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Explore an advanced mathematical lecture on persistence functions as an extension of persistent homology, focusing on steady and ranging sets methodology. Learn about the foundational 2020 work by M. Bergomi and P. Vertechi that introduced persistence functions, and discover how steady and ranging techniques have evolved from their initial applications to graphs and digraphs to encompass broader mathematical contexts including hypergraphs. Examine recent developments in the stability properties of steady and ranging persistence, gaining insights into this cutting-edge area of applied algebraic topology that operates without traditional homological methods.
