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arXiv · 2308.11314

A Study of Particle Motion in the Presence of Clusters

Christian Wald·Gabriele Steidl
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Abstract

The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data.

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Christian Wald, Gabriele Steidl. 2023-08-22. A Study of Particle Motion in the Presence of Clusters. https://arxiv.org/abs/2308.11314

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