The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is in...The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is introduced,which is the variable projection order Ekblom norm-promoted adaptive algorithm(VPO-EPAA).The method begins by examining the mean squared deviation(MSD)of the EPAA,deriving a formula for its MSD.Next,it compares the MSD of EPAA at two different projection orders and selects the one that minimizes the MSD as the parameter for the current iteration.Furthermore,the algorithm’s computational complexity is analyzed theoretically.Simulation results from system identification and self-interference cancellation show that the proposed algorithm performs exceptionally well in airborne radar signal self-interference cancellation,even under various noise intensities and types of interference.展开更多
Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. How...Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.展开更多
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These so...In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.展开更多
Statistical models can efficiently establish the relationships between crop growth and environmental conditions while explicitly quantifying uncertainties. This study aimed to test the efficiency of statistical models...Statistical models can efficiently establish the relationships between crop growth and environmental conditions while explicitly quantifying uncertainties. This study aimed to test the efficiency of statistical models established using partial least squares regression(PLSR) and artificial neural network(ANN) in predicting seed yields of sunflower(Helianthus annuus). Two-year field trial data on sunflower growth under different salinity levels and nitrogen(N) application rates in the Yichang Experimental Station in Hetao Irrigation District, Inner Mongolia, China, were used to calibrate and validate the statistical models. The variable importance in projection score was calculated in order to select the sensitive crop indices for seed yield prediction. We found that when the most sensitive indices were used as inputs for seed yield estimation, the PLSR could attain a comparable accuracy(root mean square error(RMSE) = 0.93 t ha-1, coefficient of determination(R^2) = 0.69) to that when using all measured indices(RMSE = 0.81 t ha-1,R^2= 0.77). The ANN model outperformed the PLSR for yield prediction with different combinations of inputs of both microplots and field data. The results indicated that sunflower seed yield could be reasonably estimated by using a small number of crop characteristic indices under complex environmental conditions and management options(e.g., saline soils and N application). Since leaf area index and plant height were found to be the most sensitive crop indices for sunflower seed yield prediction, remotely sensed data and the ANN model may be joined for regional crop yield simulation.展开更多
The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean ...The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.展开更多
In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with p...In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with principal coefficients.We show that the new lower bound quantum cluster algebra coincides with the corresponding acyclic quantum cluster algebra.Moreover,we establish a class of formulas between these generators and obtain the dual Poincaré-Birkhoff-Witt(PBW)basis of this algebra.展开更多
A supersaturated design （SSD）, whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors ...A supersaturated design （SSD）, whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression （MPLS-SR） method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement.展开更多
Tempeh is rich in rhizoxin and vitamin B12 and is regarded as an important functional food.Black bean tempeh may be produced using the co-fermentation of Propionibacterium freudenreichii and Rhizopus oligosporus,suppl...Tempeh is rich in rhizoxin and vitamin B12 and is regarded as an important functional food.Black bean tempeh may be produced using the co-fermentation of Propionibacterium freudenreichii and Rhizopus oligosporus,supplemented with monacolin K,to enhance rhizoxin and vitamin B12 levels.This research investigated the synthesis of black bean tempeh by integrating monacolin K and P.freudenreichii,focusing on the levels of glucosamine,free amino acids(FAAs),reducing sugars,rhizoxin,vitamin B12,and phenolic compounds over a 48-h fermentation period.The maximum glucosamine concentration in R.oligosporus from the combination of monacolin K supplementation and P.freudenreichii co-fermentation(MKS+PFCF)was 897.16 mg/g substrate,reflecting a 2.48-fold increase compared to the control.Following 48 h of fermentation,the vitamin B12 con-centration in black bean tempeh from the MKS+PFCF treatment exhibited an increase exceeding 2.49-fold compared to the P.freudenreichii co-fermentation treatment.The peak production rate of rhizoxin by R.oligosporus from the MKS+PFCF treatment throughout the fermentation period of 12-48 h was 14.94-fold.The results of the principal component analysis(PCA)indicated that both FAAs and reducing sugars may serve as indicators for the secondary metabolites of vitamin B12 and rhizoxin throughout the fermentation process.The variable exerting the most substantial impact,indicated by a variable importance in projection(VIP)score above 1,was glucosamine.A comprehensive analysis of primary metabolites,including vitamin B12,rhizoxin,and phenolic compounds in black bean tempeh,revealed 17 pathways linked to amino acid metabolism,biosynthesis,and cellular respiration,including galactose metabolism and starch and sucrose metabolism.These findings may represent an innovative approach to the co-fermentation of R.oligosporus and P.freudenreichii,supplemented with monacolin K,for the industrial manufacture of black bean tempeh enriched with substantial levels of vitamin B12 and rhizoxin.Data derived from PCA,VIP,and metabolomic analysis of primary and secondary metabolites in black bean tempeh were used as scientific evidence to elucidate their interrelationships and pathways for tempeh generated from a black bean substrate.展开更多
Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad appl...Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.展开更多
High-rise intake towers in high-intensity seismic areas are prone to structural safety problems under vibration.Therefore,effective and low-cost anti-seismic engineering measures must be designed for protection.An int...High-rise intake towers in high-intensity seismic areas are prone to structural safety problems under vibration.Therefore,effective and low-cost anti-seismic engineering measures must be designed for protection.An intake tower in northwest China was considered the research object,and its natural vibration characteristics and dynamic response were first analyzed using the mode decomposition response spectrum method based on a three-dimensional finite element model.The non-dominated sorting genetic algorithm-II(NSGA-II)was adopted to optimize the anti-seismic scheme combination by comprehensively considering the dynamic tower response and variable project cost.Finally,the rationality of the original intake tower antiseismic design scheme was evaluated according to the obtained optimal solution set,and recommendations for improvement were proposed.The method adopted in this study may provide significant references for designing anti-seismic measures for high-rise structures such as intake towers located in high-intensity earthquake areas.展开更多
基金supported by the Shan⁃dong Provincial Natural Science Foundation(No.ZR2022MF314).
文摘The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is introduced,which is the variable projection order Ekblom norm-promoted adaptive algorithm(VPO-EPAA).The method begins by examining the mean squared deviation(MSD)of the EPAA,deriving a formula for its MSD.Next,it compares the MSD of EPAA at two different projection orders and selects the one that minimizes the MSD as the parameter for the current iteration.Furthermore,the algorithm’s computational complexity is analyzed theoretically.Simulation results from system identification and self-interference cancellation show that the proposed algorithm performs exceptionally well in airborne radar signal self-interference cancellation,even under various noise intensities and types of interference.
基金supported in part by the National Nature Science Foundation of China(Nos.62173091,62073082)in part by the Natural Science Foundation of Fujian Province(No.2023J01268)in part by the Taishan Scholar Program of Shandong Province.
文摘Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.
基金supported by National Natural Science Foundation of China undcr Grant No. 10172056 .
文摘In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.
基金supported by the National Natural Science Foundation of China (Nos. 51609175, 51790533, 51879196, and 51439006)
文摘Statistical models can efficiently establish the relationships between crop growth and environmental conditions while explicitly quantifying uncertainties. This study aimed to test the efficiency of statistical models established using partial least squares regression(PLSR) and artificial neural network(ANN) in predicting seed yields of sunflower(Helianthus annuus). Two-year field trial data on sunflower growth under different salinity levels and nitrogen(N) application rates in the Yichang Experimental Station in Hetao Irrigation District, Inner Mongolia, China, were used to calibrate and validate the statistical models. The variable importance in projection score was calculated in order to select the sensitive crop indices for seed yield prediction. We found that when the most sensitive indices were used as inputs for seed yield estimation, the PLSR could attain a comparable accuracy(root mean square error(RMSE) = 0.93 t ha-1, coefficient of determination(R^2) = 0.69) to that when using all measured indices(RMSE = 0.81 t ha-1,R^2= 0.77). The ANN model outperformed the PLSR for yield prediction with different combinations of inputs of both microplots and field data. The results indicated that sunflower seed yield could be reasonably estimated by using a small number of crop characteristic indices under complex environmental conditions and management options(e.g., saline soils and N application). Since leaf area index and plant height were found to be the most sensitive crop indices for sunflower seed yield prediction, remotely sensed data and the ANN model may be joined for regional crop yield simulation.
文摘The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.
基金supported by Innovation Research for the Postgraduates of Guangzhou University(Grant No.JCCX2024-053)supported by National Natural Science Foundation of China(Grant No.12371036)+1 种基金supported by National Natural Science Foundation of China(GrantNo.12031007)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011739)。
文摘In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with principal coefficients.We show that the new lower bound quantum cluster algebra coincides with the corresponding acyclic quantum cluster algebra.Moreover,we establish a class of formulas between these generators and obtain the dual Poincaré-Birkhoff-Witt(PBW)basis of this algebra.
基金supported by the National Natural Science Foundation of China （Grant Nos. 10971107, 11271205）, the ＂131＂ Talents Program of Tianjin, and the Fundamental Research Funds for the Central Universities （Grant Nos. 65030011, 65011481）.
文摘A supersaturated design （SSD）, whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression （MPLS-SR） method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement.
文摘Tempeh is rich in rhizoxin and vitamin B12 and is regarded as an important functional food.Black bean tempeh may be produced using the co-fermentation of Propionibacterium freudenreichii and Rhizopus oligosporus,supplemented with monacolin K,to enhance rhizoxin and vitamin B12 levels.This research investigated the synthesis of black bean tempeh by integrating monacolin K and P.freudenreichii,focusing on the levels of glucosamine,free amino acids(FAAs),reducing sugars,rhizoxin,vitamin B12,and phenolic compounds over a 48-h fermentation period.The maximum glucosamine concentration in R.oligosporus from the combination of monacolin K supplementation and P.freudenreichii co-fermentation(MKS+PFCF)was 897.16 mg/g substrate,reflecting a 2.48-fold increase compared to the control.Following 48 h of fermentation,the vitamin B12 con-centration in black bean tempeh from the MKS+PFCF treatment exhibited an increase exceeding 2.49-fold compared to the P.freudenreichii co-fermentation treatment.The peak production rate of rhizoxin by R.oligosporus from the MKS+PFCF treatment throughout the fermentation period of 12-48 h was 14.94-fold.The results of the principal component analysis(PCA)indicated that both FAAs and reducing sugars may serve as indicators for the secondary metabolites of vitamin B12 and rhizoxin throughout the fermentation process.The variable exerting the most substantial impact,indicated by a variable importance in projection(VIP)score above 1,was glucosamine.A comprehensive analysis of primary metabolites,including vitamin B12,rhizoxin,and phenolic compounds in black bean tempeh,revealed 17 pathways linked to amino acid metabolism,biosynthesis,and cellular respiration,including galactose metabolism and starch and sucrose metabolism.These findings may represent an innovative approach to the co-fermentation of R.oligosporus and P.freudenreichii,supplemented with monacolin K,for the industrial manufacture of black bean tempeh enriched with substantial levels of vitamin B12 and rhizoxin.Data derived from PCA,VIP,and metabolomic analysis of primary and secondary metabolites in black bean tempeh were used as scientific evidence to elucidate their interrelationships and pathways for tempeh generated from a black bean substrate.
基金Chinese NSF grant 10231060the CAS Knowledge Innovation Program
文摘Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.
基金supported by the National Natural Science Foundation of the China/Yalong River Joint Fund Project (No.U1765205).
文摘High-rise intake towers in high-intensity seismic areas are prone to structural safety problems under vibration.Therefore,effective and low-cost anti-seismic engineering measures must be designed for protection.An intake tower in northwest China was considered the research object,and its natural vibration characteristics and dynamic response were first analyzed using the mode decomposition response spectrum method based on a three-dimensional finite element model.The non-dominated sorting genetic algorithm-II(NSGA-II)was adopted to optimize the anti-seismic scheme combination by comprehensively considering the dynamic tower response and variable project cost.Finally,the rationality of the original intake tower antiseismic design scheme was evaluated according to the obtained optimal solution set,and recommendations for improvement were proposed.The method adopted in this study may provide significant references for designing anti-seismic measures for high-rise structures such as intake towers located in high-intensity earthquake areas.
