A multivariate Student’s t-distribution is derived by analogy to the derivation of a multivariate normal (Gaussian) probability density function. This multivariate Student’s t-distribution can have different shape p...A multivariate Student’s t-distribution is derived by analogy to the derivation of a multivariate normal (Gaussian) probability density function. This multivariate Student’s t-distribution can have different shape parameters for the marginal probability density functions of the multivariate distribution. Expressions for the probability density function, for the variances, and for the covariances of the multivariate t-distribution with arbitrary shape parameters for the marginals are given.展开更多
The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA...The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA,poor ability to avoid local optimum,and slow convergence speed,this paper proposes a multi-strategy improved HBA based on periodical mutation and t-distribution perturbation,called MHBA.Firstly,a good point set population initialization is introduced to get a uniform initial population.Secondly,periodic mutation and t-distribution perturbation are successively used to improve the algorithm’s ability to avoid local optimum.Finally,the density factor is improved for balancing exploration and exploitation.By comparing MHBA with HBA and 7 other SIs on 6 benchmark functions,it is evident that the performance of MHBA is far superior to HBA.In addition,by applying MHBA to robot path planning,MHBA can identify the shortest path more quickly and consistently compared with competitors.展开更多
It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional ...It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional Sparrow Search Algorithm(SSA)suffers from limited global search capability,insufficient population diversity,and slow convergence,which often leads to premature stagnation in local optima.Despite the proposal of various enhanced versions,the effective balancing of exploration and exploitation remains an unsolved challenge.To address the previously mentioned problems,this study proposes a multi-strategy collaborative improved SSA,which systematically integrates four complementary strategies:(1)the Northern Goshawk Optimization(NGO)mechanism enhances global exploration through guided prey-attacking dynamics;(2)an adaptive t-distribution mutation strategy balances the transition between exploration and exploitation via dynamic adjustment of the degrees of freedom;(3)a dual chaotic initialization method(Bernoulli and Sinusoidal maps)increases population diversity and distribution uniformity;and(4)an elite retention strategy maintains solution quality and prevents degradation during iterations.These strategies cooperate synergistically,forming a tightly coupled optimization framework that significantly improves search efficiency and robustness.Therefore,this paper names it NTSSA:A Novel Multi-Strategy Enhanced Sparrow Search Algorithm with Northern Goshawk Optimization and Adaptive t-Distribution for Global Optimization.Extensive experiments on the CEC2005 benchmark set demonstrate that NTSSA achieves theoretical optimal accuracy on unimodal functions and significantly enhances global optimum discovery for multimodal functions by 2–5 orders of magnitude.Compared with SSA,GWO,ISSA,and CSSOA,NTSSA improves solution accuracy by up to 14.3%(F8)and 99.8%(F12),while accelerating convergence by approximately 1.5–2×.The Wilcoxon rank-sum test(p<0.05)indicates that NTSSA demonstrates a statistically substantial performance advantage.Theoretical analysis demonstrates that the collaborative synergy among adaptive mutation,chaos-based diversification,and elite preservation ensures both high convergence accuracy and global stability.This work bridges a key research gap in SSA by realizing a coordinated optimization mechanism between exploration and exploitation,offering a robust and efficient solution framework for complex high-dimensional problems in intelligent computation and engineering design.展开更多
Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents...Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents the model that integrates Osprey and adaptive T-distribution dung beetle algorithm for optimizing a convolutional neural network.The CNN-BiLSTM-Attention model combines bidirectional long short-term memory neural networks with an attention mechanism,thereby improving the accuracy of wind power generation predictions.The original data is subjected to Variational Mode Decomposition(VMD)for analysis,taking into account the fluctuations in wind power across different periods.The BiLSTM network with short-term memory processes time-series wind power data,yielding an optimal predictive performance.The integration of the osprey algorithm and adaptive T-distribution within the Dung Beetle Optimization Algorithm was utilized to optimize the hyperparameters of the CNN-BiLSTM-Attention model,thereby enhancing its predictive performance.To assess the efficacy of the CNN-BiLSTM-Attention algorithm,enhanced by Ospreys and adaptive T-distributed dung beetle algorithm,we conducted experiments using the CEC2021 benchmark function.The integrated Osprey and adaptive T-distribution Dung Beetle algorithm has excellent global optimization performance when dealing with complex optimization problems.The fusion of Osprey and the adaptive T-distribution Dung beetle algorithm optimized the CNN-BiLSTM-Attention algorithm as well as other optimization algorithms for ablation experiments.The results show that the improved algorithm performs well in predicting wind power.The experimental findings suggest that the model’s predictive efficiency has enhanced by a minimum of 17.74%.展开更多
The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first dis...The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.展开更多
The significance of accurately forecasting natural gas prices is far-reaching and significant,not only for the stable operation of the energy market,but also as a key element in promoting sustainable development and a...The significance of accurately forecasting natural gas prices is far-reaching and significant,not only for the stable operation of the energy market,but also as a key element in promoting sustainable development and addressing environmental challenges.However,natural gas prices are affected by multiple source factors,presenting complex,unstable nonlinear characteristics hindering the improvement of the prediction accuracy of existing models.To address this issue,this study proposes an innovative multivariate combined forecasting model for natural gas prices.Initially,the study meticulously identifies and introduces 16 variables impacting natural gas prices across five crucial dimensions:the production,marketing,commodities,political and economic indicators of the United States and temperature.Subsequently,this study employs the least absolute shrinkage and selection operator,grey relation analysis,and random forest for dimensionality reduction,effectively screening out the most influential key variables to serve as input features for the subsequent learning model.Building upon this foundation,a suite of machine learning models is constructed to ensure precise natural gas price prediction.To further elevate the predictive performance,an intelligent algorithm for parameter optimization is incorporated,addressing potential limitations of individual models.To thoroughly assess the prediction accuracy of the proposed model,this study conducts three experiments using monthly natural gas trading prices.These experiments incorporate 19 benchmark models for comparative analysis,utilizing five evaluation metrics to quantify forecasting effectiveness.Furthermore,this study conducts in-depth validation of the proposed model's effectiveness through hypothesis testing,discussions on the improvement ratio of forecasting performance,and case studies on other energy prices.The empirical results demonstrate that the multivariate combined forecasting method developed in this study surpasses other comparative models in forecasting accuracy.It offers new perspectives and methodologies for natural gas price forecasting while also providing valuable insights for other energy price forecasting studies.展开更多
The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic tim...The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.展开更多
[Objective] The plankton and macrobenthos samples in municipal polluted river were analyzed by different methods, so as to explore the method suitable for biological data analysis in heavy polluted area. [Method] Shan...[Objective] The plankton and macrobenthos samples in municipal polluted river were analyzed by different methods, so as to explore the method suitable for biological data analysis in heavy polluted area. [Method] Shannon-Wiener diversity index, cluster analysis of multivariate statistical analysis and MDS （Non-matric Multi- dimentional Scaling）analysis were used to analyze biological data of phytoplankton, zooplankton and Zoobenthos collected from the representative municipal polluted river in Pearl River Delta. The sediment samples were also collected to determine. Pb, Cd, Hg, Cr, As, Cu, Ni, Zn, as well as CODe, and NH3-N of porewater. Hakanson potential ecological risk index method was used to evaluate the ecological risk. [Re- suit] Shannon-Wiener diversity index analysis results can not effectively reflect the difference of pollution status of various stations in heavy polluted area; despite the presence of some problems, multivariate analysis method is superior to the Shannon-Wiener diversity index method in biological monitoring of heavy polluted river in the city. [Conclusion] The paper provided theoretical basis for biological data analysis in heavy polluted area.展开更多
The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence ba...The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.展开更多
This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tai...This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.展开更多
Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was foun...Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was found that the molar refractivity of the C3′substituent of the C13 side chain has significant correlation with its activity. We deduce that structural changes in the C3′substituents may be critical to the anticancer function. It would be useful to the design and synthesis of taxol like compounds with improved activities.展开更多
Multivariate statistical techniques,cluster analysis,non-parametric tests,and factor analysis were applied to analyze a water quality dataset including 13 parameters at 37 sites of the Three Gorges area,China,from 200...Multivariate statistical techniques,cluster analysis,non-parametric tests,and factor analysis were applied to analyze a water quality dataset including 13 parameters at 37 sites of the Three Gorges area,China,from 2003–2008 to investigate spatio-temporal variations and identify potential pollution sources.Using cluster analysis,the twelve months of the year were classified into three periods of lowflow （LF）,normal-flow （NF）,and high-flow （HF）;and the 37 monitoring sites were divided into low pollution （LP）,moderate pollution （MP）,and high pollution （HP）.Dissolved oxygen （DO）,potassium permanganate index （COD Mn ）,and ammonia-nitrogen （NH 4 ＋-N） were identified as significant variables affecting temporal and spatial variations by non-parametric tests.Factor analysis identified that the major pollutants in the HP region were organic matters and nutrients during NF,heavy metals during LF,and petroleum during HF.In the MP region,the identified pollutants primarily included organic matter and heavy metals year-around,while in the LP region,organic pollution was significant during both NF and HF,and nutrient and heavy metal levels were high during both LF and HF.The main sources of pollution came from domestic wastewater and agricultural activities and runoff;however,they contributed differently to each region in regards to pollution levels.For the HP region,inputs from wastewater treatment plants were significant;but for MP and LP regions,water pollution was more likely from the combined effects of agriculture,domestic wastewater,and chemical industry.These results provide fundamental information for developing better water pollution control strategies for the Three Gorges area.展开更多
Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and...Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.展开更多
A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, struc...A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.展开更多
In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar re...In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.展开更多
Understanding the controlling factor of groundwater quality can enhance promoting sustainable development of groundwater resources. To this end, multivariate statistical analysis（MA） and hydrochemical analysis were ...Understanding the controlling factor of groundwater quality can enhance promoting sustainable development of groundwater resources. To this end, multivariate statistical analysis（MA） and hydrochemical analysis were introduced in this work. The results indicate that the canonical discriminant function with 7 parameters was established using the discriminant analysis（DA） method, which can afford 100% correct assignation according to the 3 different clusters（good water（GW）, poor water（PW）, and very poor water（VPW）） obtained from cluster analysis（CA）. According to factor analysis（FA）, 8 factors were extracted from 25 hydrochemical elements and account for 80.897% of the total data variance, suggesting that groundwater with higher concentrations of sodium, calcium, magnesium, chloride, and sulfate in southeastern study area are mainly affected by the natural process; the higher level of arsenic and chromium in groundwater extracted from northwestern part of study area are derived by industrial activities; domestic and agriculture sewage have important contribution to copper, iron, iodine, and phosphate in the northern study area. Therefore, this work can help identify the main controlling factor of groundwater quality in North China plain so as to make better and more informed decisions about how to achieve groundwater resources sustainable development.展开更多
Multivariate pattern analysis（MVPA） is a recently-developed approach for functional magnetic resonance imaging（fMRI） data analyses.Compared with the traditional univariate methods,MVPA is more sensitive to subtle ...Multivariate pattern analysis（MVPA） is a recently-developed approach for functional magnetic resonance imaging（fMRI） data analyses.Compared with the traditional univariate methods,MVPA is more sensitive to subtle changes in multivariate patterns in fMRI data.In this review,we introduce several significant advances in MVPA applications and summarize various combinations of algorithms and parameters in different problem settings.The limitations of MVPA and some critical questions that need to be addressed in future research are also discussed.展开更多
文摘A multivariate Student’s t-distribution is derived by analogy to the derivation of a multivariate normal (Gaussian) probability density function. This multivariate Student’s t-distribution can have different shape parameters for the marginal probability density functions of the multivariate distribution. Expressions for the probability density function, for the variances, and for the covariances of the multivariate t-distribution with arbitrary shape parameters for the marginals are given.
基金Supported by the National Key Research and Development Program of China(No.2022ZD0119001)。
文摘The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA,poor ability to avoid local optimum,and slow convergence speed,this paper proposes a multi-strategy improved HBA based on periodical mutation and t-distribution perturbation,called MHBA.Firstly,a good point set population initialization is introduced to get a uniform initial population.Secondly,periodic mutation and t-distribution perturbation are successively used to improve the algorithm’s ability to avoid local optimum.Finally,the density factor is improved for balancing exploration and exploitation.By comparing MHBA with HBA and 7 other SIs on 6 benchmark functions,it is evident that the performance of MHBA is far superior to HBA.In addition,by applying MHBA to robot path planning,MHBA can identify the shortest path more quickly and consistently compared with competitors.
文摘It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional Sparrow Search Algorithm(SSA)suffers from limited global search capability,insufficient population diversity,and slow convergence,which often leads to premature stagnation in local optima.Despite the proposal of various enhanced versions,the effective balancing of exploration and exploitation remains an unsolved challenge.To address the previously mentioned problems,this study proposes a multi-strategy collaborative improved SSA,which systematically integrates four complementary strategies:(1)the Northern Goshawk Optimization(NGO)mechanism enhances global exploration through guided prey-attacking dynamics;(2)an adaptive t-distribution mutation strategy balances the transition between exploration and exploitation via dynamic adjustment of the degrees of freedom;(3)a dual chaotic initialization method(Bernoulli and Sinusoidal maps)increases population diversity and distribution uniformity;and(4)an elite retention strategy maintains solution quality and prevents degradation during iterations.These strategies cooperate synergistically,forming a tightly coupled optimization framework that significantly improves search efficiency and robustness.Therefore,this paper names it NTSSA:A Novel Multi-Strategy Enhanced Sparrow Search Algorithm with Northern Goshawk Optimization and Adaptive t-Distribution for Global Optimization.Extensive experiments on the CEC2005 benchmark set demonstrate that NTSSA achieves theoretical optimal accuracy on unimodal functions and significantly enhances global optimum discovery for multimodal functions by 2–5 orders of magnitude.Compared with SSA,GWO,ISSA,and CSSOA,NTSSA improves solution accuracy by up to 14.3%(F8)and 99.8%(F12),while accelerating convergence by approximately 1.5–2×.The Wilcoxon rank-sum test(p<0.05)indicates that NTSSA demonstrates a statistically substantial performance advantage.Theoretical analysis demonstrates that the collaborative synergy among adaptive mutation,chaos-based diversification,and elite preservation ensures both high convergence accuracy and global stability.This work bridges a key research gap in SSA by realizing a coordinated optimization mechanism between exploration and exploitation,offering a robust and efficient solution framework for complex high-dimensional problems in intelligent computation and engineering design.
基金supported by the National Natural Science Foundation of China[Grant No.12371378]the Fujian Natural Science Foundation[Grant No.2022J01378,Grant No.2023J011127].
文摘Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents the model that integrates Osprey and adaptive T-distribution dung beetle algorithm for optimizing a convolutional neural network.The CNN-BiLSTM-Attention model combines bidirectional long short-term memory neural networks with an attention mechanism,thereby improving the accuracy of wind power generation predictions.The original data is subjected to Variational Mode Decomposition(VMD)for analysis,taking into account the fluctuations in wind power across different periods.The BiLSTM network with short-term memory processes time-series wind power data,yielding an optimal predictive performance.The integration of the osprey algorithm and adaptive T-distribution within the Dung Beetle Optimization Algorithm was utilized to optimize the hyperparameters of the CNN-BiLSTM-Attention model,thereby enhancing its predictive performance.To assess the efficacy of the CNN-BiLSTM-Attention algorithm,enhanced by Ospreys and adaptive T-distributed dung beetle algorithm,we conducted experiments using the CEC2021 benchmark function.The integrated Osprey and adaptive T-distribution Dung Beetle algorithm has excellent global optimization performance when dealing with complex optimization problems.The fusion of Osprey and the adaptive T-distribution Dung beetle algorithm optimized the CNN-BiLSTM-Attention algorithm as well as other optimization algorithms for ablation experiments.The results show that the improved algorithm performs well in predicting wind power.The experimental findings suggest that the model’s predictive efficiency has enhanced by a minimum of 17.74%.
基金Supported by the National Natural Science Foundation of China(12271154)the Natural Science Foundation of Hunan Province(2022JJ30234)the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231032)。
文摘The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.
基金supported by the funding from the Humanities and Social Science Fund of Ministry of Education of China(No.22YJCZH028)National Natural Science Foundation of China(Grant No.72303001)+3 种基金Fundamental Research Funds for the Central Universities(No.JUSRP124043)Anhui Provincial Excellent Young Scientists Fund for Universities(No.2024AH030001)Anhui Education Department Excellent Young Teachers Fund(No.YQYB2024021)Basic Research Program of Jiangsu(No.BK20251593)。
文摘The significance of accurately forecasting natural gas prices is far-reaching and significant,not only for the stable operation of the energy market,but also as a key element in promoting sustainable development and addressing environmental challenges.However,natural gas prices are affected by multiple source factors,presenting complex,unstable nonlinear characteristics hindering the improvement of the prediction accuracy of existing models.To address this issue,this study proposes an innovative multivariate combined forecasting model for natural gas prices.Initially,the study meticulously identifies and introduces 16 variables impacting natural gas prices across five crucial dimensions:the production,marketing,commodities,political and economic indicators of the United States and temperature.Subsequently,this study employs the least absolute shrinkage and selection operator,grey relation analysis,and random forest for dimensionality reduction,effectively screening out the most influential key variables to serve as input features for the subsequent learning model.Building upon this foundation,a suite of machine learning models is constructed to ensure precise natural gas price prediction.To further elevate the predictive performance,an intelligent algorithm for parameter optimization is incorporated,addressing potential limitations of individual models.To thoroughly assess the prediction accuracy of the proposed model,this study conducts three experiments using monthly natural gas trading prices.These experiments incorporate 19 benchmark models for comparative analysis,utilizing five evaluation metrics to quantify forecasting effectiveness.Furthermore,this study conducts in-depth validation of the proposed model's effectiveness through hypothesis testing,discussions on the improvement ratio of forecasting performance,and case studies on other energy prices.The empirical results demonstrate that the multivariate combined forecasting method developed in this study surpasses other comparative models in forecasting accuracy.It offers new perspectives and methodologies for natural gas price forecasting while also providing valuable insights for other energy price forecasting studies.
文摘The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.
基金Supported by National Natural Science Foundation of China(41001341)Natural Science Foundation of Guangdong Province(9152800001000007)+1 种基金Open Fund ofState Key Laboratory of Subtropical Building Science(2011KB12)Basic Scientific Research Expenses Project of Central Universities(2012ZM0082)~~
文摘[Objective] The plankton and macrobenthos samples in municipal polluted river were analyzed by different methods, so as to explore the method suitable for biological data analysis in heavy polluted area. [Method] Shannon-Wiener diversity index, cluster analysis of multivariate statistical analysis and MDS （Non-matric Multi- dimentional Scaling）analysis were used to analyze biological data of phytoplankton, zooplankton and Zoobenthos collected from the representative municipal polluted river in Pearl River Delta. The sediment samples were also collected to determine. Pb, Cd, Hg, Cr, As, Cu, Ni, Zn, as well as CODe, and NH3-N of porewater. Hakanson potential ecological risk index method was used to evaluate the ecological risk. [Re- suit] Shannon-Wiener diversity index analysis results can not effectively reflect the difference of pollution status of various stations in heavy polluted area; despite the presence of some problems, multivariate analysis method is superior to the Shannon-Wiener diversity index method in biological monitoring of heavy polluted river in the city. [Conclusion] The paper provided theoretical basis for biological data analysis in heavy polluted area.
基金Supported by the National Natural Science Foundation of China(71101043,70901041,71171113)the Joint Research Project of National Natural Science Foundation of China and Royal Society of UK(71111130211)+4 种基金the Major Program of National Funds of Social Science of China(10ZD&014,11&ZD168)the Doctoral Fundof Ministry of Education of China(20093218120032,200802870020)the Qinglan Project for Excellent Youth Teacherin Jiangsu Province(China)Research Funding in Nanjing University of Aeronautics and Astronautics(NR2011002)the Central University Scientific Research Expenses of HoHai University(2011B09914,2010B11114)~~
文摘The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.
基金The National Natural Science Foundation of China(No.11001052,11171065)the National Science Foundation of Jiangsu Province(No.BK2011058)the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57)
文摘This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.
文摘Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was found that the molar refractivity of the C3′substituent of the C13 side chain has significant correlation with its activity. We deduce that structural changes in the C3′substituents may be critical to the anticancer function. It would be useful to the design and synthesis of taxol like compounds with improved activities.
基金supported by the National Water Special Project (No.2009ZX07526-005)the Strategic Environmental Assessment Project (No.HP1080901)
文摘Multivariate statistical techniques,cluster analysis,non-parametric tests,and factor analysis were applied to analyze a water quality dataset including 13 parameters at 37 sites of the Three Gorges area,China,from 2003–2008 to investigate spatio-temporal variations and identify potential pollution sources.Using cluster analysis,the twelve months of the year were classified into three periods of lowflow （LF）,normal-flow （NF）,and high-flow （HF）;and the 37 monitoring sites were divided into low pollution （LP）,moderate pollution （MP）,and high pollution （HP）.Dissolved oxygen （DO）,potassium permanganate index （COD Mn ）,and ammonia-nitrogen （NH 4 ＋-N） were identified as significant variables affecting temporal and spatial variations by non-parametric tests.Factor analysis identified that the major pollutants in the HP region were organic matters and nutrients during NF,heavy metals during LF,and petroleum during HF.In the MP region,the identified pollutants primarily included organic matter and heavy metals year-around,while in the LP region,organic pollution was significant during both NF and HF,and nutrient and heavy metal levels were high during both LF and HF.The main sources of pollution came from domestic wastewater and agricultural activities and runoff;however,they contributed differently to each region in regards to pollution levels.For the HP region,inputs from wastewater treatment plants were significant;but for MP and LP regions,water pollution was more likely from the combined effects of agriculture,domestic wastewater,and chemical industry.These results provide fundamental information for developing better water pollution control strategies for the Three Gorges area.
文摘Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.
基金The National Natural Science Foundation of China(No.51378407,51578431)
文摘A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.
基金supported by the Centre for Advanced Modelling and Geospatial Information Systems(CAMGIS),UTS under grant numbers 321740.2232335,323930,and 321740.2232357
文摘In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.
基金supported by the Major State Basic Research Development Program (No. 2010CB428800)the Geological Survey Projects Foundation of Institute of Hydrogeology and Environmental Geology (No. SK201308)
文摘Understanding the controlling factor of groundwater quality can enhance promoting sustainable development of groundwater resources. To this end, multivariate statistical analysis（MA） and hydrochemical analysis were introduced in this work. The results indicate that the canonical discriminant function with 7 parameters was established using the discriminant analysis（DA） method, which can afford 100% correct assignation according to the 3 different clusters（good water（GW）, poor water（PW）, and very poor water（VPW）） obtained from cluster analysis（CA）. According to factor analysis（FA）, 8 factors were extracted from 25 hydrochemical elements and account for 80.897% of the total data variance, suggesting that groundwater with higher concentrations of sodium, calcium, magnesium, chloride, and sulfate in southeastern study area are mainly affected by the natural process; the higher level of arsenic and chromium in groundwater extracted from northwestern part of study area are derived by industrial activities; domestic and agriculture sewage have important contribution to copper, iron, iodine, and phosphate in the northern study area. Therefore, this work can help identify the main controlling factor of groundwater quality in North China plain so as to make better and more informed decisions about how to achieve groundwater resources sustainable development.
基金supported by grants from the National Natural Science Foundation of China (30900366,31070905)
文摘Multivariate pattern analysis（MVPA） is a recently-developed approach for functional magnetic resonance imaging（fMRI） data analyses.Compared with the traditional univariate methods,MVPA is more sensitive to subtle changes in multivariate patterns in fMRI data.In this review,we introduce several significant advances in MVPA applications and summarize various combinations of algorithms and parameters in different problem settings.The limitations of MVPA and some critical questions that need to be addressed in future research are also discussed.
