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The Asymptotics of Betti Numbers in Preferential Attachment Clique Complexes

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Asymptotic Analysis Courses Network Topologies Courses Topological Data Analysis Courses Betti Numbers Courses

Course Description

Overview

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Explore the higher-order connectivity of preferential attachment networks through an in-depth analysis of Betti numbers in clique complexes. Delve into a 46-minute lecture that examines the asymptotic growth rates of expected Betti numbers as network size increases, revealing sublinear growth patterns with a notable exception of linear growth for the first Betti number. Gain insights from theoretical findings supported by simulation results, based on collaborative research presented in the associated preprint. Enhance understanding of complex network structures and their topological properties in this Applied Algebraic Topology Network presentation.

Syllabus

Chunyin Siu (11/1/23): The Asymptotics of Betti Numbers of Preferential Attachment Clique Complexes


Taught by

Applied Algebraic Topology Network

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