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New theory uses persistent homology to explain emergent structures

By PulseAugur Editorial · [1 sources] ·

A new research paper proposes persistent homology as a mathematical framework to understand emergent structures across various systems. The theory suggests that persistent, non-trivial homology classes represent macro-features that remain stable despite underlying microscopic changes. This approach frames emergence as a measurement problem, using tools like contractive-similarity graphs and Hodge decomposition to predict robustness and hierarchical organization in phenomena ranging from fluid dynamics to neural networks and social systems. AI

RANK_REASON The cluster contains a research paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New theory uses persistent homology to explain emergent structures

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The cluster contains a research paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Xin Li ·

    Persistent Homology as a Theory of Emergent Structure

    arXiv:2507.03065v2 Announce Type: replace Abstract: Why do some macroscopic structures remain identifiable even though their microscopic constituents continually change? Vortices persist while fluid parcels turn over, neural memories persist while spikes and synapses fluctuate, a…

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