Question
Answer the following about persistent homology, a subdiscipline of topological data analysis. For 10 points each:
[10h] In a data cloud, persistent homology forms these structures named for Vietoris and Rips under specific conditions. A 2-dimensional one of these structures is a set of points, lines, and triangles.
ANSWER: simplicial complexes [prompt on delta complexes; prompt on CW complexes; prompt on simplex or simplices by asking “simplices are part of what type of set?]
[10e] One way to visualize the expansion of the Vietoris-Rips complex is by imagining a circle with an increasing value for this parameter. This quantity is cubed and multiplied by 4/3π (“four-thirds pi”) to get the volume of a sphere.
ANSWER: radius [accept r]
[10m] Homology groups are calculated by taking images and these subspaces of the boundary functions. For a function, this is the set of inputs that map to the zero vector.
ANSWER: kernel [accept null space]
<Ezra Santos, Other Science>
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