簡介／

講題：On the Dynamics of the Maximin Flow

本次演講將深入探討動態系統中的 Maximin Flow。

我們將關注複雜系統中 saddle points 的角色和影響 ( saddle points 通常象徵系統中的轉變點)，我們將介紹一種動態系統方法，能夠準確找到 saddle points 的位置，並展示其周圍的動態行為。

此外，我們還會討論 Maximin Flow 在解析向量場中的應用，以及它如何解析複雜系統的轉變。

讓我們一同揭示複雜系統中轉變的神秘面紗，探索科學背後的精彩世界

【Abstract】
In a complex system, such as the molecular dynamics, chemical kinetics, nucleation mechanism, or even the Lagrangian of a constrained convex programming problem, the presence of a saddle point often represents that a transition of events has occurred. Determining the locations of saddle points in the con guration space and the way they a ect the transition provide critical information about the underlying complex system. This paper proposes a dynamical system approach to explore this problem. In addition to being capable of nding saddle points, the ow exhibits some intriguing behavior nearby a saddle point, which is demonstrated by graphic examples in various settings. Maximin ows also arise naturally from complex-valued di erential equations over analytic vector elds due to the Cauchy-Riemann equations. The maximin ow can be cast as a gradient ow in the Kre in space under inde nite inner product, whence the Lojasiewicz gradient inequality can be generalized. It is proved that a solution trajectory has nite arc length and, hence, converges to a singleton saddle point.

<<本活動報名確認者提供餐點>>
<<本場次為中文演講>>

報名資訊／