Exploring Diffusion and Persistence Homology

Jones' research demonstrates that diffusion geometry outperforms multi-parameter persistent homology as a biomarker for tumor histology data, both real and simulated. It also shows promise in robustly measuring the manifold hypothesis by detecting singularities in manifold-like data.

This episode offers listeners a fascinating glimpse into the intersection of advanced mathematics, data analysis, and real-world applications, showcasing how these innovative techniques are reshaping our understanding of complex datasets and geometric structures.

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• Paper: https://arxiv.org/abs/2405.10858

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Keywords: mathematics, math, riemannian geometry, diffusion, stochastic processes, game theory, calculus, linear algebra, category theory, signal processing, statistics, probability, solo auditor, public auditing platforms, private audits, scalability, freedom, Scraping Bits podcast, blockchain technology, audit industry, flashbots, reverse engineering, cybersecurity, infosec, mev, mev bot, quant.