For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are ...For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.展开更多
In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure i...In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.展开更多
Objective For computer-aided Chinese medical diagnosis and aiming at the problem of insufficient segmentation,a novel multi-level method based on the multi-scale fusion residual neural network(MF2ResU-Net)model is pro...Objective For computer-aided Chinese medical diagnosis and aiming at the problem of insufficient segmentation,a novel multi-level method based on the multi-scale fusion residual neural network(MF2ResU-Net)model is proposed.Methods To obtain refined features of retinal blood vessels,three cascade connected UNet networks are employed.To deal with the problem of difference between the parts of encoder and decoder,in MF2ResU-Net,shortcut connections are used to combine the encoder and decoder layers in the blocks.To refine the feature of segmentation,atrous spatial pyramid pooling(ASPP)is embedded to achieve multi-scale features for the final segmentation networks.Results The MF2ResU-Net was superior to the existing methods on the criteria of sensitivity(Sen),specificity(Spe),accuracy(ACC),and area under curve(AUC),the values of which are 0.8013 and 0.8102,0.9842 and 0.9809,0.9700 and 0.9776,and 0.9797 and 0.9837,respectively for DRIVE and CHASE DB1.The results of experiments demonstrated the effectiveness and robustness of the model in the segmentation of complex curvature and small blood vessels.Conclusion Based on residual connections and multi-feature fusion,the proposed method can obtain accurate segmentation of retinal blood vessels by refining the segmentation features,which can provide another diagnosis method for computer-aided Chinese medical diagnosis.展开更多
基金Supported by the Natural Science Foundation of Henan(004051900)
文摘For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.
基金Supported by the National Natural Science Foundation of China(No.61173052)the Natural Science Foundation of Hunan Province(No.14JJ4007)
文摘In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.
基金Key R&D Projects in Hebei Province(22370301D)Scientific Research Foundation of Hebei University for Distinguished Young Scholars(521100221081)Scientific Research Foundation of Colleges and Universities in Hebei Province(QN2022107)。
文摘Objective For computer-aided Chinese medical diagnosis and aiming at the problem of insufficient segmentation,a novel multi-level method based on the multi-scale fusion residual neural network(MF2ResU-Net)model is proposed.Methods To obtain refined features of retinal blood vessels,three cascade connected UNet networks are employed.To deal with the problem of difference between the parts of encoder and decoder,in MF2ResU-Net,shortcut connections are used to combine the encoder and decoder layers in the blocks.To refine the feature of segmentation,atrous spatial pyramid pooling(ASPP)is embedded to achieve multi-scale features for the final segmentation networks.Results The MF2ResU-Net was superior to the existing methods on the criteria of sensitivity(Sen),specificity(Spe),accuracy(ACC),and area under curve(AUC),the values of which are 0.8013 and 0.8102,0.9842 and 0.9809,0.9700 and 0.9776,and 0.9797 and 0.9837,respectively for DRIVE and CHASE DB1.The results of experiments demonstrated the effectiveness and robustness of the model in the segmentation of complex curvature and small blood vessels.Conclusion Based on residual connections and multi-feature fusion,the proposed method can obtain accurate segmentation of retinal blood vessels by refining the segmentation features,which can provide another diagnosis method for computer-aided Chinese medical diagnosis.
