponents also enables the extension of sensitivity analysis to chaotic flows via the shadowing method. We compare the computed shadowing sensitivities to traditional sensitivity analysis. These Lyapunov based methodologies do not rely on mean flow assumptions, and are mathematically rigorous for calculating sensitivities of fully unsteady flow simulations.

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

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.

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the

Profiled Roller Stress/Fatigue Life Analysis Methodology and Establishment of an Appropriate Stress/Life Exponent

NASA Technical Reports Server (NTRS)

1997-01-01

The objective of this work was to determine the three dimensional volumetric stress field, surface pressure distribution and actual contact area between a 0.50" square roller with different crown profiles and a flat raceway surface using Finite Element Analysis. The 3-dimensional stress field data was used in conjunction with several bearing fatigue life theories to extract appropriate values for stress-life exponents. Also, results of the FEA runs were used to evaluate the laminated roller model presently used for stress and life prediction.

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

Chaotic dynamics of Comet 1P/Halley: Lyapunov exponent and survival time expectancy

NASA Astrophysics Data System (ADS)

Muñoz-Gutiérrez, M. A.; Reyes-Ruiz, M.; Pichardo, B.

2015-03-01

The orbital elements of Comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit of Comet Halley and to quantify the time-scale over which its motion can be predicted confidently. In addition, we attempt to determine the time-scale over which its present day orbit will remain stable. Numerical simulations of the dynamics of test particles in orbits similar to that of Comet Halley are carried out with the MERCURY 6.2 code. On the basis of these we construct survival time maps to assess the absolute stability of Halley's orbit, frequency analysis maps to study the variability of the orbit, and we calculate the Lyapunov exponent for the orbit for variations in initial conditions at the level of the present day uncertainties in our knowledge of its orbital parameters. On the basis of our calculations of the Lyapunov exponent for Comet Halley, the chaotic nature of its motion is demonstrated. The e-folding time-scale for the divergence of initially very similar orbits is approximately 70 yr. The sensitivity of the dynamics on initial conditions is also evident in the self-similarity character of the survival time and frequency analysis maps in the vicinity of Halley's orbit, which indicates that, on average, it is unstable on a time-scale of hundreds of thousands of years. The chaotic nature of Halley's present day orbit implies that a precise determination of its motion, at the level of the present-day observational uncertainty, is difficult to predict on a time-scale of approximately 100 yr. Furthermore, we also find that the ejection of Halley from the Solar system or its collision with another body could occur on a time-scale as short as 10 000 yr.

LETTER TO THE EDITOR: Two-centre exchange integrals for complex exponent Slater orbitals

NASA Astrophysics Data System (ADS)

Kuang, Jiyun; Lin, C. D.

1996-12-01

The one-dimensional integral representation for the Fourier transform of a two-centre product of B functions (finite linear combinations of Slater orbitals) with real parameters is generalized to include B functions with complex parameters. This one-dimensional integral representation allows for an efficient method of calculating two-centre exchange integrals with plane-wave electronic translational factors (ETF) over Slater orbitals of real/complex exponents. This method is a significant improvement on the previous two-dimensional quadrature method of the integrals. A new basis set of the form 0953-4075/29/24/005/img1 is proposed to improve the description of pseudo-continuum states in the close-coupling treatment of ion - atom collisions.

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.

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.

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.

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.

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

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.

Orbital Exponent Optimization in Elementary VB Calculations of the Chemical Bond in the Ground State of Simple Molecular Systems

ERIC Educational Resources Information Center

Magnasco, Valerio

2008-01-01

Orbital exponent optimization in the elementary ab-initio VB calculation of the ground states of H[subscript 2][superscript +], H[subscript 2], He[subscript 2][superscript +], He[subscript 2] gives a fair description of the exchange-overlap component of the interatomic interaction that is important in the bond region. Correct bond lengths and…

Fractional-exponent behavior of magnetization near Tc in Bi2Sr2CaCu2O8

NASA Astrophysics Data System (ADS)

Li, Lu; Naughton, M. J.; Ono, S.; Ong, N. P.

2005-03-01

Using high-resolution torque magnetometry, we have investigated in detail how long-range phase coherence develops as the critical temperature Tc (88.7 K) is approached in optimally-doped Bi2Sr2CaCuO8+δ with field H||c. Three distinct regimes are observed. Above ˜92 K, |M| increases rapidly as T->Tc in step with the vortex Nernst signal. M is strictly linear in H in weak H, but shows strong curvature at large H (5-14 T). The curvature provides a determination of the correlation length ξsc which grows as a power law, viz. ξsc˜1/t^ν. In the second regime, 86 < T < 92 K, M becomes nonlinear in H, viz. M˜H^α(T), where the exponent α(T) decreases from 1 to 0. This interesting fractional-exponent behavior is highly unusual and fits poorly with conventional pictures of `fluctuating diamagnetism.' As previously known, M is virtually H independent below 2 Tesla at the ``crossing temperature'' Tcr = 86 K. Below Tcr, M is a function of H. We compare this behavior with predictions of the 3DXY and Kosterlitz-Thouless theory. Supported by funds from the U.S. National Science Foundation under grant DMR 0213706.

The largest Lyapunov exponent of gait in young and elderly individuals: A systematic review.

PubMed

Mehdizadeh, Sina

2018-02-01

The largest Lyapunov exponent (LyE) is an accepted method to quantify gait stability in young and old adults. However, a range of LyE values has been reported in the literature for healthy young and elderly adults in normal walking. Therefore, it has been impractical to use the LyE as a clinical measure of gait stability. The aims of this systematic review were to summarize different methodological approaches of quantifying LyE, as well as to classify LyE values of different body segments and joints in young and elderly individuals during normal walking. The Pubmed, Ovid Medline, Scopus and ISI Web of Knowledge databases were searched using keywords related to gait, stability, variability, and LyE. Only English language articles using the Lyapunov exponent to quantify the stability of healthy normal young and old subjects walking on a level surface were considered. 102 papers were included for full-text review and data extraction. Data associated with the walking surface, data recording method, sampling rate, walking speed, body segments and joints, number of strides/steps, variable type, filtering, time-normalizing, state space dimension, time delay, LyE algorithm, and the LyE values were extracted. The disparity in implementation and calculation of the LyE was from, (i) experiment design, (ii) data pre-processing, and (iii) LyE calculation method. For practical implementation of LyE as a measure of gait stability in clinical settings, a standard and universally accepted approach of calculating LyE is required. Therefore, future studies should look for a standard and generalized procedure to apply and calculate LyE. Copyright © 2017 Elsevier B.V. All rights reserved.

Effects of external intermittency and mean shear on the spectral inertial-range exponent in a turbulent square jet

NASA Astrophysics Data System (ADS)

Zhang, J.; Xu, M.; Pollard, A.; Mi, J.

2013-05-01

This study investigates by experiment the dependence of the inertial-range exponent m of the streamwise velocity spectrum on the external intermittency factor γ (≡ the fraction of time the flow is fully turbulent) and the mean shear S in a turbulent square jet. Velocity measurements were made using hot-wire anemometry in the jet at 15 < x/De < 40, where De denotes the exit equivalent diameter, and for an exit Reynolds number of Re = 50 000. The Taylor microscale Reynolds number Rλ varies from about 70 to 450 in the present study. The TERA (turbulent energy recognition algorithm) method proposed by Falco and Gendrich [in Near-Wall Turbulence: 1988 Zoran Zariç Memorial Conference, edited by S. J. Kline and N. H. Afgan (Hemisphere Publishing Corp., Washington, DC, 1990), pp. 911-931] is discussed and applied to estimate the intermittency factor from velocity signals. It is shown that m depends strongly on γ but negligibly on S. More specifically, m varies with γ following m=mt+(lnγ-0.0173)1/2, where mt denotes the spectral exponent found in fully turbulent regions.

Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model

NASA Astrophysics Data System (ADS)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs' statistical mechanics.

PubMed

Plastino, A; Rocca, M C

2017-06-01

Appealing to the 1902 Gibbs formalism for classical statistical mechanics (SM)-the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics-we show that already at the classical level there is a strong correlation between Renyi's exponent α and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.

Importance sampling with imperfect cloning for the computation of generalized Lyapunov exponents

NASA Astrophysics Data System (ADS)

Anteneodo, Celia; Camargo, Sabrina; Vallejos, Raúl O.

2017-12-01

We revisit the numerical calculation of generalized Lyapunov exponents, L (q ) , in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then L (q ) is obtained by taking the limit noise-amplitude → 0 after the calculation. We focus on a particular method that involves periodic cloning and pruning of a set of trajectories. However, instead of considering a noisy dynamics, we implement an imperfect (noisy) cloning. This alternative method is compared with the standard one and, when possible, with analytical results. As a workbench we use the asymmetric tent map, the standard map, and a system of coupled symplectic maps. The general conclusion of this study is that the imperfect-cloning method performs as well as the standard one, with the advantage of preserving the deterministic dynamics.

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

NASA Astrophysics Data System (ADS)

Schlief, Andres; Lunts, Peter; Lee, Sung-Sik

2017-04-01

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

Non-Gaussian Nature of Fracture and the Survival of Fat-Tail Exponents

NASA Astrophysics Data System (ADS)

Tallakstad, Ken Tore; Toussaint, Renaud; Santucci, Stephane; Måløy, Knut Jørgen

2013-04-01

We study the fluctuations of the global velocity Vl(t), computed at various length scales l, during the intermittent mode-I propagation of a crack front. The statistics converge to a non-Gaussian distribution, with an asymmetric shape and a fat tail. This breakdown of the central limit theorem (CLT) is due to the diverging variance of the underlying local crack front velocity distribution, displaying a power law tail. Indeed, by the application of a generalized CLT, the full shape of our experimental velocity distribution at large scale is shown to follow the stable Levy distribution, which preserves the power law tail exponent under upscaling. This study aims to demonstrate in general for crackling noise systems how one can infer the complete scale dependence of the activity—and extreme event distributions—by measuring only at a global scale.

Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

2011-11-15

We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for noninteracting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudodisorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andre model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the noninteracting quantum critical point of the Aubry-Andre model.

Strong Converse Exponents for a Quantum Channel Discrimination Problem and Quantum-Feedback-Assisted Communication

NASA Astrophysics Data System (ADS)

Cooney, Tom; Mosonyi, Milán; Wilde, Mark M.

2016-06-01

This paper studies the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. The results obtained here generalize those known in the theory of quantum hypothesis testing for binary state discrimination. We show that, in this particular setting, the most general adaptive discrimination strategies provide no asymptotic advantage over non-adaptive tensor-power strategies. This conclusion follows by proving a quantum Stein's lemma for this channel discrimination setting, showing that a constant bound on the Type I error leads to the Type II error decreasing to zero exponentially quickly at a rate determined by the maximum relative entropy registered between the channels. The strong converse part of the lemma states that any attempt to make the Type II error decay to zero at a rate faster than the channel relative entropy implies that the Type I error necessarily converges to one. We then refine this latter result by identifying the optimal strong converse exponent for this task. As a consequence of these results, we can establish a strong converse theorem for the quantum-feedback-assisted capacity of a channel, sharpening a result due to Bowen. Furthermore, our channel discrimination result demonstrates the asymptotic optimality of a non-adaptive tensor-power strategy in the setting of quantum illumination, as was used in prior work on the topic. The sandwiched Rényi relative entropy is a key tool in our analysis. Finally, by combining our results with recent results of Hayashi and Tomamichel, we find a novel operational interpretation of the mutual information of a quantum channel {mathcal{N}} as the optimal Type II error exponent when discriminating between a large number of independent instances of {mathcal{N}} and an arbitrary "worst-case" replacer channel chosen from the set of all replacer channels.

Different Coefficients and Exponents for Metabolic Body Weight in a Model to Estimate Individual Feed Intake for Growing-finishing Pigs

PubMed Central

Lee, S. A.; Kong, C.; Adeola, O.; Kim, B. G.

2016-01-01

Estimation of feed intake (FI) for individual animals within a pen is needed in situations where more than one animal share a feeder during feeding trials. A partitioning method (PM) was previously published as a model to estimate the individual FI (IFI). Briefly, the IFI of a pig within the pen was calculated by partitioning IFI into IFI for maintenance (IFIm) and IFI for growth. In the PM, IFIm is determined based on the metabolic body weight (BW), which is calculated using the coefficient of 106 and exponent of 0.75. Two simulation studies were conducted to test the hypothesis that the use of different coefficients and exponents for metabolic BW to calculate IFIm improves the accuracy of the estimates of IFI for pigs, and that PM is applied to pigs fed in group-housing systems. The accuracy of prediction represented by difference between actual and estimated IFI was compared using PM, ratio (RM), or averaging method (AM). In simulation studies 1 and 2, the PM estimated IFI better than the AM and RM during most of the periods (p<0.05). The use of 0.60 as the exponent and the coefficient of 197 to calculate metabolic BW did not improve the accuracy of the IFI estimates in both simulation studies 1 and 2. The results imply that the use of 197 kcal×kg BW0.60 as metabolizable energy for maintenance in PM does not improve the accuracy of IFI estimations compared with the use of 106 kcal×kg BW0.75 and that the PM estimates the IFI of pigs with greater accuracy compared with the averaging or ratio methods in group-housing systems. PMID:27608642

Surface exponents of trails in two dimensions at tricriticality: Computer simulation study

NASA Astrophysics Data System (ADS)

Meirovitch, H.; Chang, I. S.; Shapir, Y.

1989-09-01

Using the scanning simulation method, we study self-attracting trails (with energy ɛ per intersection) terminally attached to an im- penetrable linear boundary on a square lattice at their tricrital collapse transition. Our results for the exponents of the partition functions are γ1=0.634+/-0.025 (one end attached to the surface) and γ11=-0.44+/-0.02 (both ends attached). These values (with 95% significance limits) are within the error bars of the numerical estimates of Seno and Stella [Europhys. Lett. 7, 605 (1989)] for self-avoiding walks (SAW's) at the FTHETA-point on the same lattice. Our results, however, differ significantly from the exact values derived by Duplantier and Saleur for SAW's on a dilute hexagonal lattice at the FTHETA' point. The collapse temperature Tt and the tricritical growth parameter μ are very close to their analytic bounds -ɛ/kBTt=ln3 and μ=3.

Retrievals of aerosol optical depth and Angström exponent from ground-based Sun-photometer data of Singapore.

PubMed

Salinas, Santo V; Chew, Boon N; Liew, Soo C

2009-03-10

The role of aerosols in climate and climate change is one of the factors that is least understood at the present. Aerosols' direct interaction with solar radiation is a well understood mechanism that affects Earth's net radiative forcing. However, quantifying its magnitude is more problematic because of the temporal and spatial variability of aerosol particles. To enhance our understanding of the radiative effects of aerosols on the global climate, Singapore has joined the AERONET (Aerosol Robotic Network) worldwide network by contributing ground-based direct Sun measurements performed by means of a multiwavelength Sun-photometer instrument. Data are collected on an hourly basis, then are uploaded to be fully screened and quality assured by AERONET. We use a one year data record (level 1.5/2.0) of measured columnar atmospheric optical depth, spanning from November 2006 to October 2007, to study the monthly and seasonal variability of the aerosol optical depth and the Angström exponent. We performed independent retrievals of these parameters (aerosol optical depth and Angström exponent) by using the photometer's six available bands covering the near-UV to near-IR (380-1080 nm). As a validation, our independent retrievals were compared with AERONET 1.5/2.0 level direct Sun product.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Presence of nonlinearity in intracranial EEG recordings: detected by Lyapunov exponents

NASA Astrophysics Data System (ADS)

Liu, Chang-Chia; Shiau, Deng-Shan; Chaovalitwongse, W. Art; Pardalos, Panos M.; Sackellares, J. C.

2007-11-01

In this communication, we performed nonlinearity analysis in the EEG signals recorded from patients with temporal lobe epilepsy (TLE). The largest Lyapunov exponent (Lmax) and phase randomization surrogate data technique were employed to form the statistical test. EEG recordings were acquired invasively from three patients in six brain regions (left and right temporal depth, sub-temporal and orbitofrontal) with 28-32 depth electrodes placed in depth and subdural of the brain. All three patients in this study have unilateral epileptic focus region on the right hippocampus(RH). Nonlinearity was detected by comparing the Lmax profiles of the EEG recordings to its surrogates. The nonlinearity was seen in all different states of the patient with the highest found in post-ictal state. Further our results for all patients exhibited higher degree of differences, quantified by paired t-test, in Lmax values between original and its surrogate from EEG signals recorded from epileptic focus regions. The results of this study demonstrated the Lmax is capable to capture spatio-temporal dynamics that may not be able to detect by linear measurements in the intracranial EEG recordings.

Continuously varying of critical exponents with the bismuth doped in the La0.8Na0.2Mn1-xBixO3 (0 ≤ x ≤ 0.06) manganites

NASA Astrophysics Data System (ADS)

Laouyenne, M. R.; Baazaoui, M.; Mahjoub, Sa.; Cheikhrouhou-Koubaa, W.; Farah, Kh.; Oumezzine, M.

2018-04-01

A comprehensive analysis of the critical phenomena for the nominal compositions La0.8Na0.2Mn1-xBixO3 (0 ≤ x ≤ 0.06) was carried out. The critical exponents values were calculated by various techniques such as Modified Arrott plot (MAP), Kouvel Fisher (KF) method and critical isotherm (CI). Comparison of the experimental data with the above theoretical models showed that the critical exponents β, γ and δ for the undoped sample are quite well described by the tricritical mean-field model (TMF). Furthermore, the substitution of Mn by Bi ions led to the increase of γ which approached the 3D-Heisenberg model (γ = 1 325 and β took similar values to those predicted by the TMF model. The validity of the exponents values was confirmed with the scaling hypothesis; the M (T, ε) curves collapse onto two independent universal branches below and above Tc.

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

On the improvement of Wiener attack on RSA with small private exponent.

PubMed

Wu, Mu-En; Chen, Chien-Ming; Lin, Yue-Hsun; Sun, Hung-Min

2014-01-01

RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus N = pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r + 8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r + 8 bits to 2r + 2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r - 6 bits when we extend Weiner's boundary r bits. It means that our result is 2(14) times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.

On the Improvement of Wiener Attack on RSA with Small Private Exponent

PubMed Central

Chen, Chien-Ming; Lin, Yue-Hsun

2014-01-01

RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus N = pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r + 8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r + 8 bits to 2r + 2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r − 6 bits when we extend Weiner's boundary r bits. It means that our result is 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits. PMID:24982974

FAST TRACK COMMUNICATION Critical exponents of domain walls in the two-dimensional Potts model

NASA Astrophysics Data System (ADS)

Dubail, Jérôme; Lykke Jacobsen, Jesper; Saleur, Hubert

2010-12-01

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e. connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{\\ell _1-\\ell _2,2\\ell _1}, valid for 0 <= Q <= 4, that describe the insertion of ell1 thin and ell2 thick domain walls.

A generalization of the power law distribution with nonlinear exponent

NASA Astrophysics Data System (ADS)

Prieto, Faustino; Sarabia, José María

2017-01-01

The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.

Characterizing Submonolayer Growth of 6P on Mica: Capture Zone Distributions vs. Growth Exponents and the Role of Hot Precursors

NASA Astrophysics Data System (ADS)

Einstein, T. L.; Morales-Cifuentes, Josue; Pimpinelli, Alberto

2015-03-01

Analyzing capture-zone distributions (CZD) using the generalized Wigner distribution (GWD) has proved a powerful way to access the critical nucleus size i. Of the several systems to which the GWD has been applied, we consider 6P on mica, for which Winkler's group found i ~ 3 . Subsequently they measured the growth exponent α (island density ~Fα , for flux F) of this system and found good scaling but different values at small and large F, which they attributed to DLA and ALA dynamics, but with larger values of i than found from the CZD analysis. We investigate this result in some detail. The third talk of this group describes a new universal relation between α and the characteristic exponent β of the GWD. The second talk reports the results of a proposed model that takes long-known transient ballistic adsorption into account, for the first time in a quantitative way. We find several intermediate scaling regimes, with distinctive values of α and an effective activation energy. One of these, rather than ALA, gives the best fit of the experimental data and a value of i consistent with the CZD analysis. Work at UMD supported by NSF CHE 13-05892.

On the effects of surrogacy of energy dissipation in determining the intermittency exponent in fully developed turbulence

NASA Astrophysics Data System (ADS)

Cleve, J.; Greiner, M.; Sreenivasan, K. R.

2003-03-01

The two-point correlation function of the energy dissipation, obtained from a one-point time record of an atmospheric boundary layer, reveals a rigorous power law scaling with intermittency exponent μ approx 0.20 over almost the entire inertial range of scales. However, for the related integral moment, the power law scaling is restricted to the upper part of the inertial range only. This observation is explained in terms of the operational surrogacy of the construction of energy dissipation, which influences the behaviour of the correlation function for small separation distances.

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

Wavefunctions, quantum diffusion, and scaling exponents in golden-mean quasiperiodic tilings.

PubMed

Thiem, Stefanie; Schreiber, Michael

2013-02-20

We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.

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

(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

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

How large a dataset should be in order to estimate scaling exponents and other statistics correctly in studies of solar wind turbulence

NASA Astrophysics Data System (ADS)

Rowlands, G.; Kiyani, K. H.; Chapman, S. C.; Watkins, N. W.

2009-12-01

Quantitative analysis of solar wind fluctuations are often performed in the context of intermittent turbulence and center around methods to quantify statistical scaling, such as power spectra and structure functions which assume a stationary process. The solar wind exhibits large scale secular changes and so the question arises as to whether the timeseries of the fluctuations is non-stationary. One approach is to seek a local stationarity by parsing the time interval over which statistical analysis is performed. Hence, natural systems such as the solar wind unavoidably provide observations over restricted intervals. Consequently, due to a reduction of sample size leading to poorer estimates, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as ~1/N as N becomes large for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and “real world” time series, and we find that in particular for heavy tailed processes, for realizable N, one is far from this ~1/N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some “real world” time series from the solar wind. With fewer datapoints the stationary timeseries becomes indistinguishable from a nonstationary process and we illustrate this with nonstationary synthetic datasets. Reference article: K. H. Kiyani, S. C. Chapman and N. W. Watkins, Phys. Rev. E 79, 036109 (2009).

Gradual multifractal reconstruction of time-series: Formulation of the method and an application to the coupling between stock market indices and their Hölder exponents

NASA Astrophysics Data System (ADS)

Keylock, Christopher J.

2018-04-01

A technique termed gradual multifractal reconstruction (GMR) is formulated. A continuum is defined from a signal that preserves the pointwise Hölder exponent (multifractal) structure of a signal but randomises the locations of the original data values with respect to this (φ = 0), to the original signal itself(φ = 1). We demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual-tree complex wavelet transform. That is, the φ = 0 end of the continuum is realised using the recently proposed iterated, amplitude adjusted wavelet transform algorithm (Keylock, 2017) that fully randomises the wavelet phases. This is extended to the GMR formulation by selective phase randomisation depending on whether or not the wavelet coefficient amplitudes exceeds a threshold criterion. An econophysics application of the technique is presented. The relation between the normalised log-returns and their Hölder exponents for the daily returns of eight financial indices are compared. One particularly noticeable result is the change for the two American indices (NASDAQ 100 and S&P 500) from a non-significant to a strongly significant (as determined using GMR) cross-correlation between the returns and their Hölder exponents from before the 2008 crash to afterwards. This is also reflected in the skewness of the phase difference distributions, which exhibit a geographical structure, with Asian markets not exhibiting significant skewness in contrast to those from elsewhere globally.

Application of AERONET Single Scattering Albedo and Absorption Angstrom Exponent to Classify Dominant Aerosol Types during DRAGON Campaigns

NASA Astrophysics Data System (ADS)

Giles, D. M.; Holben, B. N.; Eck, T. F.; Schafer, J.; Crawford, J. H.; Kim, J.; Sano, I.; Liew, S.; Salinas Cortijo, S. V.; Chew, B. N.; Lim, H.; Smirnov, A.; Sorokin, M.; Kenny, P.; Slutsker, I.

2013-12-01

Aerosols can have major implications on human health by inducing respiratory diseases due to inhalation of fine particles from biomass burning smoke or industrial pollution and on radiative forcing whereby the presence of absorbing aerosol particles (e.g., black carbon) increases atmospheric heating. Aerosol classification techniques have utilized aerosol loading and aerosol properties derived from multi-spectral and multi-angle observations by ground-based (e.g., AERONET) and satellite instrumentation (e.g., MISR). Aerosol Robotic Network (AERONET) data have been utilized to determine aerosol types by implementing various combinations of measured aerosol optical depth or retrieved size and absorption aerosol properties (e.g., Gobbi et al., 2007; Russell et al., 2010). Giles et al. [2012] showed single scattering albedo (SSA) relationship with extinction Angstrom exponent (EAE) can provide an estimate of the general classification of dominant aerosol types (i.e., desert dust, urban/industrial pollution, biomass burning smoke, and mixtures) based on data from ~20 AERONET sites located in known aerosol source regions. In addition, the absorption Angstrom exponent relationship with EAE can provide an indication of the dominant absorbing aerosol type such as dust, black carbon, brown carbon, or mixtures of them. These classification techniques are applied to the AERONET Level 2.0 quality assured data sets collected during Distributed Regional Aerosol Gridded Observational Network (DRAGON) campaigns in Maryland (USA), Japan, South Korea, Singapore, Penang (Malaysia), and California (USA). An analysis of aerosol type classification for DRAGON sites is performed as well as an assessment of the spatial variability of the aerosol types for selected DRAGON campaigns. Giles, D. M., B. N. Holben, T. F. Eck, A. Sinyuk, A. Smirnov, I. Slutsker, R. R. Dickerson, A. M. Thompson, and J. S. Schafer (2012), An analysis of AERONET aerosol absorption properties and classifications

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.

PubMed

Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue

2018-02-01

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

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.

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

Henry Currey FRIBA (1820-1900): leading Victorian hospital architect, and early exponent of the "pavilion principle".

PubMed

Cook, G C

2002-06-01

The "pavilion plan" for hospital design originated in France in the 18th century and was popularised in England by John Roberton and George Godwin in the mid-19th century; the underlying rationale was that with improved ventilation the mortality rate (at that time exceedingly high) was significantly reduced. Among the enthusiasts for this new style was Florence Nightingale (herself a miasmatist)--who had experienced astronomically high death rates in the hospital at Scutari during the Crimean War (1854-6). One of the leading exponents of this style of hospital architecture was Henry Currey (1820-1900) whose greatest achievement was undoubtedly the design for the new St Thomas's Hospital on the Lambeth Palace Road.

Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by finite Fourier-Haar series

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

Sharapudinov, I I

2014-02-28

The paper deals with the space L{sup p(x)} consisting of classes of real measurable functions f(x) on [0,1] with finite integral ∫{sub 0}{sup 1}|f(x)|{sup p(x)} dx. If 1≤p(x)≤ p-bar <∞, then the space L{sup p(x)} can be made into a Banach space with the norm ∥f∥{sub p(⋅)}=inf(α > 0:∫{sub 0}{sup 1}|f(x)/α|{sup p(x)} dx≤ 1). The inequality ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)Ω(f,1/n){sub p(⋅)}, which is an analogue of the first Jackson theorem, is shown to hold for the finite Fourier-Haar series Q{sub n}(f), provided that the variable exponent p(x) satisfies the condition |p(x)−p(y)|ln (1/|x−y|)≤ c. Here, Ω(f,δ){sub p(⋅)} is the modulus of continuity in L{sup p(x)} defined inmore » terms of Steklov functions. If the function f(x) lies in the Sobolev space W{sub p(⋅)}{sup 1} with variable exponent p(x), it is shown that ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)/n∥f{sup ′}∥{sub p(⋅)}. Methods for estimating the deviation |f(x)−Q{sub n}(f,x)| for f(x)∈W{sub p(⋅)}{sup 1} at a given point x∈[0,1] are also examined. The value of sup{sub f∈W{sub p{sup 1}(1)}}|f(x)−Q{sub n}(f,x)| is calculated in the case when p(x)≡p= const, where W{sub p}{sup 1}(1)=(f∈W{sub p}{sup 1}:∥f{sup ′}∥{sub p(⋅)}≤1). Bibliography: 17 titles.« less

Critical exponents and universal magnetic behavior of noncentrosymmetric Fe0.6Co0.4Si

NASA Astrophysics Data System (ADS)

Shanmukharao Samatham, S.; Suresh, K. G.

2018-05-01

The critical magnetic properties of a non-centrosymmetric B20 cubic helimagnet Fe0.6Co0.4Si are investigated using magnetization isotherms. It belongs to the 3D-Heisenberg universality class with short range magnetic coupling as inferred from the self-consistent critical exponents , , and in combination with exchange interaction . Itinerant magnetic nature of the compound is realized by the Rhodes–Wholfarth analysis. Field-induced weak first (parahelical) to second (parafield-polarized) order transition is reported to occur at low critical field due to the weak spin–orbit coupling arising from the weak Dzyaloshinksii–Moriya interactions. Our study suggests the distinct phenomenological magnetic structures for Fe-based cubic magnets (Fe1‑x Co x Si and FeGe) and MnSi which cause contrasting physical properties.

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann method: Massive scalar theory and critical exponents

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

Carvalho, Paulo R. S.; Leite, Marcelo M.

2013-09-15

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar λφ{sup 4} theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents η and ν at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann (BPHZ) method at the same loop order,more » show that the proposed method requires fewer diagrams and establish a connection between the two approaches.« less