SimPers: Software for Topological Persistence under Simplicial Maps. SimPers software can be used in the following case: Given a sequence of simplicial maps f1, f2,...fn between an initial simplicial complex K and a resulting simplicial complex L, the Simpers uses the annotation-based method developed in the paper below to compute the persistence of the sequence of simplicial maps, that is the ranks of image H(K)--f1--f2--...--fn--> H(L) in all dimensions. For more details, see the paper: T. K. Dey, F. Fan and Y. Wang. Computing Topological Persistence for Simplicial Maps 30th Annu. Sympos. Comput. Geom. SoCG 2014. There are two modes for the software, elementary mode: input simplicial maps are given by elementary operations (insertion or collapse), and general mode: input simplicial maps are given by vertex maps. It is suggested to use the elementary mode in most cases since usually users build the sequence of simplicial maps incrementally, namely, compute the elementary insertions and collapses that constitute each simplicial map. Also Simpers runs faster in elementary mode because of the incremental processing. However, there are situations where users can only compute the vertex maps which induce the simplicial maps rather than the elementary operations. For these applications, we offer the general mode. This mode is not incremental and involves recomputation for each simplicial map, thus it is usually slower than elementary mode.

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  1. Alan Hylton, Gregory Henselman-Petrusek, Janche Sang, Robert Short: Tuning the Performance of a Computational Persistent Homology Package (2018) arXiv