Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Title: Estimation of one-dimensional structures in data

Abstract:  Given a data distribution which is concentrated around a one-dimensional structure, can we infer that structure? We consider versions of this problem where the 1d structure is assumed to either be the range of a curve, or a connected set of finite total length. In each of these cases, we relate the inference task to solving a variational problem where there is a tradeoff between data fidelity and simplicity of the inferred structure; the variational problems we consider are closely related to the so-called "principal curve" problem of Hastie and Stuetzle (1989) as well as the "average-distance problem" of Buttazzo, Oudet, and Stepanov (2002). For each of the variational problems under consideration, we establish existence of minimizers, stability with respect to the data distribution, and consistency of a discretization scheme which is amenable to EM-type numerical methods.

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Main speakers:

Patrick Kennedy-Hunt
Mattia Talpo

Title: Brownian motion in curved spaces

Abstract: If you randomly walk around on a plane, you will eventually return to your starting point. If you randomly fly around in three-dimensional vector space, you never return to your starting point. Why is that? What if we randomly walk around in curved spaces instead, does the dimension matter? What about the curvature? In this talk I hope to give a clue of the answers to these questions and motivate these answers further with simulations.

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!