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## Persistence Diagrams as Change Action Derivatives

### Deni Salja

#### Dalhousie , Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak8d776d3e82fe02bcb54cf327e19a47bb').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy8d776d3e82fe02bcb54cf327e19a47bb = 'dn746393' + '&#64;'; addy8d776d3e82fe02bcb54cf327e19a47bb = addy8d776d3e82fe02bcb54cf327e19a47bb + 'd&#97;l' + '&#46;' + 'c&#97;'; var addy_text8d776d3e82fe02bcb54cf327e19a47bb = 'dn746393' + '&#64;' + 'd&#97;l' + '&#46;' + 'c&#97;';document.getElementById('cloak8d776d3e82fe02bcb54cf327e19a47bb').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy8d776d3e82fe02bcb54cf327e19a47bb + '\'>'+addy_text8d776d3e82fe02bcb54cf327e19a47bb+'<\/a>';

In 2019 McCleary and Patel proposed a generalization of a persistence diagram for a multi-parameter filtration' of chain complexes of an abelian category as the Möbius inversion of the rank function of the associated birth-death-(sub)object.' At the 2019 CMS winter meeting Patel spoke at the TDA session about this work and mentioned how he thought of Möbius inversion as a derivative. This poster shows how to (extend and then) view a certain quotient object in their work as a change-action derivative in the sense of Alvarez-Picallo and Lemay.

Joint work with Dr. Kristine Bauer (University of Calgary).