Code for the NeurIPS 2019 paper: Topology-Preserving Deep Image Segmentation
DMT codes for the ICLR 2021 paper: Topology-Aware Segmentation Using Discrete Morse Theory
Computing Betti numbers from simplicial complexes.
Structure-Aware Image Segmentation with Homotopy Warping
Codes for the ICLR 2022 paper: Trigger Hunting with a Topological Prior for Trojan Detection
a mathematica notebook for computing homology groups of the vietoris-rips simplicial complex over the Z_2 ring
Detecting Topological Precursors to Technological Breakthroughs in the USPTO Patent Citation Network. Persistent homology applied to 8.4M patents and 118M citations.
Multi-agent system for automated discovery of Betti numbers and Euler characteristic from triangulated surface data. GF(2) chain-complex features + cooperative REINFORCE agents + certified Lean 4 provability oracle.
Betti Numbers for a Sub-Level Set of Volumetric Scalar Data
Topological Early Warning Signals for Flash Crashes: A Proof-of-Concept using Topological Data Analysis (TDA) and Persistent Homology to detect structural market fragility and liquidity voids in Limit Order Books before a crash occurs.
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