Research Programme

Topological Data Analysis

A ten-paper research programme applying persistent homology, Mapper, and related methods to poverty trajectory data from Understanding Society and the BHPS.

Papers

  1. Stage 0 — Foundations Paper 1 The Markov Memory Ladder
    Stage 0 Superseded
  2. Stage 1 — Core Methods Paper 2 Mapper for Interior Trajectory Structure
    Stage 1 Superseded
  3. Stage 1 — Core Methods Paper 3 Zigzag Persistence for Business Cycle Topology
    Stage 1 Superseded
  4. Stage 2 — Extensions Paper 4 Multi-Parameter Persistent Homology for Poverty Trap Detection
    Stage 2 Planned
  5. Stage 2 — Extensions Paper 5 Cross-National Welfare State Topology
    Stage 2 Planned
  6. Stage 2 — Extensions Paper 6 Intergenerational Topological Inheritance
    Stage 2 Planned
  7. Stage 3 — Applications Paper 7 Geometric Trajectory Forecasting
    Stage 3 Planned
  8. Stage 3 — Applications Paper 8 Graph Neural Networks on Household Social Graphs
    Stage 3 Planned
  9. Stage 3 — Applications Paper 9 Combinatorial Complex Neural Networks for Trajectory Analysis
    Stage 3 Planned
  10. Stage 3 — Applications Paper 10 Topological Fairness Analysis of Poverty Measurement
    Stage 3 Planned
  11. Stage 0 — Foundations Paper 11 The Geometry of UK Career Inequality: Topology, Regimes, and Mobility Boundaries
    Stage 0 In Progress
  12. Stage 0 — Foundations Paper 12 Structured Hypothesis Testing for Persistent Homology of Longitudinal Social Data
    Stage 0 In Progress