Data Science & ML Claude 技能

Markov Game ACSet

Models and verifies state-dependent Markov games using Attributed C-sets and GF(3) conservation laws.

Dynamical Flow Analysis

Models and analyzes one-parameter groups of diffeomorphisms generated by vector fields within dynamical systems.

Lyapunov Function Analysis

Analyzes the stability and qualitative behavior of dynamical systems using scalar function trajectories.

Time Parameterization

Manages the reparameterization of time in flows for complex dynamical systems and topological modeling.

Dynamical System Functor

Models and analyzes the categorical structure of dynamical systems to evaluate stability and qualitative behavior.

LiveKit Omni-modal Coach

Facilitates real-time, multi-modal continuous coaching and guidance through LiveKit using dynamic modality selection and symbolic expression processing.

Datalog Fixpoint Iteration

Implements bottom-up fixpoint iteration for recursive Datalog queries using saturation-based evaluation.

Moth Actias Quantum Synth

Transforms quantum qubit states into expressive musical textures through Bloch sphere sonification and MIDI control.

Constraint Propagator Networks

Implements bidirectional constraint propagation and fixpoint derivation for complex autonomous information networks.

Möbius Color Duality

Recovers local structural seeds from global color distributions using Möbius inversion and topological duality.

Kolmogorov-Onsager-Hurst Scaling Analysis

Analyzes time-series data using scaling theory to identify turbulence regimes, persistence, and long-range dependencies.

GF(3) Task Orchestrator

Routes complex tasks to specialized subagent triads using GF(3) triadic logic to ensure balanced execution and validation.

Algebraic Graph Rewriting

Transforms structured data and acsets using category-theoretic graph rewriting techniques like DPO, SPO, and SqPO.

Fokker-Planck Convergence Analyzer

Verifies that neural network training trajectories have reached theoretical Gibbs equilibrium using Fokker-Planck equations.

Pitchfork Dynamics

Analyzes symmetric bifurcations and symmetry-breaking patterns in complex dynamical systems and differential equations.

Attractor Dynamics

Analyzes invariant sets and long-term trajectory behaviors within dynamical systems to model stable states and system evolution.

Invariant Set Analysis

Analyzes and identifies sets within dynamical systems that are preserved by the flow of differential equations and manifolds.

Multi-Agent System Consensus

Implements and analyzes agreement protocols within multi-agent dynamical systems using algebraic dynamics and topological principles.

FlowerPower Pipeline Manager

Automates the creation and management of robust data pipelines using Hamilton DAGs and the FlowerPower framework.

Latent-Latency Optimizer

Bridges representation space and execution time to optimize AI model performance through mathematical spectral analysis.

CatSharp Galois Bridge

Facilitates Galois adjunctions between local agent operations and global cognitive category theory using Mazzola’s mathematical music structures.

Bifurcation Analysis

Detects and analyzes qualitative state transitions in dynamical systems using Hopf bifurcation detection and GF(3) phase portraits.

Ordered Locale & Triadic Topology

Implements point-free topology and triadic GF(3) logic to manage causal structures and deterministic parallel execution for MCP servers.

Operad Compose

Facilitates structured generation and composition of complex multi-input operations using colored operads and category theory principles.

Trajectory Analysis

Analyzes and models the paths of solutions through phase space within dynamical systems.

Gay.jl Bisimulation Integration

Integrates deterministic color generation with bisimulation game semantics for verifiable GF(3) conservation logic.

Coupled Systems Dynamics

Models and analyzes interacting dynamical systems using topological and algebraic frameworks for complex system simulation.

Pun Decomposition Logic

Analyzes and deconstructs linguistic puns into multiple semantic and phonetic parses using algebraic and topological structures.

Advanced Excel & Spreadsheet Automation

Automates professional spreadsheet creation, data analysis, and financial modeling with a focus on formula-driven logic.

ReasoningBank with AgentDB

Implements high-performance adaptive learning and memory distillation for AI agents using the AgentDB vector engine.