Given a finite point set X, one constructs the Cech complex at scale r by taking the nerve of the subset covered by r- balls centered at the points of X. Given a direction vector u and a scale 0 < c < 1, we construct a cover by ellipsoids with major axis parallel to u and length r. The normal directions to u have length cr. We then compute the homology of the complex obtained as the nerve of this cover. This additional structure defines a generalized persistence module, yields a correspondence between rotations and interleavings of persistence modules and suggests an approach to detect directed homological features using maximum persistent length. This is joint work with Dr. Greg Bell from UNC Greensboro.

### Applied Topology Seminar

Monday, September 15, 2014 - 2:00pm

#### Thanos Gentimis

North Carolina State University