Purpose： To discuss the problems arising from hierarchical cluster analysis of co-occurrence matrices in SPSS, and the corresponding solutions. Design/methodology/approach： We design different methods of using the S...Purpose： To discuss the problems arising from hierarchical cluster analysis of co-occurrence matrices in SPSS, and the corresponding solutions. Design/methodology/approach： We design different methods of using the SPSS hierarchical clustering module for co-occurrence matrices in order to compare these methods. We offer the correct syntax to deactivate the similarity algorithm for clustering analysis within the hierarchical clustering module of SPSS. Findings： When one inputs co-occurrence matrices into the data editor of the SPSS hierarchical clustering module without deactivating the embedded similarity algorithm, the program calculates similarity twice, and thus distorts and overestimates the degree of similarity. Practical implications： We offer the correct syntax to block the similarity algorithm for clustering analysis in the SPSS hierarchical clustering module in the case of co-occurrence matrices. This syntax enables researchers to avoid obtaining incorrect results. Originality/value： This paper presents a method of editing syntax to prevent the default use of a similarity algorithm for SPSS＇s hierarchical clustering module. This will help researchers, especially those from China, to properly implement the co-occurrence matrix when using SPSS for hierarchical cluster analysis, in order to provide more scientific and rational results.展开更多
The mechanical properties of materials greatly depend on the microstructure morphology. The quantitative characterization of material microstructures is essential for the performance prediction and hence the material ...The mechanical properties of materials greatly depend on the microstructure morphology. The quantitative characterization of material microstructures is essential for the performance prediction and hence the material design. At present,the quantitative characterization methods mainly rely on the microstructure characterization of shape, size, distribution,and volume fraction, which related to the mechanical properties. These traditional methods have been applied for several decades and the subjectivity of human factors induces unavoidable errors. In this paper, we try to bypass the traditional operations and identify the relationship between the microstructures and the material properties by the texture of image itself directly. The statistical approach is based on gray level Co-occurrence matrix（GLCM）, allowing an objective and repeatable study on material microstructures. We first present how to identify GLCM with the optimal parameters, and then apply the method on three systems with different microstructures. The results show that GLCM can reveal the interface information and microstructures complexity with less human impact. Naturally, there is a good correlation between GLCM and the mechanical properties.展开更多
In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
The development of fungicides is time-consuming and costly.Introducing a fungicide-likeness assessment strategy at the early screening stage can help reduce development risks and improve the success rate.However,exist...The development of fungicides is time-consuming and costly.Introducing a fungicide-likeness assessment strategy at the early screening stage can help reduce development risks and improve the success rate.However,existing assessment methods are often plagued by low accuracy and poor generalization,while fragment-based design strategies commonly fail to account for synergistic effects between structural units.Therefore,based on a small-scale sample set,this study developed a more efficient global predictive model for fungicidal activity—-named APPf—by integrating multi-scale feature screening methods and machine learning algorithms,which also accounts for synergistic effects among different structural fragments.We utilized three independent external test sets for model validation:External Test Set 1 for general validation,External Test Set 2 for comparison with existing models,and External Test Set 3 for disease-specific fungicide evaluation.On External Test Set 1,the APPf model achieved a precision of 0.6454,a recall of 0.8535,and an F1 score of 0.7350,demonstrating its robust predictive performance.It also exhibited strong enrichment capability for positive samples in External Test Set 2.For External Test Set 3,APPf achieved a prediction accuracy exceeding 80%for each disease,suggesting its promising potential in practical fungicide development.Furthermore,we quantified the contribution of molecular descriptors to the model predictions using SHAP value analysis and identified nHdNH and NssssNp as strong indicative features for predicting fungicidal activity,thereby enhancing the interpretability of the model.APPf has been deployed on a public web server(http://pesticides.cau.edu.cn/APPf),providing a user-friendly online prediction service to support the discovery of novel fungicides.Meanwhile,we employed a molecular fragmentation strategy to analyze the co-occurrence relationships between fragments in fungicides and constructed a network map of fragment co-occurrence associated with fungicidal activity.This study provides both an active fragment library and a global fungicide-likeness assessment tool for AI-based de novo molecular generation aimed at discovering novel fungicidal leads,which is expected to enhance the efficiency of developing new fungicides.展开更多
Understanding the fundamental drivers of large-scale species co-occurrence is a critical issue in ecology and conservation research. Here, we assessed foraging guilds, habitat type and disturbances as drivers of bird ...Understanding the fundamental drivers of large-scale species co-occurrence is a critical issue in ecology and conservation research. Here, we assessed foraging guilds, habitat type and disturbances as drivers of bird species co-occurrence in Ghana's Central Region over six months. Birds were sampled in 120 points across six different habitat types (farmland, forest reserve, urban area, coastal savannah, wetland, and mangrove), using the point-centred count technique. In total, 4060 individuals belonging to 216 species were recorded across all six habitat types. We found that co-occurring species were more similar in their foraging behaviour and habitat association. About 60% of the birds were found to co-occur randomly, 15% co-occurred negatively, and 25% co-occurred positively. Carnivores like the Black Heron (Egretta ardesiaca) and Spur-winged Lapwing (Vanellus spinosus) randomly co-occurred with other guild groups and were dominant in the mangroves and wetlands. Frugivores from forest reserves had only a 25% chance of randomly co-occurring with other birds and about a 60% chance of positively co-occurring with other birds. Our findings suggest that foraging guilds and habitat type are major factors driving bird co-occurrence and community assemblages in this West African suburban region.展开更多
We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigen...We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from au...The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.展开更多
Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and muc...Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and mucin was evaluated by tensiometry.Co polymer matrices containing mucin and PEG(PEGylated mucin) in the following ratios of 1:1(A),2:1(B),1:2(C), 0:1(D) and 1:0(E) were prepared by co-precipitation.Microparticles were prepared from the matrices using a size reduction technique.Five different samples were prepared using direct mixtures in the appropriate solvenfs having mucin and PEG ratios of 1:1,2:1,1:2,0:1, 1:0 and labeled as(A-E).The matrices were evaluated for their flow properties and the in vitro bioadhesion characteristics of the samples were examined.Results:The range of flow rates of the matrices was 1.35-2.23 g/sec.The angle of repose was in the range of 37.3-39.9 degree.The bulk and tapped densities were within the ranges of 0.41- 0.49.The Hausner’s quotient(HQ) were 1.12, 1.24,1.14,1.25 and 1.2 for matrix batches A-E respectively,The bioadhesive strength of polymer matrices appeared to be directly related to amount of mucin.The order of bioadhesive strength is 2:1】1:1】1:0】1:2】0:1 of PEG:mucin in both simulated intestine fluid(SEP) and simulated gastrointestinal fluid(SGF).The physical properties of the micrometrics properties of the matrices were within the accepted values.Conclusions:OBD preparation containing PEGylated mucin can be prepared by direct compression and be used in drug delivery to the oral cavity.展开更多
Let A ∈ B（X） and B ∈ B（Y）, Me be an operator on Banach space X ＋ Y given by Mc =（A C 0 B）A generalized Drazin spectrum defined by σgD（T） = {λ∈C ： T-λI is not generalized Drazin invertible} is considere...Let A ∈ B（X） and B ∈ B（Y）, Me be an operator on Banach space X ＋ Y given by Mc =（A C 0 B）A generalized Drazin spectrum defined by σgD（T） = {λ∈C ： T-λI is not generalized Drazin invertible} is considered in this paper. It is shown that展开更多
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hen...Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the lrobust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the lrobust null space property with high probability. Besides, we prove that Weibull random matrices also possess the lquotient property with high probability. Finally, with the combination of the above mentioned properties,we give two important approximation characteristics of the solutions to the l-minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e ∈ R~n needs a priori ‖e‖≤ε, the other is on the robustness estimate without needing to estimate the bound of ‖e‖. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.展开更多
This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is trans...This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.展开更多
This paper researches the following inverse eigenvalue problem for arrow-like matrices. Give two characteristic pairs, get a generalized arrow-like matrix, let the two characteristic pairs are the characteristic pairs...This paper researches the following inverse eigenvalue problem for arrow-like matrices. Give two characteristic pairs, get a generalized arrow-like matrix, let the two characteristic pairs are the characteristic pairs of this generalized arrow-like matrix. The expression and an algorithm of the solution of the problem is given, and a numerical example is provided.展开更多
文摘Purpose： To discuss the problems arising from hierarchical cluster analysis of co-occurrence matrices in SPSS, and the corresponding solutions. Design/methodology/approach： We design different methods of using the SPSS hierarchical clustering module for co-occurrence matrices in order to compare these methods. We offer the correct syntax to deactivate the similarity algorithm for clustering analysis within the hierarchical clustering module of SPSS. Findings： When one inputs co-occurrence matrices into the data editor of the SPSS hierarchical clustering module without deactivating the embedded similarity algorithm, the program calculates similarity twice, and thus distorts and overestimates the degree of similarity. Practical implications： We offer the correct syntax to block the similarity algorithm for clustering analysis in the SPSS hierarchical clustering module in the case of co-occurrence matrices. This syntax enables researchers to avoid obtaining incorrect results. Originality/value： This paper presents a method of editing syntax to prevent the default use of a similarity algorithm for SPSS＇s hierarchical clustering module. This will help researchers, especially those from China, to properly implement the co-occurrence matrix when using SPSS for hierarchical cluster analysis, in order to provide more scientific and rational results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.5147113 and 51505037)the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant Nos.3102017zy029,310832163402,and 310832163403)
文摘The mechanical properties of materials greatly depend on the microstructure morphology. The quantitative characterization of material microstructures is essential for the performance prediction and hence the material design. At present,the quantitative characterization methods mainly rely on the microstructure characterization of shape, size, distribution,and volume fraction, which related to the mechanical properties. These traditional methods have been applied for several decades and the subjectivity of human factors induces unavoidable errors. In this paper, we try to bypass the traditional operations and identify the relationship between the microstructures and the material properties by the texture of image itself directly. The statistical approach is based on gray level Co-occurrence matrix（GLCM）, allowing an objective and repeatable study on material microstructures. We first present how to identify GLCM with the optimal parameters, and then apply the method on three systems with different microstructures. The results show that GLCM can reveal the interface information and microstructures complexity with less human impact. Naturally, there is a good correlation between GLCM and the mechanical properties.
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金the National Key R&D Program of China(No.2022YFD1700200).
文摘The development of fungicides is time-consuming and costly.Introducing a fungicide-likeness assessment strategy at the early screening stage can help reduce development risks and improve the success rate.However,existing assessment methods are often plagued by low accuracy and poor generalization,while fragment-based design strategies commonly fail to account for synergistic effects between structural units.Therefore,based on a small-scale sample set,this study developed a more efficient global predictive model for fungicidal activity—-named APPf—by integrating multi-scale feature screening methods and machine learning algorithms,which also accounts for synergistic effects among different structural fragments.We utilized three independent external test sets for model validation:External Test Set 1 for general validation,External Test Set 2 for comparison with existing models,and External Test Set 3 for disease-specific fungicide evaluation.On External Test Set 1,the APPf model achieved a precision of 0.6454,a recall of 0.8535,and an F1 score of 0.7350,demonstrating its robust predictive performance.It also exhibited strong enrichment capability for positive samples in External Test Set 2.For External Test Set 3,APPf achieved a prediction accuracy exceeding 80%for each disease,suggesting its promising potential in practical fungicide development.Furthermore,we quantified the contribution of molecular descriptors to the model predictions using SHAP value analysis and identified nHdNH and NssssNp as strong indicative features for predicting fungicidal activity,thereby enhancing the interpretability of the model.APPf has been deployed on a public web server(http://pesticides.cau.edu.cn/APPf),providing a user-friendly online prediction service to support the discovery of novel fungicides.Meanwhile,we employed a molecular fragmentation strategy to analyze the co-occurrence relationships between fragments in fungicides and constructed a network map of fragment co-occurrence associated with fungicidal activity.This study provides both an active fragment library and a global fungicide-likeness assessment tool for AI-based de novo molecular generation aimed at discovering novel fungicidal leads,which is expected to enhance the efficiency of developing new fungicides.
文摘Understanding the fundamental drivers of large-scale species co-occurrence is a critical issue in ecology and conservation research. Here, we assessed foraging guilds, habitat type and disturbances as drivers of bird species co-occurrence in Ghana's Central Region over six months. Birds were sampled in 120 points across six different habitat types (farmland, forest reserve, urban area, coastal savannah, wetland, and mangrove), using the point-centred count technique. In total, 4060 individuals belonging to 216 species were recorded across all six habitat types. We found that co-occurring species were more similar in their foraging behaviour and habitat association. About 60% of the birds were found to co-occur randomly, 15% co-occurred negatively, and 25% co-occurred positively. Carnivores like the Black Heron (Egretta ardesiaca) and Spur-winged Lapwing (Vanellus spinosus) randomly co-occurred with other guild groups and were dominant in the mangroves and wetlands. Frugivores from forest reserves had only a 25% chance of randomly co-occurring with other birds and about a 60% chance of positively co-occurring with other birds. Our findings suggest that foraging guilds and habitat type are major factors driving bird co-occurrence and community assemblages in this West African suburban region.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11771046,12101186)Beijing Natural Science Foundation(Grant No.1254039).
文摘We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
基金Project(51478036)supported by the National Natural Science Foundation of ChinaProject(20120009110016)supported by Research Fund for Doctoral Program of Higher EducationChina
文摘The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.
文摘Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and mucin was evaluated by tensiometry.Co polymer matrices containing mucin and PEG(PEGylated mucin) in the following ratios of 1:1(A),2:1(B),1:2(C), 0:1(D) and 1:0(E) were prepared by co-precipitation.Microparticles were prepared from the matrices using a size reduction technique.Five different samples were prepared using direct mixtures in the appropriate solvenfs having mucin and PEG ratios of 1:1,2:1,1:2,0:1, 1:0 and labeled as(A-E).The matrices were evaluated for their flow properties and the in vitro bioadhesion characteristics of the samples were examined.Results:The range of flow rates of the matrices was 1.35-2.23 g/sec.The angle of repose was in the range of 37.3-39.9 degree.The bulk and tapped densities were within the ranges of 0.41- 0.49.The Hausner’s quotient(HQ) were 1.12, 1.24,1.14,1.25 and 1.2 for matrix batches A-E respectively,The bioadhesive strength of polymer matrices appeared to be directly related to amount of mucin.The order of bioadhesive strength is 2:1】1:1】1:0】1:2】0:1 of PEG:mucin in both simulated intestine fluid(SEP) and simulated gastrointestinal fluid(SGF).The physical properties of the micrometrics properties of the matrices were within the accepted values.Conclusions:OBD preparation containing PEGylated mucin can be prepared by direct compression and be used in drug delivery to the oral cavity.
基金Supported by the National Natural Science Foundation of China(11301077,1117131,11171066 and11226113)Foundation of the Education Department of Fujian Province(JA12074)the Natural ScienceFoundation of Fujian Province(2012J05003)
文摘Let A ∈ B（X） and B ∈ B（Y）, Me be an operator on Banach space X ＋ Y given by Mc =（A C 0 B）A generalized Drazin spectrum defined by σgD（T） = {λ∈C ： T-λI is not generalized Drazin invertible} is considered in this paper. It is shown that
基金This work was partially supported by the Natural Science Foundation of China （No. 611 74094） the Tianjin Natural Science Foundation of China （No. 13JCYBJC1 7400） the Program for New Century Excellent Talents in University of China （No. NCET-10-0506）.
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
基金Supported by the National Natural Science Foundation of China(11761003,11771347,91730306,41390454)the Natural Science Foundation of Ningxia(NZ17097)the Horizon 2020 project STEP2DYNA(691154)
文摘Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the lrobust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the lrobust null space property with high probability. Besides, we prove that Weibull random matrices also possess the lquotient property with high probability. Finally, with the combination of the above mentioned properties,we give two important approximation characteristics of the solutions to the l-minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e ∈ R~n needs a priori ‖e‖≤ε, the other is on the robustness estimate without needing to estimate the bound of ‖e‖. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.
文摘This paper researches the following inverse eigenvalue problem for arrow-like matrices. Give two characteristic pairs, get a generalized arrow-like matrix, let the two characteristic pairs are the characteristic pairs of this generalized arrow-like matrix. The expression and an algorithm of the solution of the problem is given, and a numerical example is provided.
