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TTTTTT Hazrat Usman September 21, 2024 Biological Network (Point Cloud X) Filtration Process (F_r) Increasing r → Simplicial Complex (K) Persistence Diagram (PD) Death Birth Key Equations: 1. Filtration definition: F_r = { σ ∈ K | diam(σ) ≤ r } 2. Persistence Diagram: PD = { (b_i, d_i) | feature i appears at scale b_i and disappears at scale d_i }
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