When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
目的观察卵巢-附件报告和数据系统超声2022版(O-RADS US v2022)及其联合恶性风险指数4(RMI4)鉴别附件良、恶性肿瘤的价值。方法回顾性分析126例手术病理诊断为附件肿瘤患者,根据O-RADS US v2022将1~3类归为良性病变、4~5类归为恶性病变,...目的观察卵巢-附件报告和数据系统超声2022版(O-RADS US v2022)及其联合恶性风险指数4(RMI4)鉴别附件良、恶性肿瘤的价值。方法回顾性分析126例手术病理诊断为附件肿瘤患者,根据O-RADS US v2022将1~3类归为良性病变、4~5类归为恶性病变,以450为RMI4分类的临界值,基于二者进行联合分类。以病理结果为金标准,绘制受试者工作特征(ROC)曲线,计算曲线下面积(AUC),评估单一O-RADS US v2022、RMI4及其联合鉴别附件良、恶性肿瘤的效能。结果126例附件肿瘤中,良性94例、恶性32例。O-RADS US v2022鉴别附件良、恶性肿瘤的敏感度、特异度、准确率及AUC分别为78.13%、80.85%和80.16%、0.795,RMI4分别为71.88%、84.04%和80.95%、0.780;二者联合的特异度及准确率(93.62%、92.06%)均高于单一O-RADS US v2022(χ^(2)=7.322、5.967,P=0.007、0.015)或RMI4(χ^(2)=4.625、5.331,P=0.032、0.021),而敏感度及AUC(87.50%、0.906)差异均无统计学意义(P均>0.05)。结论O-RADS US v2022能有效鉴别附件良、恶性肿瘤,联合RMI4可提高鉴别特异度及准确率。展开更多
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
文摘目的观察卵巢-附件报告和数据系统超声2022版(O-RADS US v2022)及其联合恶性风险指数4(RMI4)鉴别附件良、恶性肿瘤的价值。方法回顾性分析126例手术病理诊断为附件肿瘤患者,根据O-RADS US v2022将1~3类归为良性病变、4~5类归为恶性病变,以450为RMI4分类的临界值,基于二者进行联合分类。以病理结果为金标准,绘制受试者工作特征(ROC)曲线,计算曲线下面积(AUC),评估单一O-RADS US v2022、RMI4及其联合鉴别附件良、恶性肿瘤的效能。结果126例附件肿瘤中,良性94例、恶性32例。O-RADS US v2022鉴别附件良、恶性肿瘤的敏感度、特异度、准确率及AUC分别为78.13%、80.85%和80.16%、0.795,RMI4分别为71.88%、84.04%和80.95%、0.780;二者联合的特异度及准确率(93.62%、92.06%)均高于单一O-RADS US v2022(χ^(2)=7.322、5.967,P=0.007、0.015)或RMI4(χ^(2)=4.625、5.331,P=0.032、0.021),而敏感度及AUC(87.50%、0.906)差异均无统计学意义(P均>0.05)。结论O-RADS US v2022能有效鉴别附件良、恶性肿瘤,联合RMI4可提高鉴别特异度及准确率。
