4 papers
Learning non-equilibrium diffusions with Schrödinger bridges: from exactly solvable to simulation-free
Stephen Y. Zhang, Michael P H Stumpf
We consider the Schrödinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on…
Topological Optimal Transport for Geometric Cycle Matching
Stephen Y Zhang, Michael P H Stumpf, Tom Needham +1
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant t…
Towards a mathematical framework for modelling cell fate dynamics
Sean T. Vittadello, Léo Diaz, Yujing Liu +2
An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their…
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework
Stephen Y Zhang, Fangfei Lan, Youjia Zhou +4
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however,…