directed-interval
Directed interval type 2 axiomatizing (0 → 1). Time-directed homotopy
Directed interval type 2 axiomatizing (0 → 1). Time-directed homotopy
Deploy Nozomi Networks Guardian sensors for passive OT network traffic analysis to achieve comprehensive asset visibility, real-time threat detection, and vulnerability assessment across industrial control systems without disrupting operations, leveraging behavioral anomaly detection and protocol-aware monitoring.
Modelica acausal equation-based multi-domain modeling via Wolfram Language. Chemputation-native simulation with automatic conservation laws. Lambda-Modelica bridge for string diagram semantics. Fixed point classification for 3-coloring/3-MATCH systems.
Generate phase portraits for 2D dynamical systems. Use when visualizing vector fields, nullclines, and trajectories.
Taxonomy of ACSet skills with morphisms to semantically similar categorical/relational skills
ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional navigation. Category-theoretic formalism for relational databases.
Chemical reaction network modeling with Catalyst.jl. Autopoietic systems, unit-aware ODEs, and interacting subsystems.
CatColab Decapodes - Discrete Exterior Calculus for PDE modeling on meshes via Decapodes.jl integration. Model physics equations compositionally with automatic code generation.
CatColab Petri Nets - concurrent system modeling via places (states), transitions (events), and token flow. Foundation for process algebra, workflow, and chemical reaction networks.
CatColab Regulatory Networks - signed graphs for molecular biology modeling gene regulatory networks with positive (activating) and negative (inhibiting) edges.
**Category:** Phase 3 Core - Autopoietic Systems
Semantic analysis for DuckLake ACSet models with GF(3) conservation
Fisher-Rao metric on statistical manifolds with natural gradient and divergence analysis
Lawvere theories: categorical universal algebra.
Natural transformations: morphisms of functors.
Presheaves: contravariant Set-valued functors.
Fourier-Laplacian eigenmodes for frequency domain analysis of graph and signal structures
Virtual double categories: loose morphisms.