BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anton Nikitenko (Institute of Science and Technology Austria) DTSTART:20230208T140000Z DTEND:20230208T150000Z DTSTAMP:20260423T035542Z UID:ADPS/13 DESCRIPTION:Title: Me asuring shapes with random Delaunay mosaics\nby Anton Nikitenko (Insti tute of Science and Technology Austria) as part of Abu Dhabi Stochastics S eminar\n\n\nAbstract\nClassically\, we are used to working with shapes emb edded into the square lattice. It might be anything\, a pixelated photo of a maple leaf\, or a 3d-scanned voxelated image of a human organ. And desp ite being simple and intuitive\, such a way of representation can totally distort the internal geometry of the object. While it is pretty simple to estimate the area of the leaf from a pixelated photograph\, there is no st raightforward way to compute its perimeter: the pixel approximation of the boundary varies dramatically\, depending on how good the object is “ali gned” with the lattice. By changing the square lattice for an isotropic mosaic\, we can expect that the misalignment problem will fade away\, as t he isotropic background equalizes all directions. In the talk\, we will be moving objects and mosaics in all possible ways\, and utilizing the archa ic probability theory approach of counting how many points or lines are th ere in the space\, to lead us to the precise answer of how an approximatio n of a p-dimensional object in d-dimensional space distorts its p-dimensio nal volume.\n LOCATION:https://researchseminars.org/talk/ADPS/13/ END:VEVENT END:VCALENDAR