Research Pipeline
A force-directed graph of the ten-paper TDA research programme. Each node is a paper; directed edges indicate prerequisite dependencies. Click any node to open the paper page.
- Paper 1: The Markov Memory Ladder — superseded
- Paper 2: Mapper for Interior Trajectory Structure — superseded (depends on: Paper 1)
- Paper 3: Zigzag Persistence for Business Cycle Topology — superseded (depends on: Paper 1)
- Paper 4: Multi-Parameter Persistent Homology for Poverty Trap Detection — planned (depends on: Paper 2, Paper 3)
- Paper 5: Cross-National Welfare State Topology — planned (depends on: Paper 2)
- Paper 6: Intergenerational Topological Inheritance — planned (depends on: Paper 3)
- Paper 7: Geometric Trajectory Forecasting — planned (depends on: Paper 4)
- Paper 8: Graph Neural Networks on Household Social Graphs — planned (depends on: Paper 4)
- Paper 9: Combinatorial Complex Neural Networks for Trajectory Analysis — planned (depends on: Paper 5)
- Paper 10: Topological Fairness Analysis of Poverty Measurement — planned (depends on: Paper 6)
- Paper 11: The Geometry of UK Career Inequality: Topology, Regimes, and Mobility Boundaries — in-progress
- Paper 12: Structured Hypothesis Testing for Persistent Homology of Longitudinal Social Data — in-progress
Show text description of pipeline
TDA research pipeline with 12 papers across 4 stages. Paper 1: The Markov Memory Ladder — Foundations, superseded. Enables: Paper 2, Paper 3. Paper 2: Mapper for Interior Trajectory Structure — Core Methods, superseded. Depends on: Paper 1. Enables: Paper 4, Paper 5. Paper 3: Zigzag Persistence for Business Cycle Topology — Core Methods, superseded. Depends on: Paper 1. Enables: Paper 4, Paper 6. Paper 4: Multi-Parameter Persistent Homology for Poverty Trap Detection — Applications, planned. Depends on: Paper 2, Paper 3. Enables: Paper 7, Paper 8. Paper 5: Cross-National Welfare State Topology — Applications, planned. Depends on: Paper 2. Enables: Paper 9. Paper 6: Intergenerational Topological Inheritance — Applications, planned. Depends on: Paper 3. Enables: Paper 10. Paper 7: Geometric Trajectory Forecasting — Synthesis, planned. Depends on: Paper 4. Paper 8: Graph Neural Networks on Household Social Graphs — Synthesis, planned. Depends on: Paper 4. Paper 9: Combinatorial Complex Neural Networks for Trajectory Analysis — Synthesis, planned. Depends on: Paper 5. Paper 10: Topological Fairness Analysis of Poverty Measurement — Synthesis, planned. Depends on: Paper 6. Paper 11: The Geometry of UK Career Inequality: Topology, Regimes, and Mobility Boundaries — Foundations, in-progress. Paper 12: Structured Hypothesis Testing for Persistent Homology of Longitudinal Social Data — Foundations, in-progress.