BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Dranishnikov (University of Florida) DTSTART:20240110T150000Z DTEND:20240110T160000Z DTSTAMP:20260423T022829Z UID:GEOTOP-A/76 DESCRIPTION:Title: On some variations of TC and the LS-category\nby Alexander Dranishni kov (University of Florida) as part of GEOTOP-A seminar\n\n\nAbstract\nDat asets can be viewed as mathematical objects (e.g.\, point clouds\, matrice s\, graphs\, images\, fields/functions) that have shape. This shape can de scribe the space that data populates (e.g.\, data that lies on a manifold) or can be used to understand the complex structures contained within data (e.g.\, the multi-scale organization of self-assembled materials). Data s hape can be exploited to improve the effectiveness of data analysis method s or provide connections between complex materials and their physical and chemical properties. However\, quantifying shape is difficult to do with c ommon methods based on statistics\, signal processing\, or with the use of machine learning. Topology and geometry are fields of mathematics that p rovide tools for the characterization and quantification of the shape of d ata directly.\n\nIn this talk I will discuss how data taken from industria l processes\, such as time series and images\, can be represented as a sha pe and how that shape can be analyzed through topological and geometrical methods such as the Euler characteristic (EC) and Riemannian manifold geom etry. I will provide a brief overview of these methods and illustrate how exploiting the topology and geometry of data can provide improvements in d ata-centric tasks such as dimensionality reduction\, anomaly detection\, a nd statistical process control in the context of textile production\, chem ical process systems\, and granular material manufacturing.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/76/ END:VEVENT END:VCALENDAR