Topological & Algebraic Models of Social Interaction
Updated September 2025. We build on evolutionary networks by modeling interaction as higher-order structures—hypergraphs, simplicial complexes, and functorial views—so dynamics and roles are captured beyond ordinary graphs.
An introductory article presenting the basic tenets of this approach can be found here.
This line of work powers our SHE™ (Social Hypergraph Engine) for clustering, navigation, and distance metrics on extended social spaces.
Multimetric Clustering
We explore clustering under multimetric and ultrametric geometries (including p-adic models) so that hierarchical semantics—shared prefixes/paths—are respected by the model.
Viewing data from several compatible metrics at once yields complementary groupings and more stable retrieval on tree-like domains.
Hypergraph Ontology
Beyond DAGs and trees, we encode higher-dimensional semantic relations among linguistic modules, producing a navigable semantic complex for long-form text. Paths through this landscape surface signals that are diffuse in the original document set.
A concise survey preprint is in preparation; a one-page summary is available on request.
<
2025 Research Threads
- HyperCat v2: commutativity checking and diagram cleanup.
- Logical GANs: logic-constrained structure generation.
- Q-Trace: weak-value analytics and classical→quantum bridges.