research Golden Ratio and Vortices How vortex dynamics reveal bifurcations at golden-ratio thresholds. Compound Burgers-KdV Solitons Refraction, reflection, and fusion in a coupled shallow-water model. Motility-Induced Phase Separation How self-propelled particles aggregate without attractive forces. Regret Minimization in the Blotto Game No-regret learning in a repeated resource-allocation game. Ising Models, Graph Similarity, QUBO, and Quantum Computing Connections between graph matching, Ising formulations, QUBO, and quantum optimization. Real-Time Light Sensing in Virtual Reality A real-time framework for evaluating visual exposure in VR scenes. Invariant Measures in Random Dynamical Systems How random dynamics can generate fractal invariant measures. essay Three Structures in Mathematics An accessible introduction to order, transformation, and metric structure.
