Thu, 10 Mar 2022
14:00 - 15:00
Lisa Maria Kreusser
University of Bath

The recent, rapid advances in modern biology and data science have opened up a whole range of challenging mathematical problems. In this talk I will discuss a class of interacting particle models with anisotropic repulsive-attractive interaction forces. These models are motivated by the simulation of fingerprint databases, which are required in forensic science and biometric applications. In existing models, the forces are isotropic and particle models lead to non-local aggregation PDEs with radially symmetric potentials. The central novelty in the models I consider is an anisotropy induced by an underlying tensor field. This innovation does not only lead to the ability to describe real-world phenomena more accurately, but also renders their analysis significantly harder compared to their isotropic counterparts. I will discuss the role of anisotropic interaction in these models, present a stability analysis of line patterns, and show numerical results for the simulation of fingerprints. I will also outline how very similar models can be used in data classification, where it is desirable to assign labels to points in a point cloud, given that a certain number of points is already correctly labeled.

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