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Mathematics

Topological Data Analysis with Persistent Homology

Quick fact

Persistent homology can detect the presence of a circle in a point cloud even when the data is contaminated with noise, by counting how long a loop survives across different connection scales.

Why this is interesting

If you looked at a cloud of points, could you tell if they form a circle or just a random blob? Turns out, noise can fool our eyes—but mathematics has a way to see through it.