Applied topology 14: Cech and Vietoris-Rips simplicial complexes

[@DavidConnerCodeaholic]

Thanks for clearing this up. This was so much simpler & clearer than reading the Greek … which will now make more sense. As for the Cech complex, assuming a Euclidean space, can’t you use the Vietoris-Rips as a starting point to search for at least one point that satisfies the condition for a simplex in the cech complex? IE: place normal vectors on each edge or triangular plane oriented towards the “center” of the potential simplex, then start searching the space between by adding a point to the simple and calculating the distance to other vertices in the same simplex. This itself is like a geometric realization of the nerve… whether it works or not it does give me some intuition into the nerve.

[@aatrn1]

That's a great point - the connection between the Vietoris-Rips and Cech complexes is definitely worth exploring!

[@muskduh]

appreciate the free video content

[@HenryAdamsMath]

You are welcome!

[@renormalization]

Beautiful visualization, thanks!

[@aatrn1]

Glad you liked it!

[@omererylmaz3619]

Thank you so much for the insightful video! I'm currently exploring Vietoris-Rips complexes in the context of 3D data. Do you have any recommendations for visualizing these complexes in 3D point cloud data? I want to use my own data to visualize the complexes. Any guidance would be greatly appreciated!

[@chetansingh5439]

sir, which software can I use for visualizing cech complex and topological data analysis?

[@HenryAdamsMath]

For the software demo used in the above video, see section VI on "Mathematica demonstrations" at www.math.colostate.edu/~adams/research/. For a longer list of applied topology software packages, see for example www.math.colostate.edu/~adams/advising/appliedTopologySoftware/.

[@chetansingh5439]

Thanks

[@luislutchoo3396]

thanks

[@HenryAdamsMath]

You're welcome!

[@evrenboyabatl4907]

Hi, can you share this app please?

[@aatrn1]

See Section VII at www.math.colostate.edu/~adams/research/ --- that might be what you are looking for.

[@evrenboyabatl4907]

@@aatrn1 Thank you very much, very important for my licence graduation.