Modeling and analysis of an agent-based model for Chinese stock market

We constructed an agent-based stock market model which concisely describe investors? heterogeneity and adaptability by introducing price sensitivity and feedback time. Under different parameters, the peak and fat-tail property of return distribution is produced and the obtained statistic values coincide with empirical results: the center peak exponents range from ?0.787 to ?0.661, and the tail exponents range from ?4.29 to ?2.37. Besides, long-term correlation in volatility is examined by DFA1 method, and the obtained exponent α is 0.803, which also coincides with the exponent of 0.78 found in real market.     

Preservation of long range temporal correlations under extreme random dilution

Many natural time series exhibit long range temporal correlations that may be characterized by power-law scaling exponents. However, in many cases, the time series have uneven time intervals due to, for example, missing data points, noisy data, and outliers. Here we study the effect of randomly missing data points on the power-law scaling exponents of time series that are long range temporally correlated. The Fourier transform and detrended fluctuation analysis (DFA) techniques are used for scaling exponent estimation. We find that even under extreme dilution of more than 50%, the value of the scaling exponent remains almost unaffected. Random dilution is also applied on heart interbeat interval time series. It is found that dilution of 70%-80% of the data points leads to a reduction of only 8% in the scaling exponent; it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90%.     

Interpretation of heart rate variability via detrended fluctuation analysis and alphabeta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alphabeta filter to DFA to determine patterns in the power-law behavior that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behavior, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

False Euro (FEUR) exchange rate correlated behaviors and investment strategy

We have searched for correlations and anticorrelations with respect to currencies as CHF, DKK, JPY, and USD in order to understand the EUR behavior. In order to do so we have invented a false euro (FEUR) dating back to 1993 and have derived simulated exchange rates of the FEUR. Within the Detrended Fluctuation Analysis (DFA) statistical method we have obtained the power law behavior describing the rms. deviation of the fluctuations as a function of time. We have compared the time-dependent exponent for these four exchange rates, and observe the role of the DEM, and the other currencies forming the EUR. A simple investment strategy based on the local DFA technique shows one can obtain appreciable gains, even taking into account some modest transaction fee. We compare the time dependent α exponent of the DFA for various exchange rates as in a correlation matrix for estimating respective influences. Received 31 August 2000     

Detection of changes in the fractal scaling of heart rate and speed in a marathon race

The aim of this study was to detect changes in the fractal scaling behavior of heart rate and speed fluctuations when the average runner’s speed decreased with fatigue. Scaling analysis in heart rate (HR) and speed (S) dynamics of marathon runners was performed using the detrended fluctuation analysis (DFA) and the wavelet based structure function. We considered both: the short-range (α₁) and the long-range (α₂) scaling exponents for the DFA method separated by a change-point, (box length), the same for all the races. The variability of HR and S decreased in the second part of the marathon race, while the cardiac cost time series (i.e. the number of cardiac beats per meter) increased due to the decreasing speed behavior. The scaling exponents α₁ and α₂ of HR and α₁ of S, increased during the race () as did the HR wavelet scaling exponent (τ). These findings provide evidence of the significant effect of fatigue induced by long exercise on the heart rate and speed variability.     

Scaling analysis of paces of fetal breathing, gross-body and extremity movements

Using detrended fluctuation analysis (DFA), we studied the scaling properties of the time instances (occurrence) of the fetal breathing, gross-body, and extremity movements scored on a second by second basis from the recorded ultrasound measurements of 49 fetuses. The DFA exponent α of all the three movements of the fetuses varied between 0.63 and 1.1. We found an increase in α obtained for the movement due to breathing as a function of the gestational age while this trend was not observed for gross-body and extremity movements. This trend was argued as the indication of the maturation of lung and functional development of respiratory aspect of the fetal central nervous system. This result may be useful in discriminating normal fetuses from high-risk fetuses.     

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Randomness and changes of heart rate and respiratory frequency during high altitude mountain ascent without acclimatization

The aim of this study was to detect and compare the changes in the time-frequency and fractal scaling behaviors of heart rate (HR) and respiratory frequency (Rf), recorded simultaneously during a high altitude mountain ascent. The time-frequency analysis was performed using the local cosine4 orthonormal bases of Coifman, Malvar and Meyer, whose spectrum is not redundant as those computed with the short Fourier transform. The fractal scaling behavior was obtained using the detrended fluctuation (DFA) and the wavelet leaders (WL) analysis. Results showed that the high altitude mountain ascent differently affected HR and Rf variability. Rf average values increased (p=0.0003) while HR average values did not change. The scaling variability of HR was altered during the mountain ascent, which was detected by the increasing HR short range DFA exponents with altitude (p<0.03). Rf scaling variability remained unchanged. These differences between HR and Rf alterations were also observed for the local cosine4 power law behavior since power law exponents, in absolute values, increased for HR (p<0.003) while those of Rf did not change. Furthermore, the ratio of low over the whole local spectrum energy of Rf decreased with altitude (p=0.04) in contrast to HR. In most of these HR and Rf analyses, one of the two time series was significantly modified but not both. Moreover, the Rf local cosine4 spectrum had higher entropy compared to HR (p<0.01), the difference between the Rf and the HR entropy increased (p=0.04) during the mountain ascent. In consequence, Rf had more randomness than HR and altitude increased this difference.     

Oscillating singularities on cantor sets: A grand-canonical multifractal formalism

The singular behavior of functions is generally characterized by their Hölder exponent. However, we show that this exponent poorly characterizes oscillating singularities. We thus introduce a second exponent that accounts for the oscillations of a singular behavior and we give a characterization of this exponent using the wavelet transform. We then elaborate on a grand-canonical multifractal formalism that describes statistically the fluctuations of both the Hölder and the oscillation exponents. We prove that this formalism allows us to recover the generalized singularity spectrum of a large class of fractal functions involving oscillating singularities.     

Permutation entropy and detrend fluctuation analysis for the natural complexity of cardiac heart interbeat signals

We compute fractal dimension and permutation entropy for healthy and people who have experienced heart failure. Our result shows that permutation entropy is a suitable approach as well as detrend fluctuation analysis (DFA). The result of DFA shows that the fractal dimensions for healthy and heart failure are different as well as the permutation entropy result. The fluctuation value for permutation entropy for an individual who has experienced heart failure is bigger than for a healthy person. There is some specific change in the interbeat signal of a person who has experienced heart failure, but there is not previous trend for a healthy person.     

Effects of Cardiac Resynchronization Therapy on Cardio-Respiratory Coupling

In this study, the effect of cardiac resynchronization therapy (CRT) on the relationship between the cardiovascular and respiratory systems in heart failure subjects was examined for the first time. We hypothesized that alterations in cardio-respiratory interactions, after CRT implantation, quantified by signal complexity, could be a marker of a favorable CRT response. Sample entropy and scaling exponents were calculated from synchronously recorded cardiac and respiratory signals 20 min in duration, collected in 47 heart failure patients at rest, before and 9 months after CRT implantation. Further, cross-sample entropy between these signals was calculated. After CRT, all patients had lower heart rate and CRT responders had reduced breathing frequency. Results revealed that higher cardiac rhythm complexity in CRT non-responders was associated with weak correlations of cardiac rhythm at baseline measurement over long scales and over short scales at follow-up recording. Unlike CRT responders, in non-responders, a significant difference in respiratory rhythm complexity between measurements could be consequence of divergent changes in correlation properties of the respiratory signal over short and long scales. Asynchrony between cardiac and respiratory rhythm increased significantly in CRT non-responders during follow-up. Quantification of complexity and synchrony between cardiac and respiratory signals shows significant associations between CRT success and stability of cardio-respiratory coupling.     

Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism: Evidence from detrended fluctuation analysis of heart rate variability

Despite many previous studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent α1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves’ disease patients (32 females and 4 males; age 30 ± 1 years, means ± SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P<0.001) in α1 (hyperthyroid 1.28±0.04 versus control 0.91±0.02), long-term scaling exponent , overall scaling exponent , low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P<0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.     

Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes

The 1D empirical mode decomposition method is applied to reduce speckle noise in the correlation fringes produced in digital speckle pattern interferometry. This method is based on the decomposition of a signal in a sum of well-behaved fast and slow oscillation modes through a sifting process, which generates a fully data-driven technique. Consequently, this is an adaptive approach and the use of basis functions in the analysis process is not required. The denoised signal is given by the residue obtained after the fast oscillation modes are removed. The performance and limitations of the denoising technique are analyzed using computer simulated fringes and these results are compared with those obtained using a wavelet sub-band removal approach. An application of the EMD method to denoise experimental correlation fringes is also presented.     

Antibunching and blinking from a single colloidal CdSe quantum dot

We have investigated the optical properties of single CdSe/ZnS nanocrystals by conducting combinations of experiments on antibunching and photoluminescence intermittence under different experimental conditions.Based on photoluminescence in an antibunching experiment,we analyzed the emission lifetime of QDs by using stretched exponentials.The difference between the parameters obtained from average lifetimes and stretched exponents were analyzed by considering the effect of nonradiative emission.An Auger-assisted tunneling model was used to explain the power law exponents of off time distribution.The power law exponent under high excitation power was correlated with a higher Auger ionization rate.Using the parameters obtained from stretched exponential function and power law,the antibunching phenomena at different time and under different excitation intensity were analyzed.     

Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity

Polyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.      

毫米波辐照下大鼠脑电的长程相关性

通过脑电长程相关性的分析,定量研究了35 GHz毫米波辐照大鼠时产生的应激反应.通过退趋势分析法,得到反映高频成分的标度指数.显示在辐照前该成分具有布朗噪声的特性,辐照时具有长程相关性;而反映低频成分的标度指数显示在辐照前该成分具有长程相关性,辐照时成为布朗噪声.引进应激指标参量低频成份标度指标数/高频成份标度指标数,...     

Distribution of anomalous exponents of natural images

Recent studies of correlations of intensity in databases of natural images revealed a remarkable property. The two point correlations are described in terms of power law behavior, with an exponent which seems to be robust. In the present Letter we consider the statistical meaning of that result. We study many individual images of one of the databases considered. We find that the same law characterizing the correlations in the whole database governs also images randomly chosen from that database, with one essential difference. The exponent characterizing each image is specific and differs from the exponent characterizing the whole database. The distribution of single image exponents has been measured and found to exhibit a rather heavy tail. The database exponent cannot, thus, be considered as a statistical representative of a single image exponent. Possible reasons for the diversity in image exponents are discussed.