In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all usef...In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.展开更多
A 2.5Gb/s/ch data recovery (DR) circuit is designed for an SFI-5 interface. To make the parallel data bit-synchronization and reduce the bit error rate (BER) ,a delay locked loop (DLL) is used to place the cente...A 2.5Gb/s/ch data recovery (DR) circuit is designed for an SFI-5 interface. To make the parallel data bit-synchronization and reduce the bit error rate (BER) ,a delay locked loop (DLL) is used to place the center of the data eye exactly at the rising edge of the data-sampling clock. A single channel DR circuit was fabricated in TSMC's standard 0. 18μm CMOS process. The chip area is 0. 46mm^2. With a 2^32 - 1 pseudorandom bit sequence (PRBS) input,the RMS jitter of the recovered 2.5Gb/s data is 3.3ps. The sensitivity of the single channel DR is less than 20mV with 10-12 BER.展开更多
In order to reduce amount of data storage and improve processing capacity of the system, this paper proposes a new classification method of data source by combining phase synchronization model in network clusteri...In order to reduce amount of data storage and improve processing capacity of the system, this paper proposes a new classification method of data source by combining phase synchronization model in network clustering with cloud model. Firstly, taking data source as a complex network, after the topography of network is obtained, the cloud model of each node data is determined by fuzzy analytic hierarchy process (AHP). Secondly, by calculating expectation, entropy and hyper entropy of the cloud model, comprehensive coupling strength is got and then it is regarded as the edge weight of topography. Finally, distribution curve is obtained by iterating the phase of each node by means of phase synchronization model. Thus classification of data source is completed. This method can not only provide convenience for storage, cleaning and compression of data, but also improve the efficiency of data analysis.展开更多
The potential field determined based on the fictitious compress recovery approach is influenced by the errors contained in the boundary (the Earth's surface or the surface corresponding to the satellite altitude) v...The potential field determined based on the fictitious compress recovery approach is influenced by the errors contained in the boundary (the Earth's surface or the surface corresponding to the satellite altitude) values. Given the boundary value with definite accuracy, the accuracy of the field determined based on the fictitious compress recovery approach is estimated, and it is theoretically shown that the determined field has the same accuracy level as the given boundary value.展开更多
By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar f...By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.展开更多
A microscopic diffusion-reaction modei was developed to simulate in-situ ozonation for the remediation of contaminated soil, i.e., to predict the temporal and spatial distribution of target contaminant in the subsurfa...A microscopic diffusion-reaction modei was developed to simulate in-situ ozonation for the remediation of contaminated soil, i.e., to predict the temporal and spatial distribution of target contaminant in the subsurface. The sequential strategy was employed to obtain the numerical solution of the modei using finite difference method. A non-uniform grid of discretization points was emploved to increase the accuracy of the numerical solution by means of coordinate transformation. One-dimensional column tests were conducted to verify the modei. The column was packed with simulated soils that were spiked with 2-chlorophenol. Ozone gas passed through the column at a flow rate of 100ml·min-1. The residual 2-chlorophenol content at different depths of the column was determined at fixed time intervals. Compared the experimental data with the simulated values, it was found that the mathematical modei fitted data well during most time of the experiment.展开更多
Based on the engineering background of double-unit face mining under complicated geological conditions and the lagging fully-mechanized face surpassing the fore mechanized face of double-unit face in Zhou Yuanshan coa...Based on the engineering background of double-unit face mining under complicated geological conditions and the lagging fully-mechanized face surpassing the fore mechanized face of double-unit face in Zhou Yuanshan coal mine, strata-pressure behavior in the process was analyzed based on FLAC3D and on-site measurement. The results show that the stress concentration factor of superposition abutment pressure and the alternate distance of double-unit face are meeting gauss function, the relationship between the depth of stress concentration point and alternate distance also meets gaussian function. When the alternate distance is larger than 24 m, the superimposition of pilot support pressure in the double-unit face is weak. When the alternate distance is more than 12-15 m, the changes of the roof subsidence coefficient and the depth of stress con- centration point are stabilized; when the alternate distance is 3-6 m, the fore working face end is in the greatest impact area of superposition abutment pressure, this area should be avoided in determining the reasonable alternate distance.展开更多
The accurate understanding of atmospheric aerosol extinction coefficients is very important for at- mospheric science research. To achieve a fast and simple method for determining the parameters, the selection of opti...The accurate understanding of atmospheric aerosol extinction coefficients is very important for at- mospheric science research. To achieve a fast and simple method for determining the parameters, the selection of optimal forward-scattering angles of atmospheric aerosols is required. In this paper, the authors introduce the detec- tion basis of forward-scattering of atmospheric aerosols, and the authors verify the sensitivity of the phase function to the real part of the complex refractive index. The au- thors use the Jaenicke urban aerosol model to determine that forward-scattering angles near 33° are suitable. However, the optimal forward-scattering angles in North China are between 37° and 40°. Numerical simulation shows that certain types of particle size distribution of newly generated particles and pollution have limited in- fluences on the selection of forward-scattering angles. But the ranges of these insensitive angles shift - 10 degrees for dust intrusion, and the relative deviations of the phase function are less than 5.0% within extra angles of 0° to 3°. This study can serve as a reference for the selection of optimal forward-scattering angles for visibility meters and Present Weather Identifiers (PWIs) in addition to the de- tection of forward-scattering optical properties.展开更多
In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another ...In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.展开更多
This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is...This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is inappropriate for BMU data transmission because it is based on average level detection and requires considerable time to settle on a predefined gain. Therefore, we adopt a fast switched-mode AGC based on peak level detection. After the gain is adjusted, the peak level detectors need to re-detect the peak level of the input signal. Thus, we develop an internally created reset module. This AGC with reset module exhibits a fast operation and achieves an adjusted stable gain within one-bit, avoiding any bit loss up to 10Mb/s data rate. During power-up, the peak level detectors possibly hold an uncertain level resulting in the bit-errors. We propose a power-up reset circuit to solve this problem. Designed in a 0.5μm CMOS technology, the circuit achieves an optical sensitivity of better than -30dBm and a wide dynamic range of over 30dB with a power dissipation of only 30 mW from a 5V supply.展开更多
The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.
Efficient data management is a key issue for environments distributed on a large scale such as the data cloud. This can be taken into account by replicating the data. The replication of data reduces the time of servic...Efficient data management is a key issue for environments distributed on a large scale such as the data cloud. This can be taken into account by replicating the data. The replication of data reduces the time of service and the delay in availability, increases the availability, and optimizes the distribution of load in the system. It is worth mentioning, however, that with the replication of data, the use of resources and energy increases due to the storing of copies of the data. We suggest a replication manager that decreases the cost of using resources, energy, and the delay in the system, and also increases the availability of the system. To reach this aim, the suggested replication manager, called the locality replication manager (LRM), works by using two important algorithms that use the physical adjacency feature of blocks. In addition, a set of simulations are reported to show that LRM can be a suitable option for distributed systems as it uses less energy and resources, optimizes the distribution of load, and has more availability and less delay.展开更多
The steered response power-phase transform (SRP-PHAT) sound source localization algorithm is robust in a real environment. However, the large computation complexity limits the practical application of SRP-PHAT. For a ...The steered response power-phase transform (SRP-PHAT) sound source localization algorithm is robust in a real environment. However, the large computation complexity limits the practical application of SRP-PHAT. For a microphone array, each location corresponds to a set of time differences of arrival (TDOAs), and this paper collects them into a TDOA vector. Since the TDOA vectors in the adjacent regions are similar, we present a fast algorithm based on clustering search to reduce the computation complexity of SRP-PHAT. In the training stage, the K-means or Iterative Self-Organizing Data Analysis Technique (ISODATA) clustering algorithm is used to find the centroid in each cluster with similar TDOA vectors. In the procedure of sound localization, the optimal cluster is found by comparing the steered response powers (SRPs) of all centroids. The SRPs of all candidate locations in the optimal cluster are compared to localize the sound source. Experiments both in simulation environments and real environments have been performed to compare the localization accuracy and computational load of the proposed method with those of the conventional SRP-PHAT algorithm. The results show that the proposed method is able to reduce the computational load drastically and maintains almost the same localization accuracy and robustness as those of the conventional SRP-PHAT algorithm. The difference in localization performance brought by different clustering algorithms used in the training stage is trivial.展开更多
In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the r...In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.展开更多
Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of or...Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.展开更多
We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH mo...We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.展开更多
基金Outstanding Youth Foundation of Hunan Provincial Department of Education(Grant No.22B0911)。
文摘In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.
文摘A 2.5Gb/s/ch data recovery (DR) circuit is designed for an SFI-5 interface. To make the parallel data bit-synchronization and reduce the bit error rate (BER) ,a delay locked loop (DLL) is used to place the center of the data eye exactly at the rising edge of the data-sampling clock. A single channel DR circuit was fabricated in TSMC's standard 0. 18μm CMOS process. The chip area is 0. 46mm^2. With a 2^32 - 1 pseudorandom bit sequence (PRBS) input,the RMS jitter of the recovered 2.5Gb/s data is 3.3ps. The sensitivity of the single channel DR is less than 20mV with 10-12 BER.
基金National Natural Science Foundation of China(No.61171057,No.61503345)Science Foundation for North University of China(No.110246)+1 种基金Specialized Research Fund for Doctoral Program of Higher Education of China(No.20121420110004)International Office of Shanxi Province Education Department of China,and Basic Research Project in Shanxi Province(Young Foundation)
文摘In order to reduce amount of data storage and improve processing capacity of the system, this paper proposes a new classification method of data source by combining phase synchronization model in network clustering with cloud model. Firstly, taking data source as a complex network, after the topography of network is obtained, the cloud model of each node data is determined by fuzzy analytic hierarchy process (AHP). Secondly, by calculating expectation, entropy and hyper entropy of the cloud model, comprehensive coupling strength is got and then it is regarded as the edge weight of topography. Finally, distribution curve is obtained by iterating the phase of each node by means of phase synchronization model. Thus classification of data source is completed. This method can not only provide convenience for storage, cleaning and compression of data, but also improve the efficiency of data analysis.
基金Funded by the National Natural Science Foundation of China (No.40574004, No.40374004, No.40174004).
文摘The potential field determined based on the fictitious compress recovery approach is influenced by the errors contained in the boundary (the Earth's surface or the surface corresponding to the satellite altitude) values. Given the boundary value with definite accuracy, the accuracy of the field determined based on the fictitious compress recovery approach is estimated, and it is theoretically shown that the determined field has the same accuracy level as the given boundary value.
文摘By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.
基金China Scholarship Council(No.97842039)National Natural Science Foundation of China(No.20107005)
文摘A microscopic diffusion-reaction modei was developed to simulate in-situ ozonation for the remediation of contaminated soil, i.e., to predict the temporal and spatial distribution of target contaminant in the subsurface. The sequential strategy was employed to obtain the numerical solution of the modei using finite difference method. A non-uniform grid of discretization points was emploved to increase the accuracy of the numerical solution by means of coordinate transformation. One-dimensional column tests were conducted to verify the modei. The column was packed with simulated soils that were spiked with 2-chlorophenol. Ozone gas passed through the column at a flow rate of 100ml·min-1. The residual 2-chlorophenol content at different depths of the column was determined at fixed time intervals. Compared the experimental data with the simulated values, it was found that the mathematical modei fitted data well during most time of the experiment.
基金Supported by the National Natural Science Foundation of China (50974059)
文摘Based on the engineering background of double-unit face mining under complicated geological conditions and the lagging fully-mechanized face surpassing the fore mechanized face of double-unit face in Zhou Yuanshan coal mine, strata-pressure behavior in the process was analyzed based on FLAC3D and on-site measurement. The results show that the stress concentration factor of superposition abutment pressure and the alternate distance of double-unit face are meeting gauss function, the relationship between the depth of stress concentration point and alternate distance also meets gaussian function. When the alternate distance is larger than 24 m, the superimposition of pilot support pressure in the double-unit face is weak. When the alternate distance is more than 12-15 m, the changes of the roof subsidence coefficient and the depth of stress con- centration point are stabilized; when the alternate distance is 3-6 m, the fore working face end is in the greatest impact area of superposition abutment pressure, this area should be avoided in determining the reasonable alternate distance.
基金supported mainly by the China Meteorological Administration under Grant GYHY200806031supported by the Chinese Academy of Sciences under Grant XDA05040302
文摘The accurate understanding of atmospheric aerosol extinction coefficients is very important for at- mospheric science research. To achieve a fast and simple method for determining the parameters, the selection of optimal forward-scattering angles of atmospheric aerosols is required. In this paper, the authors introduce the detec- tion basis of forward-scattering of atmospheric aerosols, and the authors verify the sensitivity of the phase function to the real part of the complex refractive index. The au- thors use the Jaenicke urban aerosol model to determine that forward-scattering angles near 33° are suitable. However, the optimal forward-scattering angles in North China are between 37° and 40°. Numerical simulation shows that certain types of particle size distribution of newly generated particles and pollution have limited in- fluences on the selection of forward-scattering angles. But the ranges of these insensitive angles shift - 10 degrees for dust intrusion, and the relative deviations of the phase function are less than 5.0% within extra angles of 0° to 3°. This study can serve as a reference for the selection of optimal forward-scattering angles for visibility meters and Present Weather Identifiers (PWIs) in addition to the de- tection of forward-scattering optical properties.
基金Supported by National Natural Science Foundation of China (No.10971153)
文摘In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.
基金Supported by the Natural Science Foundation of Jiangsu Province ( BK2010411 ) and the National International Cooperation Project of China-Korea (2011DFA11310).
文摘This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is inappropriate for BMU data transmission because it is based on average level detection and requires considerable time to settle on a predefined gain. Therefore, we adopt a fast switched-mode AGC based on peak level detection. After the gain is adjusted, the peak level detectors need to re-detect the peak level of the input signal. Thus, we develop an internally created reset module. This AGC with reset module exhibits a fast operation and achieves an adjusted stable gain within one-bit, avoiding any bit loss up to 10Mb/s data rate. During power-up, the peak level detectors possibly hold an uncertain level resulting in the bit-errors. We propose a power-up reset circuit to solve this problem. Designed in a 0.5μm CMOS technology, the circuit achieves an optical sensitivity of better than -30dBm and a wide dynamic range of over 30dB with a power dissipation of only 30 mW from a 5V supply.
基金Project supported by the National Natural Science Foundation of China (No. 10771201)the Anhui Provincial Natural Science Foundation of China (No. 090416233)
文摘The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.
文摘Efficient data management is a key issue for environments distributed on a large scale such as the data cloud. This can be taken into account by replicating the data. The replication of data reduces the time of service and the delay in availability, increases the availability, and optimizes the distribution of load in the system. It is worth mentioning, however, that with the replication of data, the use of resources and energy increases due to the storing of copies of the data. We suggest a replication manager that decreases the cost of using resources, energy, and the delay in the system, and also increases the availability of the system. To reach this aim, the suggested replication manager, called the locality replication manager (LRM), works by using two important algorithms that use the physical adjacency feature of blocks. In addition, a set of simulations are reported to show that LRM can be a suitable option for distributed systems as it uses less energy and resources, optimizes the distribution of load, and has more availability and less delay.
基金supported by the National Natural Science Foundation of China(Grant Nos. 60971098 and 61201345)the Beijing Key Laboratory of Advanced Information Science and Network Technology(Grant No.XDXX1308)
文摘The steered response power-phase transform (SRP-PHAT) sound source localization algorithm is robust in a real environment. However, the large computation complexity limits the practical application of SRP-PHAT. For a microphone array, each location corresponds to a set of time differences of arrival (TDOAs), and this paper collects them into a TDOA vector. Since the TDOA vectors in the adjacent regions are similar, we present a fast algorithm based on clustering search to reduce the computation complexity of SRP-PHAT. In the training stage, the K-means or Iterative Self-Organizing Data Analysis Technique (ISODATA) clustering algorithm is used to find the centroid in each cluster with similar TDOA vectors. In the procedure of sound localization, the optimal cluster is found by comparing the steered response powers (SRPs) of all centroids. The SRPs of all candidate locations in the optimal cluster are compared to localize the sound source. Experiments both in simulation environments and real environments have been performed to compare the localization accuracy and computational load of the proposed method with those of the conventional SRP-PHAT algorithm. The results show that the proposed method is able to reduce the computational load drastically and maintains almost the same localization accuracy and robustness as those of the conventional SRP-PHAT algorithm. The difference in localization performance brought by different clustering algorithms used in the training stage is trivial.
基金supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 05865)Zhiqiang Xu was supported by National Natural Science Foundation of China (Grant Nos. 11422113, 91630203, 11021101 and 11331012)National Basic Research Program of China (973 Program) (Grant No. 2015CB856000)
文摘In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.
基金supported by National Natural Science Foundation of China (Grant No. 11171239)Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)
文摘Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.
基金supported by National Natural Science Foundation of China(Grant No.11371354)Key Laboratory of Random Complex Structures and Data Science+2 种基金Chinese Academy of Sciences(Grant No.2008DP173182)National Center for Mathematics and Interdisciplinary SciencesChinese Academy of Sciences
文摘We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.