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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 11th 2020

    added this pointer:

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2020
    • (edited Oct 2nd 2020)

    added pointer to today’s

    diff, v9, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2022

    I have taken the liberty of re-writing the Idea-section from scratch.

    have also included a graphics meant to indicate the role of cycles and dually of cocycles

    have not yet included the kind of graphics that most intros to TDA are showing (essentially a stage in a Vietoris-Rips complex) Maybe later.

    diff, v15, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2022
    • (edited May 23rd 2022)

    I have expanded a little more, now there are two Idea-subsections:

    In the one on persistent homology/homotopy (here) I have highlighted that the implication of persistent cycles for actually interpreting data in practice is often unclear (and certainly not provided by the mathematics).

    In the next one on persistent cohomotopy (now here) I have made explicit that persistent Cohomotopy provides the answer to a concrete and common question about data sets.

    diff, v16, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2022

    have now produced (here) an animated gif which illustrates persistency of cycles.

    (Maybe the frame rate is somewhat too high? )

    diff, v18, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 24th 2022

    now uploaded an animated gif (here) which is meant to illustrate the idea of persistent cohomotopy

    diff, v19, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 9th 2022

    Under “Applications” I have added pointer to today’s

    • Daniel Spitz, Julian M. Urban, Jan M. Pawlowski, Confinement in non-Abelian lattice gauge theory via persistent homology [arXiv:2208.03955]

    using TDA for the recognition of instantons and confinement in lattice gauge theory. This looks interesting.

    diff, v26, current

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