Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

Explore a 46-minute conference talk by Tamal Dey on computing generalized ranks of persistence modules through unfolding to zigzag modules. Delve into the concept of generalized rank for persistence modules indexed by finite posets and its calculation using limit-to-colimit map ranks. Examine the extension of a 2-parameter persistence module algorithm to d-parameter and general persistence modules using an unfolding technique. Learn about an efficient algorithm for computing generalized ranks of modules induced by simplicial complex filtrations over finite posets. Discover optimized algorithms for special cases, including a linear time algorithm for graphs in degree-1 homology. Gain insights into advanced topics in applied algebraic topology and persistent homology through this presentation from the Applied Algebraic Topology Network.