"A symphony must be like the world. It must embrace everything."
Probably the most famous quote attributed to Gustav Mahler and when you listen to some of his works it feels like he is changing direction every few notes with the vicissitudes of life. But amid the turmoil he wrote some of the most beautiful romantic music you'll hear. Here Juanjo Mena conducts the BBC Philharmonic.
Big Green Lunch, Friday 13 June
Roast Cauliflower & Chickpea Korma (v) and Vegan Keema (ve). Served with pilau rice, vegetable samosa, garlic & coriander naan, and raita - all for only £5.95. Bring your own container and get 20p off your meal.
Image: Joachim Beuckelaer (possibly) - The Vegetable Seller
13:00
Topologically good cover from gradient descent
Note: we would recommend to join the meeting using the Teams client for best user experience.
Abstract
The cover of a dataset is a fundamental concept in computational geometry and topology. In TDA (topological data analysis), it is especially used in computing persistent homology and data visualisation using Mapper. However only rudimentary methods have been used to compute a cover. In this talk, we formulate the cover computation problem as a general optimisation problem with a well-defined loss function, and use gradient descent to solve it. The resulting algorithm, ShapeDiscover, substantially improves quality of topological inference and data visualisation. We also show some preliminary applications in scRNA-seq transcriptomics and the topology of grid cells in the rats' brain. This is a joint work with Luis Scoccola and Heather Harrington.