Re: Picking Generators of Homology
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The particular cycle that you picked appears and dies at 2.14463 -- it's a 0-persistence cycle. In general, the cycle appears at the highest value of its 1-simplices and dies at the value of the 2-simplex with which it is associated.
I hope it helps.
On Tue, Sep 4, 2018 at 12:30 PM, <nukpezah@...>
I apologize for the insistent bother. I finally got to applying this to my protein cloud problem. I changed the code slightly to express the elements of the cycle as a list of tuples with each tuple comprising the coefficient and the actual simplex with its radius using the Vietoris-Rips filtration. The lists typically look like this;
<93,96,108> 2.14463:[(1, <96,108> 1.07808), (1, <93,96> 1.53489), (1, <93,108> 2.14463)]. ( I observed that the code stores the cycle represented by the list in the filtration at the point where the two-simplex <93,96,108> 2.14463 appears)
I understand from the code that this is a cycle which appears in the filtration when the one-simplex <93,108> 2.14463 appears. My question is that I am unable to connect these cycles to the H1 persistence barcodes which I show below (my cutoff distance in the rips filtration is 6 and the skeleton dimension is 3)
For the cycle above, how can I tell where it appears and where it dies. Does it appear at distance 2.14463? Thanks
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