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For example, soap bubbles:                   Image from UPenn: "A 2-dimensional foam of wet soap bubbles squashed between glass plates, after 10 hours ...

Currently I am working on applications of Bourgain Embedding (or similar embeddings of finite metric spaces to $l_2$) to automatic feature engineering for machine learning/data science ( http://www....

I am working on an optical character recognition algorithm that takes vector data (i.e. polylines) as input rather than raster picture. E.g., we have N polyline samples, and when certain polyline is ...

One of the beneficial properties of persistent homology is its stability results (so called robustness to noise). Usually the referenced paper is this paper titled "Lipschitz functions have $L_p$-...

This is the update version of this question A functional inequality which calculates the limitation of human eyes Let an Euclidean space $M$ (or a path connected metric space) be partitioned into ...

I know that dandelin spheres can be used to prove the focal properties of conic sections, but I heard that they can be used to help track the orbits of planets. All the sources I looked up only said ...