會議時間：2022年12月21日（周三）19:00—21:00

會議地點：騰訊會議488-327-722

會議簡介：

報告1：微分方程中的KAM理論

報告人：邱汶華

報告時間：19:00-20:00

內容簡介：上世紀五、六十年代，由三位著名數學家 Kolmogorov，Arnold 和 Moser 建立起來的經典KAM理論是哈密頓系統理論發展的里程碑。在微分方程的攝動理論研究中，以 KAM 為工具來研究系統的可約化性是一個十分活躍的領域。約化問題是微分方程領域的一個重要組成部分，特別是對方程解的形式及結構的研究具有重要的意義。本次論壇將著重介紹擬周期領域和概周期領域的相關進展。

報告2：Conditional Characteristic Feature Screening for Massive Imbalanced Data

報告人：王平

報告時間：20:00-21:00

內容簡介：Using conditional characteristic function as a screening index, a new modelfree screening procedure is proposed to deal with variable screening problems in large-scale high-dimensional imbalanced data analysis. For binary response, our results show that the screening index under full data is proportional to the screening index under case-control sampling, an important sampling property for imbalanced data. This conclusion implies that we can apply this screening method to imbalanced data. Surely, the most appealing feature of the screening index is that it can be expressed as a simple linear combination of two first-order moments, so it is computationally simple. In addition, we successfully extend this method to multiple response. The theoretical properties are established under regularity conditions. To compare the performance of our method with its competitors,extensive simulations are conducted, which shows that the proposed procedure performs well in both the linear and nonlinear models. Finally, a real data analysis is investigated to further illustrate the effectiveness of the new method.

數學與統計學院

2022年12月19日