Geometry

May 1, 2024

Nov 1, 2023

Mar 1, 2023

The Geometry of Creativity - Understanding Generative Models in Brains and Machines

Feb 17, 2023

Dec 1, 2022

Oct 1, 2022

Motivation When you think about random walks, what shape do you think about? Is it like this? Or this? These are good examples of random walks in two or three dimensions. But what about random walks in higher dimensions?

Jan 22, 2022

Stability Theory When a system has control, then comes the questions of whether we could make it stable under the control. Problem Setup A control affine system is this $$ \dot x =f(x)+\sum_i g_i(x)\bar u_i=f(x)+g(x)\bar u $$Interpretation:

May 10, 2021

Basic Notions Def Topological Equivalence: 2 dynamic systems are topological equivalence when there is a homeomorphism between their solutions. Def Conjugate: Two maps are connected by $$g=h^{-1}\circ f \circ h$$.

May 9, 2021

Bifurcation Normal Form Invariance and Stable Manifold Lyapnov Stability Theory Feedback Stablization

Apr 9, 2021