BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesco Vaccarino (Politecnico di Torino - Italy) DTSTART:20240405T160000Z DTEND:20240405T170000Z DTSTAMP:20260423T022925Z UID:GEOTOP-A/65 DESCRIPTION:Title: Three easy pieces for Hodge Laplacian and higher order interactions\ nby Francesco Vaccarino (Politecnico di Torino - Italy) as part of GEOTOP- A seminar\n\n\nAbstract\nFirstly\, we present a cross-order Laplacian reno rmalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a fundamental concept in the physics theory of sc aling\, scale-invariance\, and universality. An RG scheme was recently int roduced for complex networks with dyadic interactions based on diffusion d ynamics. However\, we still lack a general RG scheme for higher-order netw orks despite the mounting evidence of the importance of polyadic interacti ons. Our approach uses a diffusion process to group nodes or simplices\, w here information can flow between nodes and between simplices (higher-orde r interactions).\n\nSecondly\, we discuss simplicial Kuramoto models\, whi ch have emerged as a diverse and intriguing model that describes oscillato rs on simplices rather than nodes. We present a unified framework to descr ibe different variants of these models\, which are categorized into three main groups: "simple" models\, "Hodge-coupled" models\, and "order-coupled " (Dirac) models. We explore a potential application in reconstructing bra in functional connectivity from structural connectomes. We find that simpl e edge-based Kuramoto models perform competitively or outperform complex e xtensions of node-based models.\n\nLastly\, we consider associated games i n cooperative game theory\, which allows for the meaningful characterizati on of solution concepts. Moreover\, generalized values allow computing eac h coalition's influence or power index in a game. We view associated games through the lens of game maps and graph Laplacian\, thus defining the nov el Hodge Generalized Value (HGV). We characterize HGV via an axiomatic app roach as a generalized value. Finally\, we show how HGV is linked to the s olution of the Poisson equation derived from the Hodge decomposition of th e direct graph associated with the poset of coalitions in the game.\n\nRef erences and coauthor list:\n\nNurisso\, M.\, Morandini\, M.\, Lucas\, M.\, Vaccarino\, F.\, Gili\, T.\, & Petri\, G. (2024). Higher-order Laplacian Renormalization. arXiv preprint arXiv:2401.11298.\n\nNurisso\, M.\, Arnaud on\, A.\, Lucas\, M.\, Peach\, R. L.\, Expert\, P.\, Vaccarino\, F.\, & Pe tri\, G. (2023). A unified framework for Simplicial Kuramoto models. arXiv e-prints\, arXiv-2305.\n\nMastropietro\, Antonio\, and Francesco Vaccarin o. "The Shapley-Hodge Associated Game." arXiv preprint arXiv:2303.17151(20 23).\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/65/ END:VEVENT END:VCALENDAR