Topic
Change, patterns, feedback and connected systems.
Two positive transport networks can lose exactly the same total mass, share every eigenvalue, and still disagree about a finite-time sensor alarm. A controlled study asks what a spectrum misses, what a rigorous margin can certify, and when that margin becomes uninformative.
A folding-energy study separates minima from saddles, global energy ordering from metastability, and branch discovery from proof, asking when an optimizer's attractive shape map leaves something important out.
Equal update counts do not guarantee stable feedback. A delayed two-choice model shows why allowing one extra slot between updates can stabilize a system, and why its smallest fairness relaxation is not its fastest schedule.
A system that recovers slowly and an environment that persists can leave the same statistical signature. An exactly sampled stochastic experiment shows what passive monitoring can identify, and which extra observations change the question.
Starting over discards progress, yet it can remove the longest waits in a random search. An exact first-passage experiment separates mean speed, tail risk, restart costs, and the situations where continuing is better.
A bounded finite-state calculation and seeded direct simulation agree on one synthetic low-copy genetic-toggle event—but that Phase-1 agreement is a starting point, not a rare-event victory.
From a convincing fit to a useful guarantee: ask what the observations, evaluation and bounds actually establish.
First: When the Fit Is Not the Model
2026
A verified Schnakenberg reaction–diffusion study tracks peak birth and loss as a one-dimensional domain grows.
2026
A controlled folding-energy study audits the difference between finding the lowest known energy, recovering every stable family, and tracing unstable equilibrium branches.
2026
A reproducible Phase-1 study checks a synthetic low-copy exclusive genetic toggle with an error-bounded finite-state reference and seeded direct SSA.
2026
A nonlinear reactor study maps multiplicity, ignition and extinction hysteresis, basin dependence, and critical slowing near a thermal fold.
2026
A dropout-aware pressure-sensor placement study for distinguishing leak zones when measurements are noisy and one sensor may be unavailable.
2026
A reproducible synthetic study of memory decay, cutoff scheduling, tail latency, and evidence-aware abstention in a four-link quantum repeater chain.
