In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to ...In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.展开更多
The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to const...The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.展开更多
Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. ...Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. Since ERN in the Sequential SIR model fluctuates in multiple dimensions due to changes in the surrounding environment, it is difficult to set the appropriate accuracy of the uncertainty region of the estimated data. The challenge in this study is to build a mathematical model of infectious disease according to the characteristics and data characteristics of the infectious disease and select an appropriate estimation method. Highly accurate quantitative research that analyzes the validity of “how infectious diseases prevail” from an academic point of view is the key to prediction and estimation in appropriate infection situation analysis. In this study, we adopted a statistical multivariate analysis method (T method) that enables evaluation and prediction of important factors related to ERN estimation and analysis of phenomena that change in real time (time series analysis). It was clarified that it is possible to estimate with higher accuracy by applying the T method to the estimated value of ERN by the current SIR mathematical model.展开更多
Classification models for multivariate time series have drawn the interest of many researchers to the field with the objective of developing accurate and efficient models.However,limited research has been conducted on...Classification models for multivariate time series have drawn the interest of many researchers to the field with the objective of developing accurate and efficient models.However,limited research has been conducted on generating adversarial samples for multivariate time series classification models.Adversarial samples could become a security concern in systems with complex sets of sensors.This study proposes extending the existing gradient adversarial transformation network(GATN)in combination with adversarial autoencoders to attack multivariate time series classification models.The proposed model attacks classification models by utilizing a distilled model to imitate the output of the multivariate time series classification model.In addition,the adversarial generator function is replaced with a variational autoencoder to enhance the adversarial samples.The developed methodology is tested on two multivariate time series classification models:1-nearest neighbor dynamic time warping(1-NN DTW)and a fully convolutional network(FCN).This study utilizes 30 multivariate time series benchmarks provided by the University of East Anglia(UEA)and University of California Riverside(UCR).The use of adversarial autoencoders shows an increase in the fraction of successful adversaries generated on multivariate time series.To the best of our knowledge,this is the first study to explore adversarial attacks on multivariate time series.Additionally,we recommend future research utilizing the generated latent space from the variational autoencoders.展开更多
The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergen...The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series. The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic continuous functions spaces. Tractability is the minimal number of function samples required to solve the problem in polynomial in ε^-1 and d, and the strong tractability is the presence of only a polynomial dependence in ε^-1. This problem has been recently studied for quasi-Monte Carlo quadrature rules, quadrature rules with non-negative coefficients, and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables. The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref,[14] on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative. The arguments are not constructive.展开更多
Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximati...Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.展开更多
Groundwater is considered as one of the most important sources for water supply in Iran.The Fasa Plain in Fars Province,Southern Iran is one of the major areas of wheat production using groundwater for irrigation.A la...Groundwater is considered as one of the most important sources for water supply in Iran.The Fasa Plain in Fars Province,Southern Iran is one of the major areas of wheat production using groundwater for irrigation.A large population also uses local groundwater for drinking purposes.Therefore,in this study,this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis(CA),Discriminant Analysis(DA),and Principal Component Analysis(PCA).Water quality data was monitored at 22 different wells,for five years(2009-2014)with 10 water quality parameters.By using cluster analysis,the sampling wells were grouped into two clusters with distinct water qualities at different locations.The Lasso Discriminant Analysis(LDA)technique was used to assess the spatial variability of water quality.Based on the results,all of the variables except sodium absorption ratio(SAR)are effective in the LDA model with all variables affording 92.80%correct assignation to discriminate between the clusters from the primary 10 variables.Principal component(PC)analysis and factor analysis reduced the complex data matrix into two main components,accounting for more than 95.93%of the total variance.The first PC contained the parameters of TH,Ca2+,and Mg2+.Therefore,the first dominant factor was hardness.In the second PC,Cl-,SAR,and Na+were the dominant parameters,which may indicate salinity.The originally acquired factors illustrate natural(existence of geological formations)and anthropogenic(improper disposal of domestic and agricultural wastes)factors which affect the groundwater quality.展开更多
In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable...In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.展开更多
BACKGROUND As one of the major abdominal operations,pancreaticoduodenectomy(PD)involves many organs.The operation is complex,and the scope of the operation is large,which can cause significant trauma in patients.The o...BACKGROUND As one of the major abdominal operations,pancreaticoduodenectomy(PD)involves many organs.The operation is complex,and the scope of the operation is large,which can cause significant trauma in patients.The operation has a high rate of complications.Pancreatic leakage is the main complication after PD.When pancreatic leakage occurs after PD,it can often lead to abdominal bleeding and infection,threatening the lives of patients.One study found that pancreatic leakage was affected by many factors including the choice of pancreaticojejunostomy method which can be well controlled.AIM To investigate the choice of operative methods for pancreaticojejunostomy and to conduct a multivariate study of pancreatic leakage in PD.METHODS A total of 420 patients undergoing PD in our hospital from January 2014 to March 2019 were enrolled and divided into group A(n=198)and group B(n=222)according to the pancreatointestinal anastomosis method adopted during the operation.Duct-to-mucosa pancreatojejunostomy was performed in group A and bundled pancreaticojejunostomy was performed in group B.The operation time,intraoperative blood loss,and pancreatic leakage of the two groups were assessed.The occurrence of pancreatic leakage after the operation in different patients was analyzed.RESULTS The differences in operative time and intraoperative bleeding between groups A and B were not significant(P>0.05).In group A,the time of pancreatojejunostomy was 26.03±4.40 min and pancreatic duct diameter was 3.90±1.10 mm.These measurements were significantly higher than those in group B(P<0.05).The differences in the occurrence of pancreatic leakage,abdominal infection,abdominal hemorrhage and gastric retention between group A and group B were not significant(P>0.05).The rates of pancreatic leakage in patients with preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm,were 23.33%,33.96%,and 19.01%,respectively.These were significantly higher than those in patients with preoperative albumin≥30 g/L,preoperative jaundice time<8 wk,and pancreatic duct diameter≥3 cm(P<0.05).Logistic regression analysis showed that preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm were risk factors for pancreatic leakage after PD(odds ratio=2.038,2.416 and 2.670,P<0.05).CONCLUSION The pancreatointestinal anastomosis method during PD has no significant effect on the occurrence of pancreatic leakage.The main risk factors for pancreatic leakage include preoperative albumin,preoperative jaundice time,and pancreatic duct diameter.展开更多
We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bi...We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bivariate normal case this dependence takes the form of a parameter (here the “expected value”) of one probability density depending continuously (here linearly) on realizations of the other random variable. The point is, that such a pattern does not need to be restricted to that classical case of the bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows one to extend it far beyond the bivariate or multivariate normal probability distributions class.展开更多
Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods.Num...Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods.Numerous traditional multivariate approaches such as principal component analysis have been used broadly in various research areas,including investment analysis,image identification,and population genetic structure analysis.However,these common approaches have the limitations of ignoring the correlations between responses and a low variable selection efficiency.Therefore,in this article,we introduce the reduced rank regression method and its extensions,sparse reduced rank regression and subspace assisted regression with row sparsity,which hold potential to meet the above demands and thus improve the interpretability of regression models.We conducted a simulation study to evaluate their performance and compared them with several other variable selection methods.For different application scenarios,we also provide selection suggestions based on predictive ability and variable selection accuracy.Finally,to demonstrate the practical value of these methods in the field of microbiome research,we applied our chosen method to real population-level microbiome data,the results of which validated our method.Our method extensions provide valuable guidelines for future omics research,especially with respect to multivariate regression,and could pave the way for novel discoveries in microbiome and related research fields.展开更多
This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equati...This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.展开更多
Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equation...Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.展开更多
A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and ...A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and principles contained in the water rocket have much in common with the actual small rocket system, and are suitable as educational and research teaching materials in the field of mechanics. Especially in the field of disaster prevention and mitigation, the use of water rockets is being researched and developed as a rescue tool in the event of a flood or earthquake as a disaster countermeasure. However, since the water rocket is a flying object based on the mechanical principle, it is important to ensure the accuracy and stability of the flight path. In this paper, a mechanical simulator is developed with a numerical calculation program based on the mechanical consideration of water rocket flight performance. In addition, the correlation between the flight distance obtained in the simulation and the estimated flight distance is analyzed by applying a multivariate analysis method and verifying the validity of the flight distance calculated from the result. Based on the verification results, we will apply a statistical optimization method to approach the optimization of flight stability performance conditions for water rockets.展开更多
文摘In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.
文摘The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.
文摘Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. Since ERN in the Sequential SIR model fluctuates in multiple dimensions due to changes in the surrounding environment, it is difficult to set the appropriate accuracy of the uncertainty region of the estimated data. The challenge in this study is to build a mathematical model of infectious disease according to the characteristics and data characteristics of the infectious disease and select an appropriate estimation method. Highly accurate quantitative research that analyzes the validity of “how infectious diseases prevail” from an academic point of view is the key to prediction and estimation in appropriate infection situation analysis. In this study, we adopted a statistical multivariate analysis method (T method) that enables evaluation and prediction of important factors related to ERN estimation and analysis of phenomena that change in real time (time series analysis). It was clarified that it is possible to estimate with higher accuracy by applying the T method to the estimated value of ERN by the current SIR mathematical model.
文摘Classification models for multivariate time series have drawn the interest of many researchers to the field with the objective of developing accurate and efficient models.However,limited research has been conducted on generating adversarial samples for multivariate time series classification models.Adversarial samples could become a security concern in systems with complex sets of sensors.This study proposes extending the existing gradient adversarial transformation network(GATN)in combination with adversarial autoencoders to attack multivariate time series classification models.The proposed model attacks classification models by utilizing a distilled model to imitate the output of the multivariate time series classification model.In addition,the adversarial generator function is replaced with a variational autoencoder to enhance the adversarial samples.The developed methodology is tested on two multivariate time series classification models:1-nearest neighbor dynamic time warping(1-NN DTW)and a fully convolutional network(FCN).This study utilizes 30 multivariate time series benchmarks provided by the University of East Anglia(UEA)and University of California Riverside(UCR).The use of adversarial autoencoders shows an increase in the fraction of successful adversaries generated on multivariate time series.To the best of our knowledge,this is the first study to explore adversarial attacks on multivariate time series.Additionally,we recommend future research utilizing the generated latent space from the variational autoencoders.
基金Project supported by the National Natural Science Foundation of China(10671019)Research Fund for the Doctoral Program Higher Education(20050027007)Beijing Educational Committee(2002Kj112)
文摘The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series. The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic continuous functions spaces. Tractability is the minimal number of function samples required to solve the problem in polynomial in ε^-1 and d, and the strong tractability is the presence of only a polynomial dependence in ε^-1. This problem has been recently studied for quasi-Monte Carlo quadrature rules, quadrature rules with non-negative coefficients, and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables. The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref,[14] on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative. The arguments are not constructive.
基金Supported by National Natural Science Foundation of China (Grant No.5150261)Shandong Provincial Natural Science Foundation of China (Grant No.ZR2015AM013)
文摘Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.
基金The authors would like to thank the Laboratory of Water Engineering,Fasa University for providing the facilities to perform this research.
文摘Groundwater is considered as one of the most important sources for water supply in Iran.The Fasa Plain in Fars Province,Southern Iran is one of the major areas of wheat production using groundwater for irrigation.A large population also uses local groundwater for drinking purposes.Therefore,in this study,this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis(CA),Discriminant Analysis(DA),and Principal Component Analysis(PCA).Water quality data was monitored at 22 different wells,for five years(2009-2014)with 10 water quality parameters.By using cluster analysis,the sampling wells were grouped into two clusters with distinct water qualities at different locations.The Lasso Discriminant Analysis(LDA)technique was used to assess the spatial variability of water quality.Based on the results,all of the variables except sodium absorption ratio(SAR)are effective in the LDA model with all variables affording 92.80%correct assignation to discriminate between the clusters from the primary 10 variables.Principal component(PC)analysis and factor analysis reduced the complex data matrix into two main components,accounting for more than 95.93%of the total variance.The first PC contained the parameters of TH,Ca2+,and Mg2+.Therefore,the first dominant factor was hardness.In the second PC,Cl-,SAR,and Na+were the dominant parameters,which may indicate salinity.The originally acquired factors illustrate natural(existence of geological formations)and anthropogenic(improper disposal of domestic and agricultural wastes)factors which affect the groundwater quality.
文摘In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
基金Scientific Research Programme for Health Commission of Jiangxi Province,No.20204269.
文摘BACKGROUND As one of the major abdominal operations,pancreaticoduodenectomy(PD)involves many organs.The operation is complex,and the scope of the operation is large,which can cause significant trauma in patients.The operation has a high rate of complications.Pancreatic leakage is the main complication after PD.When pancreatic leakage occurs after PD,it can often lead to abdominal bleeding and infection,threatening the lives of patients.One study found that pancreatic leakage was affected by many factors including the choice of pancreaticojejunostomy method which can be well controlled.AIM To investigate the choice of operative methods for pancreaticojejunostomy and to conduct a multivariate study of pancreatic leakage in PD.METHODS A total of 420 patients undergoing PD in our hospital from January 2014 to March 2019 were enrolled and divided into group A(n=198)and group B(n=222)according to the pancreatointestinal anastomosis method adopted during the operation.Duct-to-mucosa pancreatojejunostomy was performed in group A and bundled pancreaticojejunostomy was performed in group B.The operation time,intraoperative blood loss,and pancreatic leakage of the two groups were assessed.The occurrence of pancreatic leakage after the operation in different patients was analyzed.RESULTS The differences in operative time and intraoperative bleeding between groups A and B were not significant(P>0.05).In group A,the time of pancreatojejunostomy was 26.03±4.40 min and pancreatic duct diameter was 3.90±1.10 mm.These measurements were significantly higher than those in group B(P<0.05).The differences in the occurrence of pancreatic leakage,abdominal infection,abdominal hemorrhage and gastric retention between group A and group B were not significant(P>0.05).The rates of pancreatic leakage in patients with preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm,were 23.33%,33.96%,and 19.01%,respectively.These were significantly higher than those in patients with preoperative albumin≥30 g/L,preoperative jaundice time<8 wk,and pancreatic duct diameter≥3 cm(P<0.05).Logistic regression analysis showed that preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm were risk factors for pancreatic leakage after PD(odds ratio=2.038,2.416 and 2.670,P<0.05).CONCLUSION The pancreatointestinal anastomosis method during PD has no significant effect on the occurrence of pancreatic leakage.The main risk factors for pancreatic leakage include preoperative albumin,preoperative jaundice time,and pancreatic duct diameter.
文摘We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bivariate normal case this dependence takes the form of a parameter (here the “expected value”) of one probability density depending continuously (here linearly) on realizations of the other random variable. The point is, that such a pattern does not need to be restricted to that classical case of the bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows one to extend it far beyond the bivariate or multivariate normal probability distributions class.
基金the National Key Research and Development Program of China(2018YFC2000500)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB29020000)+1 种基金the National Natural Science Foundation of China(31771481 and 91857101)the Key Research Program of the Chinese Academy of Sciences(KFZD-SW-219),“China Microbiome Initiative.”。
文摘Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods.Numerous traditional multivariate approaches such as principal component analysis have been used broadly in various research areas,including investment analysis,image identification,and population genetic structure analysis.However,these common approaches have the limitations of ignoring the correlations between responses and a low variable selection efficiency.Therefore,in this article,we introduce the reduced rank regression method and its extensions,sparse reduced rank regression and subspace assisted regression with row sparsity,which hold potential to meet the above demands and thus improve the interpretability of regression models.We conducted a simulation study to evaluate their performance and compared them with several other variable selection methods.For different application scenarios,we also provide selection suggestions based on predictive ability and variable selection accuracy.Finally,to demonstrate the practical value of these methods in the field of microbiome research,we applied our chosen method to real population-level microbiome data,the results of which validated our method.Our method extensions provide valuable guidelines for future omics research,especially with respect to multivariate regression,and could pave the way for novel discoveries in microbiome and related research fields.
文摘This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.
文摘Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.
文摘A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and principles contained in the water rocket have much in common with the actual small rocket system, and are suitable as educational and research teaching materials in the field of mechanics. Especially in the field of disaster prevention and mitigation, the use of water rockets is being researched and developed as a rescue tool in the event of a flood or earthquake as a disaster countermeasure. However, since the water rocket is a flying object based on the mechanical principle, it is important to ensure the accuracy and stability of the flight path. In this paper, a mechanical simulator is developed with a numerical calculation program based on the mechanical consideration of water rocket flight performance. In addition, the correlation between the flight distance obtained in the simulation and the estimated flight distance is analyzed by applying a multivariate analysis method and verifying the validity of the flight distance calculated from the result. Based on the verification results, we will apply a statistical optimization method to approach the optimization of flight stability performance conditions for water rockets.
