BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Omer Eryilmaz (University of Birmingham) DTSTART:20260316T113000Z DTEND:20260316T133000Z DTSTAMP:20260423T024549Z UID:BNAT/18 DESCRIPTION:Title: Fl ow-Aware Ellipsoidal Filtration for Persistent Homology of Recurrent Signa ls\nby Omer Eryilmaz (University of Birmingham) as part of Basic Notio ns and Applied Topology Seminar\n\nLecture held in Room 1 at the IMPAS\, R oom 1.14 at the Institute of Informatics (University of Gdańsk).\n\nAbstr act\nRecurrent signals give rise to trajectories that repeatedly return cl ose to earlier states in state space. Analysing such data therefore requir es a principled notion of similarity between states. In practice\, this de pends on how local neighbourhoods are defined and scaled. These neighbourh oods are also important for topology-preserving denoising in state space\, where the aim is to reduce noise without distorting the underlying trajec tory structure. This talk introduces a flow-aware ellipsoidal filtration f or persistent homology based on a spatio-temporal covariance construction that estimates local flow geometry from both temporal and spatial neighbou rs. Unlike isotropic constructions based on balls\, such as the Vietoris-- Rips filtration\, the proposed method assigns an ellipsoid to each point\, with orientation and axis lengths determined by local flow variances. Whe n a dominant $H_1$ feature captures the main recurrent loop structure\, it s persistence interval can be used as a data-driven scale selection rule. Experiments on synthetic and real signals suggest that flow-aware ellipsoi dal neighbourhoods can improve topology-preserving denoising and first-rec urrence-time estimation compared with the Vietoris--Rips filtration. More broadly\, the results illustrate how incorporating anisotropy into persist ent homology can provide a more informative description of recurrent dynam ical systems.\n LOCATION:https://researchseminars.org/talk/BNAT/18/ END:VEVENT END:VCALENDAR