The CUNY Data Science and Applied Topology Reading Group is joint between the Mathematics and Computer Science programmes. We meet Fridays 11.45 -- 12.45 in GC 3209. You can contact us at cunygc@appliedtopology.nyc.

Our plan is to primarily read and discuss seminal papers in data science, in applied topology and in topological data analysis. Each seminar one participant takes the responsibility to present a paper and prepare items for discussion. We expect occasionally to be able to invite external speakers.

## Schedule

Current schedule can be found here.

We will be sending out announcements through a mailing list; you can subscribe here.

## Organizers

- Mikael Vejdemo-Johansson, Computer Science Programme, CUNY Graduate Center; Department of Mathematics, CUNY College of Staten Island
- Azita Mayeli, Mathematics Programme, CUNY Graduate Center; Department of Mathematics, CUNY Queensborough Community College

## Suggested papers

We have compiled a list of papers that might be interesting to present.

# Schedule

### Functional Data Analysis Using a Topological Summary Statistic: The Smooth Euler Characteristic Transform

We introduce a novel statistic, the smooth Euler characteristic transform (SECT), which is designed to integrate shape information into regression models by representing shapes and surfaces as a collection of curves. Its construction is based on theory from topological data analysis (TDA). Due to its well-defined inner product structure, the SECT can be used in a wider range of functional and nonparametric modeling approaches than other previously proposed topological summary statistics. We provide mathematical properties of this statistic, notably, its injectivity, which is an implication for statistical sufficiency.

We illustrate the utility of the SECT in a radiomics context by showing that the topological quantification of tumors, assayed by magnetic resonance imaging (MRI), are better predictors of clinical outcomes in patients with glioblastoma multiforme (GBM). We show that topological features of tumors captured by the SECT alone explain more of the variance in patient survival than gene expression, volumetric features, and morphometric features.