By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of ...By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.展开更多
Geological disasters not only cause economic losses and ecological destruction, but also seriously threaten human survival. Selecting an appropriate method to evaluate susceptibility to geological disasters is an impo...Geological disasters not only cause economic losses and ecological destruction, but also seriously threaten human survival. Selecting an appropriate method to evaluate susceptibility to geological disasters is an important part of geological disaster research. The aims of this study are to explore the accuracy and reliability of multi-regression methods for geological disaster susceptibility evaluation, including Logistic Regression(LR), Spatial Autoregression(SAR), Geographical Weighted Regression(GWR), and Support Vector Regression(SVR), all of which have been widely discussed in the literature. In this study, we selected Yunnan Province of China as the research site and collected data on typical geological disaster events and the associated hazards that occurred within the study area to construct a corresponding index system for geological disaster assessment. Four methods were used to model and evaluate geological disaster susceptibility. The predictive capabilities of the methods were verified using the receiver operating characteristic(ROC) curve and the success rate curve. Lastly, spatial accuracy validation was introduced to improve the results of the evaluation, which was demonstrated by the spatial receiver operating characteristic(SROC) curve and the spatial success rate(SSR) curve. The results suggest that: 1) these methods are all valid with respect to the SROC and SSR curves, and the spatial accuracy validation method improved their modelling results and accuracy, such that the area under the curve(AUC) values of the ROC curves increased by about 3%–13% and the AUC of the success rate curve values increased by 15%–20%; 2) the evaluation accuracies of LR, SAR, GWR, and SVR were 0.8325, 0.8393, 0.8370 and 0.8539, which proved the four statistical regression methods all have good evaluation capability for geological disaster susceptibility evaluation and the evaluation results of SVR are more reasonable than others; 3) according to the evaluation results of SVR, the central-southern Yunnan Province are the highest sus-ceptibility areas and the lowest susceptibility is mainly located in the central and northern parts of the study area.展开更多
基金supported by the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.
基金National Natural Science Foundation of China,No.41571077,No.41171318The Fundamental Research Funds for the Central Universities
文摘Geological disasters not only cause economic losses and ecological destruction, but also seriously threaten human survival. Selecting an appropriate method to evaluate susceptibility to geological disasters is an important part of geological disaster research. The aims of this study are to explore the accuracy and reliability of multi-regression methods for geological disaster susceptibility evaluation, including Logistic Regression(LR), Spatial Autoregression(SAR), Geographical Weighted Regression(GWR), and Support Vector Regression(SVR), all of which have been widely discussed in the literature. In this study, we selected Yunnan Province of China as the research site and collected data on typical geological disaster events and the associated hazards that occurred within the study area to construct a corresponding index system for geological disaster assessment. Four methods were used to model and evaluate geological disaster susceptibility. The predictive capabilities of the methods were verified using the receiver operating characteristic(ROC) curve and the success rate curve. Lastly, spatial accuracy validation was introduced to improve the results of the evaluation, which was demonstrated by the spatial receiver operating characteristic(SROC) curve and the spatial success rate(SSR) curve. The results suggest that: 1) these methods are all valid with respect to the SROC and SSR curves, and the spatial accuracy validation method improved their modelling results and accuracy, such that the area under the curve(AUC) values of the ROC curves increased by about 3%–13% and the AUC of the success rate curve values increased by 15%–20%; 2) the evaluation accuracies of LR, SAR, GWR, and SVR were 0.8325, 0.8393, 0.8370 and 0.8539, which proved the four statistical regression methods all have good evaluation capability for geological disaster susceptibility evaluation and the evaluation results of SVR are more reasonable than others; 3) according to the evaluation results of SVR, the central-southern Yunnan Province are the highest sus-ceptibility areas and the lowest susceptibility is mainly located in the central and northern parts of the study area.
