The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network. This p...The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network. This paper applies functional network to approximate the multidimension function under the ridgelet theory. The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.展开更多
Based on the density functional theory,we described here a method to investigate the quantitative relationship between nucleophilicity/basicity and HSAB-theory-based properties of compounds with lone-pair electrons.De...Based on the density functional theory,we described here a method to investigate the quantitative relationship between nucleophilicity/basicity and HSAB-theory-based properties of compounds with lone-pair electrons.Descriptors including global softness,Fukui function,local softness and local mulliken charge were calculated at SVWN/DN~* level of DFT with PC Spartan Pro.Nucleophilicity and basicity of 28 selected compounds were classified based on intensity.BP algorithm of artificial neural network(ANN) was employed to study the relationship between the descriptors and nucleophilicity/basicity.Cross-validation was carried out to avoid the over-fitting in training of ANN.A BP network was trained to quantify the relationship between HSAB-theory-based properties and nucleophilicity/basicity of compounds with lone-pair electrons.The results show that the prediction based on the network matches with the experimental results well.The local softness and Fukui function have a better relationship with nucleophilicity and local mulliken charge than with the basicity.The trained BP network could be utilized for predicting the nucleophilicity/basicity of compounds or functional groups with lone-pair electrons.展开更多
In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the sta...In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the states starting from the origin by inputs with peak values.The maximal Lyapunov functional is proposed to derive a sufficient condition for the existence of a non-ellipsoidal bound to estimate the states of neural networks.It is theoretically shown that this method is superior to the traditional one based on the common Lyapunov function.Finally,two examples illustrate the advantages of our proposed result.展开更多
基金Partly supported by the National Natura Science Foundation of China(No.60133010)the Natura Science Foundation of Education Department of Shaanxi Province(No.05JK312)the Natura Science Foundation of Xianyang Normal University(No.04XSYK101)
文摘The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network. This paper applies functional network to approximate the multidimension function under the ridgelet theory. The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.
基金National Science & Technology Major Project of China(Grant No.2009ZX09501-002)National Natural Science Foundation of China(Grant No.20802006).
文摘Based on the density functional theory,we described here a method to investigate the quantitative relationship between nucleophilicity/basicity and HSAB-theory-based properties of compounds with lone-pair electrons.Descriptors including global softness,Fukui function,local softness and local mulliken charge were calculated at SVWN/DN~* level of DFT with PC Spartan Pro.Nucleophilicity and basicity of 28 selected compounds were classified based on intensity.BP algorithm of artificial neural network(ANN) was employed to study the relationship between the descriptors and nucleophilicity/basicity.Cross-validation was carried out to avoid the over-fitting in training of ANN.A BP network was trained to quantify the relationship between HSAB-theory-based properties and nucleophilicity/basicity of compounds with lone-pair electrons.The results show that the prediction based on the network matches with the experimental results well.The local softness and Fukui function have a better relationship with nucleophilicity and local mulliken charge than with the basicity.The trained BP network could be utilized for predicting the nucleophilicity/basicity of compounds or functional groups with lone-pair electrons.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60774039,60974024,61074089,61174129Program for New Century Excellent Talents in University under Grant No.NCET-11-0379the Independent Innovation Foundation of Tianjin University
文摘In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the states starting from the origin by inputs with peak values.The maximal Lyapunov functional is proposed to derive a sufficient condition for the existence of a non-ellipsoidal bound to estimate the states of neural networks.It is theoretically shown that this method is superior to the traditional one based on the common Lyapunov function.Finally,two examples illustrate the advantages of our proposed result.
