The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the...The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters.展开更多
Statistical properties of stock market time series and the implication of their Hurst exponents are discussed. Hurst exponents of DJIA (Dow Jones Industrial Average) components are tested using re scaled range analy...Statistical properties of stock market time series and the implication of their Hurst exponents are discussed. Hurst exponents of DJIA (Dow Jones Industrial Average) components are tested using re scaled range analysis. In addition to the original stock return series, the linear prediction errors of the daily returns are also tested. Numerical results show that the Hurst exponent analysis can provide some information about the statistical properties of the financial time series.展开更多
In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range corre...In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.展开更多
This research aims to improve the efficiency in estimating the Hurst exponent in financial time series.A new procedure is developed based on equality in distribution and is applicable to the estimation methods of the ...This research aims to improve the efficiency in estimating the Hurst exponent in financial time series.A new procedure is developed based on equality in distribution and is applicable to the estimation methods of the Hurst exponent.We show how to use this new procedure with three of the most popular algorithms(generalized Hurst exponet,total triangles area,and fractal dimension)in the literature.Findings show that this new approach improves the accuracy of the original methods,mainly for longer series.The second contribution of this study is that we show how to use this methodology to test whether the series is self-similar,constructing a confidence interval for the Hurst exponent for which the series satisfies this property.Finally,we present an empirical application of this new procedure to stocks of the S&P500 index.Similar to previous contributions,we consider this to be relevant to financial literature,as it helps to avoid inappropriate interpretations of market efficiency that can lead to erroneous decisions not only by market participants but also by policymakers.展开更多
This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g d...This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.展开更多
By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we exten...By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.展开更多
Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range ...Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.展开更多
Eco-environmental quality is a measure of the suitability of the ecological environment for human survival and socioeconomic development.Understanding the spatial-temporal distribution and variation trend of eco-envir...Eco-environmental quality is a measure of the suitability of the ecological environment for human survival and socioeconomic development.Understanding the spatial-temporal distribution and variation trend of eco-environmental quality is essential for environmental protection and ecological balance.The remote sensing ecological index(RSEI)can quickly and objectively quantify eco-environmental quality and has been extensively utilized in regional ecological environment assessment.In this paper,Moderate Resolution Imaging Spectroradiometer(MODIS)images during the growing period(July-September)from 2000 to 2020 were obtained from the Google Earth Engine(GEE)platform to calculate the RSEI in the three northern regions of China(the Three-North region).The Theil-Sen median trend method combined with the Mann-Kendall test was used to analyze the spatial-temporal variation trend of eco-environmental quality,and the Hurst exponent and the Theil-Sen median trend were superimposed to predict the future evolution trend of eco-environmental quality.In addition,ten variables from two categories of natural and anthropogenic factors were analyzed to determine the drivers of the spatial differentiation of eco-environmental quality by the geographical detector.The results showed that from 2000 to 2020,the RSEI in the Three-North region exhibited obvious regional characteristics:the RSEI values in Northwest China were generally between 0.2 and 0.4;the RSEI values in North China gradually increased from north to south,ranging from 0.2 to 0.8;and the RSEI values in Northeast China were mostly above 0.6.The average RSEI value in the Three-North region increased at an average growth rate of 0.0016/a,showing the spatial distribution characteristics of overall improvement and local degradation in eco-environmental quality,of which the areas with improved,basically stable and degraded eco-environmental quality accounted for 65.39%,26.82%and 7.79%of the total study area,respectively.The Hurst exponent of the RSEI ranged from 0.20 to 0.76 and the future trend of eco-environmental quality was generally consistent with the trend over the past 21 years.However,the areas exhibiting an improvement trend in eco-environmental quality mainly had weak persistence,and there was a possibility of degradation in eco-environmental quality without strengthening ecological protection.Average relative humidity,accumulated precipitation and land use type were the dominant factors driving the spatial distribution of eco-environmental quality in the Three-North region,and two-factor interaction also had a greater influence on eco-environmental quality than single factors.The explanatory power of meteorological factors on the spatial distribution of eco-environmental quality was stronger than that of topographic factors.The effect of anthropogenic factors(such as population density and land use type)on eco-environmental quality gradually increased over time.This study can serve as a reference to protect the ecological environment in arid and semi-arid regions.展开更多
In this paper, the status quo and modeling principles of R/S analysis of non-linear theory are introduced and reviewed. Given the hydro-geological conditions of the Wutongzhuang coal mine, Hurst exponents of mine infl...In this paper, the status quo and modeling principles of R/S analysis of non-linear theory are introduced and reviewed. Given the hydro-geological conditions of the Wutongzhuang coal mine, Hurst exponents of mine inflow for the main shaft, venti- lating shaft and auxiliary shaft were obtained using R/S analysis, which are 0.772 0, 0.824 7 and 0.905 1 respectively. Since all of the three Hurst exponents are larger than 0.5, it can be concluded that the trend of mine inflow are a long-term as well as persistent problem. Based on the level of duration, the shafts can be listed in decreasing order as the auxiliary shaft, the ventilation shaft and the main shaft, which appears identical with the actual situation of the mine inflow. With R/S analysis, a new method for long-term forecasting of mine inflows is provided.展开更多
Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtain...Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.展开更多
Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different character...Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different characteristics of the spatial-temporal changes of vegetation cover in Guizhou Province of Southern China using the data set of SPOT VEGETATION(1999–2015) at spatial resolution of 1-km and temporal resolution of 10-day. The coefficient of variation, the Theil-Sen median trend analysis, and the Mann-Kendall test are used to investigate the spatial-temporal change of vegetation cover and its future trend. Results show that: 1) the spatial distribution pattern of vegetation cover in Guizhou Plateau is high in the east whereas low in the west. The average annual normalized difference vegetation index(NDVI) from west to east is higher than that from south to north. 2) Average annual NDVI improved obviously in the past 17 years. The growth rate of average annual NDVI is 0.028/10 yr, which is slower than that of vegetation in the country(0.048/10 yr) from 1998 to 2007. Average annual NDVI in karst area is lower than that in non-karst area. However, the growing rate of average annual NDVI in karst area(0.030/10 yr) is faster than that in non-karst area(0.023/10 yr), indicating that vegetation coverage increases more rapidly in karst area. 3) Vegetation coverage in the study area is stable overall, but fluctuates in the local scales. 4) Vegetation coverage presents a continuous increasing trend. The Hurst exponent of NDVI in different vegetation types has an obvious threshold in various elevations. 5) The proportion of vegetation cover with sustainable increase is higher than that of vegetation cover with sustainable decrease. The improvement in vegetation cover may expand to most parts of the study area.展开更多
The characteristics of coal seam development,and the prospects of a favorable coal-forming area,were evaluated for the Liaohe Basin located in China.The Number 3 and Number 9 coal seam thickness series from 60 nearly ...The characteristics of coal seam development,and the prospects of a favorable coal-forming area,were evaluated for the Liaohe Basin located in China.The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis.The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68,respectively.This suggests the presence of persistence.As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases（H changes from 0.69 to 0.52） and shifts from persistence to randomness.The Hurst exponent of the Number 9 thickness data gradually increases（H changes from 0.68 to 0.91） and always shows the characteristic of persistence.A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam.展开更多
This paper attempted to identify fractal and chaotic characteristics of the annual runoff processes in headwaters of the Tarim River.Methods of fractal analyses were used to explore several aspects of the temporal cha...This paper attempted to identify fractal and chaotic characteristics of the annual runoff processes in headwaters of the Tarim River.Methods of fractal analyses were used to explore several aspects of the temporal changes from 1957 to 2002.The main findings are as follows:(1) The annual runoff processes of the three headwaters of the Tarim River are com-plex nonlinear systems with fractal as well as chaotic dynamics.(2) The correlation dimensions of attractor derived from the time series of the annual runoff for the Hotan,Yarkand and Aksu rivers are all greater than 3.0 and non-integral,implying that all three rivers are chaotic dynamical systems that are sensitive to initial conditions,and the dynamic modeling of their annual runoff process requires at least four independent variables.(3) The time series of annual runoff in each river presents a long-term correlation characteristic.The Hurst exponent for the period of 1989 to 2002 suggests that we may expect to see an increasing trend in the annual runoff of the Aksu and Yarkand rivers in the years after 2002,but a decreasing tendency for the Hotan River in the same period.展开更多
This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random ...This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.展开更多
The complex behavior and predictability of the Dry Spell Lengths (DSL) series obtained in Benin synoptic stations, from 1951 to 2010 are analyzed in this paper using a fractal approach. The synoptic stations are locat...The complex behavior and predictability of the Dry Spell Lengths (DSL) series obtained in Benin synoptic stations, from 1951 to 2010 are analyzed in this paper using a fractal approach. The synoptic stations are located in Cotonou, Bohicon, Save (subequatorial climate), and Parakou, Natitingou, Kandi (Sudanian climate). The DSLs are computed by considering four thresholds level, R0 = {1.0, 1.5, 2.0 and 5.0} mm/day. The fractal trace is estimated for dry spell density by the mean of the “Dry Spell Spell” (DSS) n-index. The rescaled range method is used to determine the predictability of DSL. By analyzing the DSS, results show that low DSS n-index values (n-index < 0.4) are more favored in the northern part of Benin than in the southern region, whereas, high values of DSS n-index (n-index > 0.4) occur preferentially in the southern part. Therefore, during 1951-2010, the Sudanian region presents frequent wet spells, alternated with short dry spells than in the subequatorial one. However, a high degree of long dry spell persistence, followed by short dry events is observed in the subequatorial region than in the Sudanian one. The longest DSL is observed in the subequatorial region, especially in Cotonou. Except for the Kandi station, the DSLs series obtained at synoptic stations are characterized by persistence. Therefore, autoregressive processes could be applied to the DSL series. Generally, the physical process governing dry spells observed at Save, Natitingou, and Bohicon are consistently predictable than the process governing the stations of the Cotonou and Parakou. However, at Kandi station, the DSL process approximates the usual Brownian motion, and it is, therefore, unpredictable or difficult to predict.展开更多
In this paper, the long-term dependence phenomenon （the Hurst Effect） which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly strea...In this paper, the long-term dependence phenomenon （the Hurst Effect） which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi, Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series. Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series （extreme event）. Hypothesis testing was conducted by using original and modified versions of rescaled range statistic. When the modified rescaled range, which accounts for short-term memory in the series, is used, the null hypothesis is accepted for both the average monthly and maximum monthly flow series, indicating little or no probable presence of long-term memory in the series. An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested. Therefore, apart from the mean daily flow series, there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi. However, considering the limited length of data used, the results are inconclusive.展开更多
Coronaviruses are responsible for various diseases ranging from the common cold to severe infections like the Middle East syndromes and the severe acute respiratory syndrome.However,a new coronavirus strain known as C...Coronaviruses are responsible for various diseases ranging from the common cold to severe infections like the Middle East syndromes and the severe acute respiratory syndrome.However,a new coronavirus strain known as COVID-19 developed into a pandemic resulting in an ongoing global public health crisis.Therefore,there is a need to understand the genomic transformations that occur within this family of viruses in order to limit disease spread and develop new therapeutic targets.The nucleotide sequences of SARS-CoV-2 are consist of several bases.These bases can be classified into purines and pyrimidines according to their chemical composition.Purines include adenine(A)and guanine(G),while pyrimidines include cytosine(C)and tyrosine(T).There is a need to understand the spatial distribution of these bases on the nucleotide sequence to facilitate the development of antivirals(including neutralizing antibodies)and epitomes necessary for vaccine development.This study aimed to evaluate all the purine and pyrimidine associations within the SARS-CoV-2 genome sequence by measuring mathematical parameters including;Shannon entropy,Hurst exponent,and the nucleotide guanine-cytosine content.The Shannon entropy is used to identify closely associated sequences.Whereas Hurst exponent is used to identifying the auto-correlation of purine-pyrimidine bases even if their organization differs.Different frequency patterns can be used to determine the distribution of all four proteins and the density of each base.The GC-content is used to understand the stability of the DNA.The relevant genome sequences were extracted from the National Center for Biotechnology Information(NCBI)virus database.Furthermore,the phylogenetic properties of the COVID-19 virus were characterized to compare the closeness of the COVID-19 virus with other coronaviruses by evaluating the purine and pyrimidine distribution.展开更多
On the basis of fractal theory, one of the nonlinear theories, this paper studies the validity of Chinese fund market fractal time sequence through Hurst exponent, calculates the H value and proposes a new close-end f...On the basis of fractal theory, one of the nonlinear theories, this paper studies the validity of Chinese fund market fractal time sequence through Hurst exponent, calculates the H value and proposes a new close-end fund mean reversion model. Meanwhile, this paper validates the mean reversion time sequence for consecutive 54 week data of fund market. The result indicates that this model can effectively prove that Chinese close-end fund market follows the biased random walk. The research also proves that the fund discount does have mean reversion tendency and averagely the fund with high discount has a higher excess yield than that of the fund with low discount. The mean excess yield and the ratio between discount rate deviation and standard deviation demonstrate a descending relationship. The optimum investment period based on ＂mean reversion＂ is one month. Consequently this model provides a new arbitrage method through the discount of close-end fund.展开更多
How to reduce downtime and improve availability of the complex equipment is very important. Although the unscheduled downtime（USDT） issues of the equipment are very complex, the self-organized criticality（SOC） is ...How to reduce downtime and improve availability of the complex equipment is very important. Although the unscheduled downtime（USDT） issues of the equipment are very complex, the self-organized criticality（SOC） is the right theory to study complex systems evolution and opens up a new window to the investigation of disasters, such as the sudden failure of the equipment. Firstly,SOC theory and its validation method are introduced. Then an SOC validation method for USDT of the equipment is proposed based on the above theory. Case study is done on bottleneck equipment in a factory and corresponding data pre-process work is done. The rescaled-range（R/S） analysis method is used to calculate the Hurst exponent of USDT time-series data in order to determine the long-range correlation of USDT data on time scale;at the same time the spatial power-law characteristic of USDT time series data is studied. The result shows that the characteristics of SOC are revealed in USDT data of the equipment according to the criterion of SOC. In addition, based on the characteristics of SOC,the overall framework of the prediction method for major sudden failure of the equipment is proposed based on SOC.展开更多
Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signal...Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension, and the Hurst exponent within the rescaled range analysis （R/S）. We lind that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.展开更多
基金support from the National Key R&D Program of China(Grant No.2021YFB3901403)Project supported by graduate research and innovation foundation of Chongqing,China(Grant No.CYS23115)Special project for performance incentive and guidance of scientific research institutions in Chongqing(Grant No.cstc2021jxjl120011)are greatly appreciated。
文摘The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters.
文摘Statistical properties of stock market time series and the implication of their Hurst exponents are discussed. Hurst exponents of DJIA (Dow Jones Industrial Average) components are tested using re scaled range analysis. In addition to the original stock return series, the linear prediction errors of the daily returns are also tested. Numerical results show that the Hurst exponent analysis can provide some information about the statistical properties of the financial time series.
基金Project supported by the National Natural Science Foundation of China(Grant No60501003)
文摘In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.
基金supported by grants PGC2018-101555-B-I00(Ministerio Español de Ciencia,Innovación y Universidades and FEDER),PID2021-127836NB-I00(Ministerio Español de Ciencia e Innovación and FEDER)and UAL18-FQM-B038-A(UAL/CECEU/FEDER).
文摘This research aims to improve the efficiency in estimating the Hurst exponent in financial time series.A new procedure is developed based on equality in distribution and is applicable to the estimation methods of the Hurst exponent.We show how to use this new procedure with three of the most popular algorithms(generalized Hurst exponet,total triangles area,and fractal dimension)in the literature.Findings show that this new approach improves the accuracy of the original methods,mainly for longer series.The second contribution of this study is that we show how to use this methodology to test whether the series is self-similar,constructing a confidence interval for the Hurst exponent for which the series satisfies this property.Finally,we present an empirical application of this new procedure to stocks of the S&P500 index.Similar to previous contributions,we consider this to be relevant to financial literature,as it helps to avoid inappropriate interpretations of market efficiency that can lead to erroneous decisions not only by market participants but also by policymakers.
基金National Key Technology R&D Program of China,No.2013BAK05B01,No.2013BAK05B02National Natural Science Foundation of China,No.41571491,No.61631011Program of Introducing Talents of Discipline to Universities,No.B16011
文摘This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.
文摘By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.
基金Project supported by the National Natural Science Foundation of China (Grant No.11071282)the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)
文摘Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.
基金supported by the National Natural Science Foundation of China(31971578)the Scientific Research Fund of Changsha Science and Technology Bureau(kq2004095)+2 种基金the National Bureau to Combat Desertification,State Forestry Administration of China(101-9899)the Training Fund of Young Professors from Hunan Provincial Education Department(90102-7070220090001)the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20220707)。
文摘Eco-environmental quality is a measure of the suitability of the ecological environment for human survival and socioeconomic development.Understanding the spatial-temporal distribution and variation trend of eco-environmental quality is essential for environmental protection and ecological balance.The remote sensing ecological index(RSEI)can quickly and objectively quantify eco-environmental quality and has been extensively utilized in regional ecological environment assessment.In this paper,Moderate Resolution Imaging Spectroradiometer(MODIS)images during the growing period(July-September)from 2000 to 2020 were obtained from the Google Earth Engine(GEE)platform to calculate the RSEI in the three northern regions of China(the Three-North region).The Theil-Sen median trend method combined with the Mann-Kendall test was used to analyze the spatial-temporal variation trend of eco-environmental quality,and the Hurst exponent and the Theil-Sen median trend were superimposed to predict the future evolution trend of eco-environmental quality.In addition,ten variables from two categories of natural and anthropogenic factors were analyzed to determine the drivers of the spatial differentiation of eco-environmental quality by the geographical detector.The results showed that from 2000 to 2020,the RSEI in the Three-North region exhibited obvious regional characteristics:the RSEI values in Northwest China were generally between 0.2 and 0.4;the RSEI values in North China gradually increased from north to south,ranging from 0.2 to 0.8;and the RSEI values in Northeast China were mostly above 0.6.The average RSEI value in the Three-North region increased at an average growth rate of 0.0016/a,showing the spatial distribution characteristics of overall improvement and local degradation in eco-environmental quality,of which the areas with improved,basically stable and degraded eco-environmental quality accounted for 65.39%,26.82%and 7.79%of the total study area,respectively.The Hurst exponent of the RSEI ranged from 0.20 to 0.76 and the future trend of eco-environmental quality was generally consistent with the trend over the past 21 years.However,the areas exhibiting an improvement trend in eco-environmental quality mainly had weak persistence,and there was a possibility of degradation in eco-environmental quality without strengthening ecological protection.Average relative humidity,accumulated precipitation and land use type were the dominant factors driving the spatial distribution of eco-environmental quality in the Three-North region,and two-factor interaction also had a greater influence on eco-environmental quality than single factors.The explanatory power of meteorological factors on the spatial distribution of eco-environmental quality was stronger than that of topographic factors.The effect of anthropogenic factors(such as population density and land use type)on eco-environmental quality gradually increased over time.This study can serve as a reference to protect the ecological environment in arid and semi-arid regions.
基金Project 40472146 supported by the National Natural Science Foundation of China
文摘In this paper, the status quo and modeling principles of R/S analysis of non-linear theory are introduced and reviewed. Given the hydro-geological conditions of the Wutongzhuang coal mine, Hurst exponents of mine inflow for the main shaft, venti- lating shaft and auxiliary shaft were obtained using R/S analysis, which are 0.772 0, 0.824 7 and 0.905 1 respectively. Since all of the three Hurst exponents are larger than 0.5, it can be concluded that the trend of mine inflow are a long-term as well as persistent problem. Based on the level of duration, the shafts can be listed in decreasing order as the auxiliary shaft, the ventilation shaft and the main shaft, which appears identical with the actual situation of the mine inflow. With R/S analysis, a new method for long-term forecasting of mine inflows is provided.
基金Supported by the National Natural Science Foundation of China （50976018） the Natural Science Foundation of JilinProvince （20101562）
文摘Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.
基金Under the auspices of National Key Research Program of China(No.2016YFC0502300,2016YFC0502102,2014BAB03B00)National Key Research and Development Program(No.2014BAB03B02)+3 种基金Agricultural Science and Technology Key Project of Guizhou Province of China(No.2014-3039)Science and Technology Plan Projects of Guiyang Municipal Bureau of Science and Technology of China(No.2012-205)Science and Technology Plan of Guizhou Province of China(No.2012-6015)Guangxi Natural Science Foundation of China(No.2014GXNSFBA118221)
文摘Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different characteristics of the spatial-temporal changes of vegetation cover in Guizhou Province of Southern China using the data set of SPOT VEGETATION(1999–2015) at spatial resolution of 1-km and temporal resolution of 10-day. The coefficient of variation, the Theil-Sen median trend analysis, and the Mann-Kendall test are used to investigate the spatial-temporal change of vegetation cover and its future trend. Results show that: 1) the spatial distribution pattern of vegetation cover in Guizhou Plateau is high in the east whereas low in the west. The average annual normalized difference vegetation index(NDVI) from west to east is higher than that from south to north. 2) Average annual NDVI improved obviously in the past 17 years. The growth rate of average annual NDVI is 0.028/10 yr, which is slower than that of vegetation in the country(0.048/10 yr) from 1998 to 2007. Average annual NDVI in karst area is lower than that in non-karst area. However, the growing rate of average annual NDVI in karst area(0.030/10 yr) is faster than that in non-karst area(0.023/10 yr), indicating that vegetation coverage increases more rapidly in karst area. 3) Vegetation coverage in the study area is stable overall, but fluctuates in the local scales. 4) Vegetation coverage presents a continuous increasing trend. The Hurst exponent of NDVI in different vegetation types has an obvious threshold in various elevations. 5) The proportion of vegetation cover with sustainable increase is higher than that of vegetation cover with sustainable decrease. The improvement in vegetation cover may expand to most parts of the study area.
基金supported by National Basic Research Program of China(No.2007CB209503)
文摘The characteristics of coal seam development,and the prospects of a favorable coal-forming area,were evaluated for the Liaohe Basin located in China.The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis.The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68,respectively.This suggests the presence of persistence.As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases（H changes from 0.69 to 0.52） and shifts from persistence to randomness.The Hurst exponent of the Number 9 thickness data gradually increases（H changes from 0.68 to 0.91） and always shows the characteristic of persistence.A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam.
基金Knowledge Innovation Project of CAS, No.KZCX2-XB2-03Major Direction of Knowledge Innovation Project of CAS,No.KZCX2-YW-127Shanghai Academic Discipline Project (Human Geography),No.B410
文摘This paper attempted to identify fractal and chaotic characteristics of the annual runoff processes in headwaters of the Tarim River.Methods of fractal analyses were used to explore several aspects of the temporal changes from 1957 to 2002.The main findings are as follows:(1) The annual runoff processes of the three headwaters of the Tarim River are com-plex nonlinear systems with fractal as well as chaotic dynamics.(2) The correlation dimensions of attractor derived from the time series of the annual runoff for the Hotan,Yarkand and Aksu rivers are all greater than 3.0 and non-integral,implying that all three rivers are chaotic dynamical systems that are sensitive to initial conditions,and the dynamic modeling of their annual runoff process requires at least four independent variables.(3) The time series of annual runoff in each river presents a long-term correlation characteristic.The Hurst exponent for the period of 1989 to 2002 suggests that we may expect to see an increasing trend in the annual runoff of the Aksu and Yarkand rivers in the years after 2002,but a decreasing tendency for the Hotan River in the same period.
文摘This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.
文摘The complex behavior and predictability of the Dry Spell Lengths (DSL) series obtained in Benin synoptic stations, from 1951 to 2010 are analyzed in this paper using a fractal approach. The synoptic stations are located in Cotonou, Bohicon, Save (subequatorial climate), and Parakou, Natitingou, Kandi (Sudanian climate). The DSLs are computed by considering four thresholds level, R0 = {1.0, 1.5, 2.0 and 5.0} mm/day. The fractal trace is estimated for dry spell density by the mean of the “Dry Spell Spell” (DSS) n-index. The rescaled range method is used to determine the predictability of DSL. By analyzing the DSS, results show that low DSS n-index values (n-index < 0.4) are more favored in the northern part of Benin than in the southern region, whereas, high values of DSS n-index (n-index > 0.4) occur preferentially in the southern part. Therefore, during 1951-2010, the Sudanian region presents frequent wet spells, alternated with short dry spells than in the subequatorial one. However, a high degree of long dry spell persistence, followed by short dry events is observed in the subequatorial region than in the Sudanian one. The longest DSL is observed in the subequatorial region, especially in Cotonou. Except for the Kandi station, the DSLs series obtained at synoptic stations are characterized by persistence. Therefore, autoregressive processes could be applied to the DSL series. Generally, the physical process governing dry spells observed at Save, Natitingou, and Bohicon are consistently predictable than the process governing the stations of the Cotonou and Parakou. However, at Kandi station, the DSL process approximates the usual Brownian motion, and it is, therefore, unpredictable or difficult to predict.
基金Supported by the Post Graduate Research Fund from Federal Government of Nigeria under BEA Scholarship Program （No. CSC2001566010）,
文摘In this paper, the long-term dependence phenomenon （the Hurst Effect） which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi, Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series. Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series （extreme event）. Hypothesis testing was conducted by using original and modified versions of rescaled range statistic. When the modified rescaled range, which accounts for short-term memory in the series, is used, the null hypothesis is accepted for both the average monthly and maximum monthly flow series, indicating little or no probable presence of long-term memory in the series. An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested. Therefore, apart from the mean daily flow series, there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi. However, considering the limited length of data used, the results are inconclusive.
基金We are thankful to King Addulaziz City for Science and Technology(KACST)Saudi Arabia for providing support.We are thankful to the Center of Smart Society 5.0[CSS5]for the support to complete this research.
文摘Coronaviruses are responsible for various diseases ranging from the common cold to severe infections like the Middle East syndromes and the severe acute respiratory syndrome.However,a new coronavirus strain known as COVID-19 developed into a pandemic resulting in an ongoing global public health crisis.Therefore,there is a need to understand the genomic transformations that occur within this family of viruses in order to limit disease spread and develop new therapeutic targets.The nucleotide sequences of SARS-CoV-2 are consist of several bases.These bases can be classified into purines and pyrimidines according to their chemical composition.Purines include adenine(A)and guanine(G),while pyrimidines include cytosine(C)and tyrosine(T).There is a need to understand the spatial distribution of these bases on the nucleotide sequence to facilitate the development of antivirals(including neutralizing antibodies)and epitomes necessary for vaccine development.This study aimed to evaluate all the purine and pyrimidine associations within the SARS-CoV-2 genome sequence by measuring mathematical parameters including;Shannon entropy,Hurst exponent,and the nucleotide guanine-cytosine content.The Shannon entropy is used to identify closely associated sequences.Whereas Hurst exponent is used to identifying the auto-correlation of purine-pyrimidine bases even if their organization differs.Different frequency patterns can be used to determine the distribution of all four proteins and the density of each base.The GC-content is used to understand the stability of the DNA.The relevant genome sequences were extracted from the National Center for Biotechnology Information(NCBI)virus database.Furthermore,the phylogenetic properties of the COVID-19 virus were characterized to compare the closeness of the COVID-19 virus with other coronaviruses by evaluating the purine and pyrimidine distribution.
基金Supported by Chenguang Plan Project of Science and Technology Bureau in Wuhan (20065004116-11)
文摘On the basis of fractal theory, one of the nonlinear theories, this paper studies the validity of Chinese fund market fractal time sequence through Hurst exponent, calculates the H value and proposes a new close-end fund mean reversion model. Meanwhile, this paper validates the mean reversion time sequence for consecutive 54 week data of fund market. The result indicates that this model can effectively prove that Chinese close-end fund market follows the biased random walk. The research also proves that the fund discount does have mean reversion tendency and averagely the fund with high discount has a higher excess yield than that of the fund with low discount. The mean excess yield and the ratio between discount rate deviation and standard deviation demonstrate a descending relationship. The optimum investment period based on ＂mean reversion＂ is one month. Consequently this model provides a new arbitrage method through the discount of close-end fund.
基金supported by the National Natural Science Foundation of China(51075060)
文摘How to reduce downtime and improve availability of the complex equipment is very important. Although the unscheduled downtime（USDT） issues of the equipment are very complex, the self-organized criticality（SOC） is the right theory to study complex systems evolution and opens up a new window to the investigation of disasters, such as the sudden failure of the equipment. Firstly,SOC theory and its validation method are introduced. Then an SOC validation method for USDT of the equipment is proposed based on the above theory. Case study is done on bottleneck equipment in a factory and corresponding data pre-process work is done. The rescaled-range（R/S） analysis method is used to calculate the Hurst exponent of USDT time-series data in order to determine the long-range correlation of USDT data on time scale;at the same time the spatial power-law characteristic of USDT time series data is studied. The result shows that the characteristics of SOC are revealed in USDT data of the equipment according to the criterion of SOC. In addition, based on the characteristics of SOC,the overall framework of the prediction method for major sudden failure of the equipment is proposed based on SOC.
基金＊The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of the Ministry of Education of China
文摘Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension, and the Hurst exponent within the rescaled range analysis （R/S）. We lind that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.
