Ricky J. Mathews

Hybrid adaptive Baker-Campbell-Hausdorff solver using kinematic curvature diagnostic for finite-deformation crystal plasticity. Achieves hierarchical FE² speedup with zero false negatives through geometric proof of curvature connection and universal scaling law. Enables predictive diagnostics in materials modeling with multi-purpose diagnostic capabilities.

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Comprehensive framework for predictive diagnostics using non-commutativity of dynamical generators. Representation-agnostic method applicable across quantum error correction, robotics pose/sensor fault prediction, seismic stress-regime detection, and adaptive mesh refinement in CFD. Provides first-principles, computationally efficient predictive alarms with sufficient lead time for pre-emptive action in critical systems.

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Predictive geometric control framework preventing non-adiabatic transitions and leakage in electrically controlled qubits. Introduces spectral curvature functional Λ(t) = ∥[B(t), Ḃ(t)]∥ that provides pointwise control law: minimizing peak curvature at avoided crossings exponentially suppresses leakage. Enables predictive feedback control without requiring counter-diabatic fields or full Hamiltonian inversion.

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Quantum-state-aware schema for multidimensional data analysis using Clifford algebra as foundational data architecture. Proposes multivector fact tables where algebraic structure serves as schema, enabling geometry-aware data systems. Introduces Lie-Jordan decomposition for separating incompatibility from alignment, with applications to spatial data systems and quantum data representations.

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Two-signal framework for market regime detection combining commutator-based rotation detection with correlation synchronization. Detects institutional repositioning preceding major market transitions through non-commutativity analysis of factor covariance dynamics. Achieves 100% detection rate across 33 major market events (2000-2024) with 14-90 day lead times. Extended with game-theoretic layer incorporating Von Neumann-Nash equilibrium concepts.

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Formulation-to-validation pipeline for QUBO-based sensor placement on power grid stress monitoring. Discovers stress-information duality: dispersion-dominant QUBO objectives produce placements worse than 99% of random alternatives on radial networks due to MI-distance anti-correlation (r = -0.37 proxy, -0.45 cascade). Sharp alpha phase transition at ~0.8. QAOA validated on 20-qubit subproblem (exact optimum, p=1-4). Cross-topology confirmation on IEEE 57-bus meshed system. Corrected Hadamard test with honest quantum roadmap.

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Theoretical connection between spherical code optimization (packing) and codebook design for approximate nearest neighbor search (covering). Proposes gap-based regularization for vector quantization achieving +10-13% better separation with only +3% MSE cost. Validates that kissing number methodology transfers successfully to codebook learning when using achievable targets and proper regularization strength.

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Multi-scale structured diagnostic family for early warning of pedestal events (edge localized modes, large pedestal collapses) in tokamak plasmas. Combines derivative-free noncommutativity ladder, projector-drift signals, adiabatic-mixing parameters, and energy-conversion proxies. Provides reproducible pipeline for predictive and interpretive value in specified regimes with explicit experimental embodiments, enabling safer fusion reactor operation.

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