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- W4286972912 abstract "Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective/cyclic/chiral flows over networks, particularly those that arise for irreversible Markov chains (MCs). As two applications, we study convection cycles arising under the PageRank algorithm, and we investigate chiral edges flows for a stochastic model of a bi-monomer's configuration dynamics. Our experiments highlight how system parameters -- e.g., the teleportation rate for PageRank and the transition rates of external and internal state changes for a monomer -- can act as homology regularizers of convection, which we summarize with persistence barcodes and homological bifurcation diagrams. Our approach establishes a new connection between the study of convection cycles and homology, the branch of mathematics that formally studies cycles, which has diverse potential applications throughout the sciences and engineering." @default.
- W4286972912 created "2022-07-25" @default.
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- W4286972912 date "2021-09-17" @default.
- W4286972912 modified "2023-09-28" @default.
- W4286972912 title "Persistent homology of convection cycles in network flows" @default.
- W4286972912 doi "https://doi.org/10.48550/arxiv.2109.08746" @default.
- W4286972912 hasPublicationYear "2021" @default.
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