An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price...An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.展开更多
Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan Region is divided into two seismic regions and six seismic belts. Then, correlation f...Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan Region is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions D q and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan Region. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of D q variation with time is a good indicator for predicting strong earthquake events.展开更多
Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture des...Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme： （i） using two-dimensional Gabor filter to extract the texture features of biometric images; （ii） calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and （iii） linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach.展开更多
Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and t...Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.展开更多
In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statist...In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive setK(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distributionP k =P·K ?1, (6) the Hausdorff dimension and Hausdorff exact measure function.展开更多
The work on the paper is focused on the use of Fractal Dimension in clustering for evolving data streams. Recently Anuradha et al. proposed a new approach based on Relative Change in Fractal Dimension (RCFD) and dampe...The work on the paper is focused on the use of Fractal Dimension in clustering for evolving data streams. Recently Anuradha et al. proposed a new approach based on Relative Change in Fractal Dimension (RCFD) and damped window model for clustering evolving data streams. Through observations on the aforementioned referred paper, this paper reveals that the formation of quality cluster is heavily predominant on the suitable selection of threshold value. In the above-mentionedpaper Anuradha et al. have used a heuristic approach for fixing the threshold value. Although the outcome of the approach is acceptable, however, the approach is purely based on random selection and has no basis to claim the acceptability in general. In this paper a novel method is proposed to optimally compute threshold value using a population based randomized approach known as particle swarm optimization (PSO). Simulations are done on two huge data sets KDD Cup 1999 data set and the Forest Covertype data set and the results of the cluster quality are compared with the fixed approach. The comparison reveals that the chosen value of threshold by Anuradha et al., is robust and can be used with confidence.展开更多
Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Wi...Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Within the framework of a statistical approach,the authors have investigated values and ranges for changes of statistical moments of thefirst to the fourth orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by blood plasma with various pathologies.In the framework of the fractal approach,determined are the dimensions of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of hominal mammary gland pathologies.展开更多
This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU an...This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. For better analysis, application of adaptive segmentation on EEG signal for estimating BIS index is evaluated and compared to fixed segmentation. Prediction probability (PK) is used as a measure of correlation between the predictors and BIS index to evaluate the proposed methods. The results show the ability of these algorithms (specifically HFD algorithm) in predicting BIS index. Also, evolving fixed and adaptive windowing methods for segmentation of EEG reveals no meaningful difference in estimating BIS index.展开更多
Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements ...Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements of statistical methods due to the closure effect.In this study,we applied an integrated approach combining compositional data,multifractal,and multivariate statistical analyses to identify the nonlinear complexity of the spatial distributions of elemental concentrations in the Er’renshan ore field.Initially,the raw concentrations were transformed into log-ratios following the principles of composition data theory to alleviate the impact of the closure effect.Multifractal analysis was then conducted to characterise the nonlinear complexity of the concentration distributions.Furthermore,principal component analysis(PCA)and factor analysis(FA)were applied to identify spurious correlations and the potential factors controlling the distribution patterns.The results demonstrate that:a)the raw data are biased,while the log-ratio data are unbiased and more reliable;b)the spatial distributions of elemental concentrations exhibit nonlinear complexity;and c)the elemental distribution in the study area is largely controlled by structural factors.展开更多
This study makes an attempt to investigate through statistical analysis the correlation between changes in ice volume and area of glaciers. Using data from nine sample glaciers in the Tian Shan, the results show that ...This study makes an attempt to investigate through statistical analysis the correlation between changes in ice volume and area of glaciers. Using data from nine sample glaciers in the Tian Shan, the results show that a linear relation exists between changes in ice volume and area, with a correlation coefficient of 0.700. However, the accuracy estimation is difficult due to the limited number of samples. The correlation was not improved after adding eleven glacier samples in other mountains. Two reference glaciers are then analyzed in more detail. The linear correlation coefficient is higher than 0.800 when using the observed changes in ice volume and area during different periods on Urumqi Glacier No. 1, which suggests that the linear relation is valid for one glacier for different periods if its shape does not change noticeably and also for other glaciers of the same shape during the same period. The relation between changes in ice volume and area of Qingbingtan Glacier No. 72 is different during different periods due to change in the shape of the glacier tongue and the influence of the debris cover. Moreover, errors in glacier-change monitoring and-volume estimation have an important influence on the correlation results. Therefore, further study needs to focus not only on the distinction between glacier types and between different periods but also on the accuracy of volume estimation.展开更多
We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometr...We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.展开更多
Soil particle size distribution(PSD) is a fundamental physical property affecting other soil properties. Characterizing spatial variability of soil texture is very important in environmental research. The objectives o...Soil particle size distribution(PSD) is a fundamental physical property affecting other soil properties. Characterizing spatial variability of soil texture is very important in environmental research. The objectives of this work were: 1) to partition PSD of 75 soil samples, collected from a flat field in the University of Guilan, Iran, into two scaling domains using a piecewise fractal model to evaluate the relationships between fractal dimensions of scaling domains and soil clay, silt, and sand fractions and 2) to assess the potential of fractal parameters as an index used in a geostatistical approach reflecting the spatial variability of soil texture. Features of PSD of soil samples were studied using fractal geometry, and geostatistical techniques were used to characterize the spatial variability of fractal and soil textural parameters. There were two scaling domains for the PSD of soil samples. The fractal dimensions of these two scaling domains(D_1 and D_2) were then used to characterize different ranges of soil particle sizes and their relationships to the soil textural parameters. There was a positive correlation between D_1 and clay content(R^2= 0.924), a negative correlation between D_1 and silt content(R^2= 0.801), and a negative correlation between D_2 and sand content(R^2= 0.913). The geometric mean diameter of soil particles had a negative correlation with D_1(R^2= 0.569) and D_2(R^2= 0.682). Semivariograms of fractal dimensions and soil textural parameters were calculated and the maps of spatial variation of D_1 and D_2 and soil PSD parameters were provided using ordinary kriging. The results showed that there were also spatial correlations between D_1 and D_2 and particle size fractions.According to the semivariogram models and validation parameters, the fractal parameters had powerful spatial structure and could better describe the spatial variability of soil texture.展开更多
The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley...The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.展开更多
Measuring the relative importance and assigning weights to conditioning factors of land- slides occurrence are significant for landslide prevention and/or mitigation. In this contribution, a fractal method is introduc...Measuring the relative importance and assigning weights to conditioning factors of land- slides occurrence are significant for landslide prevention and/or mitigation. In this contribution, a fractal method is introduced for measuring the spatial relationships between landslides and condition- ing factors （such as faults, rivers, geological boundaries, and roads）, and for assigning weights to condi- tioning factors for mapping of landslide susceptibility. This method can be expressed as p=C~, where d is the fractal dimension, and C is a constant. This relationship indicates a fractal relation between land- slide density （p） and distances to conditioning factors （6）. The case of d〉0 suggests a significant spatial correlation between landslides and conditioning factors. The larger the d （〉0） value, the stronger the spatial correlation is between landslides and a specific conditioning factor. Two case studies in South China were examined to demonstrate the usefulness of this novel method.展开更多
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder expon...The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.展开更多
This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-cou...This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.展开更多
We analyze muscular dystrophy recorded by sEMG and use standard methodologies and nonlinear chaotic methods here including the RQA. We reach sufficient evidence that the sEMG signal contains a large chaotic component....We analyze muscular dystrophy recorded by sEMG and use standard methodologies and nonlinear chaotic methods here including the RQA. We reach sufficient evidence that the sEMG signal contains a large chaotic component. We have estimated the correlation dimension (fractal measure), the largest Lyapunov exponent, the LZ complexity and the %Rec and %Det of the RQA demonstrating that such indexes are able to detect the presence of repetitive hidden patterns in sEMG which, in turn, senses the level of MU synchronization within the muscle. The results give also an interesting methodological indication in the sense that it evidences the manner in which nonlinear methods and RQA must be arranged and applied in clinical routine in order to obtain results of clinical interest. We have studied the muscular dystrophy and evidence that the continuous regime of chaotic transitions that we have in muscular mechanisms may benefit in this pathology by the use of the NPT treatment that we have considered in detail in our previous publications.展开更多
In this study,geochemical anomaly separation was carried out with methods based on the distribution model,which includes probability diagram(MPD),fractal(concentration-area technique),and U-statistic methods.The main ...In this study,geochemical anomaly separation was carried out with methods based on the distribution model,which includes probability diagram(MPD),fractal(concentration-area technique),and U-statistic methods.The main objective is to evaluate the efficiency and accuracy of the methods in separation of anomalies on the shear zone gold mineralization.For this purpose,samples were taken from the secondary lithogeochemical environment(stream sediment samples)on the gold mineralization in Saqqez,NW of Iran.Interpretation of the histograms and diagrams showed that the MPD is capable of identifying two phases of mineralization.The fractal method could separate only one phase of change based on the fractal dimension with high concentration areas of the Au element.The spatial analysis showed two mixed subpopulations after U=0 and another subpopulation with very high U values.The MPD analysis followed spatial analysis,which shows the detail of the variations.Six mineralized zones detected from local geochemical exploration results were used for validating the methods mentioned above.The MPD method was able to identify the anomalous areas higher than 90%,whereas the two other methods identified 60%(maximum)of the anomalous areas.The raw data without any estimation for the concentration was used by the MPD method using aminimum of calculations to determine the threshold values.Therefore,the MPD method is more robust than the other methods.The spatial analysis identified the detail soft hegeological and mineralization events that were affected in the study area.MPD is recommended as the best,and the spatial U-analysis is the next reliable method to be used.The fractal method could show more detail of the events and variations in the area with asymmetrical grid net and a higher density of sampling or at the detailed exploration stage.展开更多
This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
According to the definition of correlation dimension in fractal theory, this paper presented a method to determine and assess noise part in detected transient signal. Such work is essential to decrease the noise part ...According to the definition of correlation dimension in fractal theory, this paper presented a method to determine and assess noise part in detected transient signal. Such work is essential to decrease the noise part in the detected signal. It is proved that heart period signal (HPS) is one typical sort of transient chaotic signal. Through experiment and simulation, the analysis of chaotic HPS in the detected signal was done. In the end, we deepen the researches on attractor dimension of HPS for persons who are different in age.展开更多
基金Project(13&ZD024)supported by the Major Program of the National Social Science Fund of ChinaProject(71073177)supported by the National Natural Science Foundation of China+3 种基金Project(CX2012B107)supported by the Graduate Student Innovation Project of Hunan Province,ChinaProject(13YJAZH149)supported by the Social Science Fund of Ministry of Education of ChinaProject(2011ZK2043)supported by the Key Program of the Soft Science Research Project of Hunan Province,ChinaProject(12JJ4077)supported by Natural Science Foundation of Hunan Province of China
文摘An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.
基金the Joint Earthquake Science Foundation grant number 100070 the NationalNatural Science Foundation of Chinagrant number40272111.
文摘Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan Region is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions D q and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan Region. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of D q variation with time is a good indicator for predicting strong earthquake events.
基金supported by the National Natural Science Foundation of China(Grant Nos.61262040,61271341,81360230,and 61271007)the Applied Basic Research Projects of Yunnan Province,China(Grant No.KKSY201203062)
文摘Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme： （i） using two-dimensional Gabor filter to extract the texture features of biometric images; （ii） calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and （iii） linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach.
文摘Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.
文摘In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive setK(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distributionP k =P·K ?1, (6) the Hausdorff dimension and Hausdorff exact measure function.
文摘The work on the paper is focused on the use of Fractal Dimension in clustering for evolving data streams. Recently Anuradha et al. proposed a new approach based on Relative Change in Fractal Dimension (RCFD) and damped window model for clustering evolving data streams. Through observations on the aforementioned referred paper, this paper reveals that the formation of quality cluster is heavily predominant on the suitable selection of threshold value. In the above-mentionedpaper Anuradha et al. have used a heuristic approach for fixing the threshold value. Although the outcome of the approach is acceptable, however, the approach is purely based on random selection and has no basis to claim the acceptability in general. In this paper a novel method is proposed to optimally compute threshold value using a population based randomized approach known as particle swarm optimization (PSO). Simulations are done on two huge data sets KDD Cup 1999 data set and the Forest Covertype data set and the results of the cluster quality are compared with the fixed approach. The comparison reveals that the chosen value of threshold by Anuradha et al., is robust and can be used with confidence.
文摘Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Within the framework of a statistical approach,the authors have investigated values and ranges for changes of statistical moments of thefirst to the fourth orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by blood plasma with various pathologies.In the framework of the fractal approach,determined are the dimensions of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of hominal mammary gland pathologies.
文摘This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. For better analysis, application of adaptive segmentation on EEG signal for estimating BIS index is evaluated and compared to fixed segmentation. Prediction probability (PK) is used as a measure of correlation between the predictors and BIS index to evaluate the proposed methods. The results show the ability of these algorithms (specifically HFD algorithm) in predicting BIS index. Also, evolving fixed and adaptive windowing methods for segmentation of EEG reveals no meaningful difference in estimating BIS index.
基金supported by the Doctoral Research Start-up Fund,East China University of Technology(DHBK2019313)the Open Research Fund Program of Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),the Ministry of Education(2020YSJS10)+1 种基金the Open Research Fund Program of Shandong Provincial Engineering Laboratory of Application and Development of Big Data for Deep Gold Exploration(SDK202224)the Basic Scientific Research Fund of the Institute of Geophysical and Geochemical Exploration,Chinese Academy of Geological Sciences(AS2022P03).
文摘Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements of statistical methods due to the closure effect.In this study,we applied an integrated approach combining compositional data,multifractal,and multivariate statistical analyses to identify the nonlinear complexity of the spatial distributions of elemental concentrations in the Er’renshan ore field.Initially,the raw concentrations were transformed into log-ratios following the principles of composition data theory to alleviate the impact of the closure effect.Multifractal analysis was then conducted to characterise the nonlinear complexity of the concentration distributions.Furthermore,principal component analysis(PCA)and factor analysis(FA)were applied to identify spurious correlations and the potential factors controlling the distribution patterns.The results demonstrate that:a)the raw data are biased,while the log-ratio data are unbiased and more reliable;b)the spatial distributions of elemental concentrations exhibit nonlinear complexity;and c)the elemental distribution in the study area is largely controlled by structural factors.
基金funded by the National Natural Science Foundation of China (41771077)the Funds for Creative Research Groups of China (41421061)+1 种基金the Strategic Priority Research Program of Chinese Acad emy of Sciences (XDA20020102)the Youth Innovation Promotion Association of CAS
文摘This study makes an attempt to investigate through statistical analysis the correlation between changes in ice volume and area of glaciers. Using data from nine sample glaciers in the Tian Shan, the results show that a linear relation exists between changes in ice volume and area, with a correlation coefficient of 0.700. However, the accuracy estimation is difficult due to the limited number of samples. The correlation was not improved after adding eleven glacier samples in other mountains. Two reference glaciers are then analyzed in more detail. The linear correlation coefficient is higher than 0.800 when using the observed changes in ice volume and area during different periods on Urumqi Glacier No. 1, which suggests that the linear relation is valid for one glacier for different periods if its shape does not change noticeably and also for other glaciers of the same shape during the same period. The relation between changes in ice volume and area of Qingbingtan Glacier No. 72 is different during different periods due to change in the shape of the glacier tongue and the influence of the debris cover. Moreover, errors in glacier-change monitoring and-volume estimation have an important influence on the correlation results. Therefore, further study needs to focus not only on the distinction between glacier types and between different periods but also on the accuracy of volume estimation.
文摘We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.
文摘Soil particle size distribution(PSD) is a fundamental physical property affecting other soil properties. Characterizing spatial variability of soil texture is very important in environmental research. The objectives of this work were: 1) to partition PSD of 75 soil samples, collected from a flat field in the University of Guilan, Iran, into two scaling domains using a piecewise fractal model to evaluate the relationships between fractal dimensions of scaling domains and soil clay, silt, and sand fractions and 2) to assess the potential of fractal parameters as an index used in a geostatistical approach reflecting the spatial variability of soil texture. Features of PSD of soil samples were studied using fractal geometry, and geostatistical techniques were used to characterize the spatial variability of fractal and soil textural parameters. There were two scaling domains for the PSD of soil samples. The fractal dimensions of these two scaling domains(D_1 and D_2) were then used to characterize different ranges of soil particle sizes and their relationships to the soil textural parameters. There was a positive correlation between D_1 and clay content(R^2= 0.924), a negative correlation between D_1 and silt content(R^2= 0.801), and a negative correlation between D_2 and sand content(R^2= 0.913). The geometric mean diameter of soil particles had a negative correlation with D_1(R^2= 0.569) and D_2(R^2= 0.682). Semivariograms of fractal dimensions and soil textural parameters were calculated and the maps of spatial variation of D_1 and D_2 and soil PSD parameters were provided using ordinary kriging. The results showed that there were also spatial correlations between D_1 and D_2 and particle size fractions.According to the semivariogram models and validation parameters, the fractal parameters had powerful spatial structure and could better describe the spatial variability of soil texture.
基金supported by Geological Survey of Canada and China University of Geosciences (Wuhan)
文摘The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
基金financial support from the National Natural Science Foundation of China (No. 41522206)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences (No. MSFGPMR03-3)
文摘Measuring the relative importance and assigning weights to conditioning factors of land- slides occurrence are significant for landslide prevention and/or mitigation. In this contribution, a fractal method is introduced for measuring the spatial relationships between landslides and condition- ing factors （such as faults, rivers, geological boundaries, and roads）, and for assigning weights to condi- tioning factors for mapping of landslide susceptibility. This method can be expressed as p=C~, where d is the fractal dimension, and C is a constant. This relationship indicates a fractal relation between land- slide density （p） and distances to conditioning factors （6）. The case of d〉0 suggests a significant spatial correlation between landslides and conditioning factors. The larger the d （〉0） value, the stronger the spatial correlation is between landslides and a specific conditioning factor. Two case studies in South China were examined to demonstrate the usefulness of this novel method.
文摘The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
基金National Natural Science Foundation of China under Grant Nos.50978047 and 11332004National Basic Research Program of China under Grant No.2010CB832703
文摘This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.
文摘We analyze muscular dystrophy recorded by sEMG and use standard methodologies and nonlinear chaotic methods here including the RQA. We reach sufficient evidence that the sEMG signal contains a large chaotic component. We have estimated the correlation dimension (fractal measure), the largest Lyapunov exponent, the LZ complexity and the %Rec and %Det of the RQA demonstrating that such indexes are able to detect the presence of repetitive hidden patterns in sEMG which, in turn, senses the level of MU synchronization within the muscle. The results give also an interesting methodological indication in the sense that it evidences the manner in which nonlinear methods and RQA must be arranged and applied in clinical routine in order to obtain results of clinical interest. We have studied the muscular dystrophy and evidence that the continuous regime of chaotic transitions that we have in muscular mechanisms may benefit in this pathology by the use of the NPT treatment that we have considered in detail in our previous publications.
文摘In this study,geochemical anomaly separation was carried out with methods based on the distribution model,which includes probability diagram(MPD),fractal(concentration-area technique),and U-statistic methods.The main objective is to evaluate the efficiency and accuracy of the methods in separation of anomalies on the shear zone gold mineralization.For this purpose,samples were taken from the secondary lithogeochemical environment(stream sediment samples)on the gold mineralization in Saqqez,NW of Iran.Interpretation of the histograms and diagrams showed that the MPD is capable of identifying two phases of mineralization.The fractal method could separate only one phase of change based on the fractal dimension with high concentration areas of the Au element.The spatial analysis showed two mixed subpopulations after U=0 and another subpopulation with very high U values.The MPD analysis followed spatial analysis,which shows the detail of the variations.Six mineralized zones detected from local geochemical exploration results were used for validating the methods mentioned above.The MPD method was able to identify the anomalous areas higher than 90%,whereas the two other methods identified 60%(maximum)of the anomalous areas.The raw data without any estimation for the concentration was used by the MPD method using aminimum of calculations to determine the threshold values.Therefore,the MPD method is more robust than the other methods.The spatial analysis identified the detail soft hegeological and mineralization events that were affected in the study area.MPD is recommended as the best,and the spatial U-analysis is the next reliable method to be used.The fractal method could show more detail of the events and variations in the area with asymmetrical grid net and a higher density of sampling or at the detailed exploration stage.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
文摘According to the definition of correlation dimension in fractal theory, this paper presented a method to determine and assess noise part in detected transient signal. Such work is essential to decrease the noise part in the detected signal. It is proved that heart period signal (HPS) is one typical sort of transient chaotic signal. Through experiment and simulation, the analysis of chaotic HPS in the detected signal was done. In the end, we deepen the researches on attractor dimension of HPS for persons who are different in age.
