GitHub

Topological Assembly Optimization in Mycelia

Mycelia's TDA layer treats topology as a quantitative assembly signal rather than a purely descriptive graph property. The current implementation is backend agnostic and starts with graph Betti invariants, which makes the workflow cheap to run on small and medium assembly graphs without introducing a persistent homology dependency.

Core idea

For an assembly graph, Mycelia measures:

  • betti0: the number of connected components, which is a proxy for assembly fragmentation
  • betti1: the cycle rank, which is a proxy for unresolved repeats, bubbles, or circular structure

These values are evaluated across threshold filtrations driven by coverage, confidence, or quality weights assigned to vertices. In practice this means you can ask not only "what is the topology of the current graph?" but also "how does the topology change as weakly supported vertices are removed?"

Current API

The graph-only backend lives in src/tda.jl and exposes:

  • Mycelia.TDAConfig
  • Mycelia.tda_betti_numbers
  • Mycelia.tda_betti_curves
  • Mycelia.tda_on_graph
  • Mycelia.tda_graph_score

The returned Mycelia.TDARunSummary packages the configuration, lightweight graph statistics, and threshold-wise Betti curves.

How to use it

The intended workflow is:

  1. Build an assembly graph with an existing Mycelia or Rhizomorph API.
  2. Extract a vertex-aligned support signal such as coverage, evidence count, or quality.
  3. Evaluate Mycelia.tda_on_graph(graph, config; vertex_weights=weights).
  4. Compare candidate thresholds or graph-cleaning outputs with Mycelia.tda_graph_score.

Lower scores are better. A useful threshold often removes cycles without increasing the number of connected components.

Tutorial

For a concrete walkthrough on synthetic assembly-like graphs, see Tutorial 21: Topological Assembly Optimization.

Roadmap

The long-term TDA plan is documented in planning-docs/TDA_INTEGRATION_PLAN.md. The next major step is an optional persistent homology backend layered behind the same API, so current graph-Betti workflows remain stable while richer topological summaries become available.