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- W4387433509 abstract "A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that achieves a holistic understanding of a fully commutative quiver's representation via synthesizing interpretations obtained from intervals. Additionally, our approach offers the flexibility to tune the balance between approximation resolution and computational complexity. This framework is evaluated on commutative ladders of both finite-type and infinite-type. For the former, we discover an efficient method for the indecomposable decomposition leveraging solely one-parameter persistent homology. For the latter, we introduce a new invariant that reveals persistence in the second parameter by connecting two standard persistence diagrams using interval approximations. We subsequently present several models for constructing commutative ladder filtration, offering fresh insights into random filtrations and demonstrating our toolkit's effectiveness in analyzing the topology of materials." @default.
- W4387433509 created "2023-10-09" @default.
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- W4387433509 date "2023-10-05" @default.
- W4387433509 modified "2023-10-09" @default.
- W4387433509 title "Refinement of Interval Approximations for Fully Commutative Quivers" @default.
- W4387433509 doi "https://doi.org/10.48550/arxiv.2310.03649" @default.
- W4387433509 hasPublicationYear "2023" @default.
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