More Like this

1. Gender, Self-Assessment, and Persistence in Computing: How gender differences in self-assessed ability reduce women’s persistence in computer science

   https://doi.org/10.1145/3501385.3543963  

   Hunt, Cynthia ; Yoder, Spencer ; Comment, Taylor ; Price, Thomas ; Akram, Bita ; Battestilli, Lina ; Barnes, Tiffany ; Fisk, Susan ( August 2022 , Proceedings of the 2022 ACM Conference on International Computing Education Research)
2. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and Its Applications

   https://doi.org/10.4230/LIPIcs.SoCG.2022.34  

   Tamal K. Dey ; Woojin Kim ; Facundo Memoli ( June 2022 , Leibniz international proceedings in informatics)

   Xavier Goaoc ; Michael Kerber (Ed.)

   The notion of generalized rank invariant in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as generalized persistence diagrams. Naturally, computing these rank invariants efficiently is a prelude to computing any of these derived structures efficiently. We show that the generalized rank over a finite interval I of a 𝐙²-indexed persistence module M is equal to the generalized rank of the zigzag module that is induced on a certain path in I tracing mostly its boundary. Hence, we can compute the generalized rank over I by computing the barcode of the zigzag module obtained by restricting the bifiltration inducing M to that path. If the bifiltration and I have at most t simplices and points respectively, this computation takes O(t^ω) time where ω ∈ [2,2.373) is the exponent of matrix multiplication. Among others, we apply this result to obtain an improved algorithm for the following problem. Given a bifiltration inducing a module M, determine whether M is interval decomposable and, if so, compute all intervals supporting its summands. 

   more » « less
3. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and Its Applications

   Tamal K. Dey, Woojin Kim ( July 2022 , Proceedings of the annual ACM Symposium on Computational Geometry)

   Xavier Goaoc and Michael Kerber (Ed.)
4. The persistence of short-term cold acclimation in Drosophila melanogaster (Diptera: Drosophilidae): Persistence of short-term acclimation

   https://doi.org/10.1111/phen.12191  

   Everman, Elizabeth R. ; Ledbetter, Nicholus ; Morgan, Theodore J. ( December 2017 , Physiological Entomology)
5. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and Its Applications

   https://doi.org/10.1007/s00454-023-00584-z  

   Dey, Tamal K. ; Kim, Woojin ; Mémoli, Facundo ( October 2023 , Discrete & Computational Geometry)

   The notion of generalized rank in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as generalized persistence diagrams. However, its efficient computation has not yet been studied in the literature. We show that the generalized rank over a finite intervalIof a$$\textbf{Z}^2$$$Z^2$-indexed persistence moduleMis equal to the generalized rank of the zigzag module that is induced on a certain path inItracing mostly its boundary. Hence, we can compute the generalized rank ofMoverIby computing the barcode of the zigzag module obtained by restricting to that path. IfMis the homology of a bifiltrationFof$$t$$$t$simplices (while accounting for multi-criticality) andIconsists of$$t$$$t$points, this computation takes$$O(t^\omega )$$$O\left(t^{\omega }\right)$time where$$\omega \in [2,2.373)$$$\omega \in [2,2.373)$is the exponent of matrix multiplication. We apply this result to obtain an improved algorithm for the following problem. Given a bifiltration inducing a moduleM, determine whetherMis interval decomposable and, if so, compute all intervals supporting its indecomposable summands.

    

   more » « less