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DTSTAMP:20230918T123103
DTSTART;TZID=America/Detroit:20230920T160000
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SUMMARY:Lecture / Discussion:Math/MCAIM Colloquium | The Theory and Application of Networks: From Mathematical Machine Learning to Simplicial Complexes
DESCRIPTION:Abstract: Networks are ubiquitous in nature and appropriate for mathematical investigation of various systems. In this talk I will discuss some aspects at the intersection of mathematics\, machine learning\, and networks to introduce interdisciplinary methods with wide application. First\, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a limiting function of a graph with infinitely many nodes. Next\, I will use these ideas to present a new method for early prediction of disease subtype\, characterized by dynamic co-evolution of multiple variables\, with remarkable success in prediction of Parkinson's subtype five years in advance. Then\, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some results on spectral theory of simplicial complexes\, as well as introduce a mathematical framework for studying the topology and dynamics of multilayer simplicial complexes using Hodge theory\, applied to brain connectome data. Finally\, I will discuss applications of such interdisciplinary methods to studying bias in society\, opinion dynamics\, hate speech propagation in social media\, and extreme mountaineering. \n\nTalk will be in-person and on Zoom: https://umich.zoom.us/j/98734707290
UID:111909-21827881@events.umich.edu
URL:https://events.umich.edu/event/111909
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4448
CONTACT:
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