{"id":2658,"date":"2022-03-11T06:19:31","date_gmt":"2022-03-11T14:19:31","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=2658"},"modified":"2022-03-28T09:07:42","modified_gmt":"2022-03-28T16:07:42","slug":"voronoi-tessellations-optimal-quantization-and-modeling-collective-behavior-prof-rustum-choksi","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/voronoi-tessellations-optimal-quantization-and-modeling-collective-behavior-prof-rustum-choksi\/","title":{"rendered":"Voronoi Tessellations:  Optimal Quantization and Modeling Collective Behavior (Prof. Rustum Choksi)"},"content":{"rendered":"<p><strong>Title<\/strong>: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior<\/p>\n<p><strong>Speaker<\/strong>: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University<\/p>\n<p><strong>Abstract<\/strong>:\u00a0 Given a set of <em>N<\/em> distinct points (generators) in a domain (a bounded subset of Euclidean space or a compact Riemannian manifold), a Voronoi tessellation is a partition of the domain into <em>N<\/em> regions (Voronoi cells) with the following property: all points in the interior of the i<sup>th<\/sup> Voronoi cell are closer to the i<sup>th<\/sup>\u00a0generating point than to any other generator.\u00a0\u00a0Voronoi tessellations give rise to a wealth of analytic, geometric, and computational questions. They are also very useful in mathematical and computational modeling.<\/p>\n<p>This talk will consist of three parts:<\/p>\n<ul>\n<li>We begin by introducing\u00a0the basic definitions and geometry of Voronoi tessellations,\u00a0\u00a0centroidal Voronoi tessellations (CVTs), and the notion of optimal quantization.<\/li>\n<li>We will then address simple, yet rich, questions on optimal quantization on the 2D and 3D torus, and on\u00a0\u00a0the 2-sphere. We will address the geometric nature of the global minimizer (the optimal CVT), presenting a few conjectures and a short discussion on rigorous asymptotic results and their proofs.<\/li>\n<li>We will then shift gears to address the use Voronoi tessellations in modeling collective behaviors.<\/li>\n<\/ul>\n<p>Collective behavior in biological systems, in particular the contrast and connection between individual and collective behavior, has fascinated researchers for decades.\u00a0A well-studied paradigm entails the tendency of groups of individual agents to form flocks, swarms, herds, schools, etc.\u00a0We will first review some well-known and widely used models for collective behavior.\u00a0 We will then present a new dynamical model for generic crowds in which individual agents are aware of their local Voronoi environment &#8212; i.e., neighboring agents and domain boundary features &#8211;and may seek static target locations. Our model incorporates features common to many other <em>active matter<\/em> models like collision avoidance, alignment among agents, and homing toward targets. However, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent&#8217;s Voronoi diagram. With only two parameters, it captures a wide range of collective behaviors. The results of many simulations will be shown.<\/p>\n<hr \/>\n<p>Rustum Choksi received the PhD degree in mathematics from Brown University, in 1994. He held post-doctoral positions with the Center for Nonlinear Analysis, Carnegie Mellon University and the Courant Institute, New York University. From 1997 to 2010, he was a faculty member with the Department of Mathematics, Simon Fraser University. In 2010, he joined McGill University where he is currently a full professor with the Department of Mathematics and Statistics. His main research interests include interaction of the calculus of variations and partial differential equations with pattern formation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior Speaker: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University Abstract:\u00a0 Given a set of N distinct points (generators) in [&hellip;]<\/p>\n","protected":false},"author":82,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[12],"class_list":["post-2658","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquium","cat_colloquium"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - 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