How Rare Is a Flip?
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.
Read articleKenneth Cheng · Macau
Mathematical models for real systems.
From pattern formation and nonlinear mechanics to scientific institutions, reliability, and experimental design: reproducible computation, explicit assumptions, and honest limits turn models into testable research questions.
Latest writing
Question, verification, and limitation belong in the same article.
Every research article is manually written from verified private ScienceProject results and supported by approved figures, numerical checks, negative findings, claim boundaries, and references.
Topology at the Edge of Resolution: Which Melt-Pond Signals Survive the Camera?
A controlled audit of when blur, pixel size, segmentation error, and finite windows make Arctic melt-pond images appear to cross a connectivity threshold that the latent surface did not.
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When Entanglement Expires: Risk-Sensitive Scheduling for Quantum Repeater Chains
A mathematical-modeling study of how a quantum repeater should trade speed against decoherence when link generation and entanglement swapping are probabilistic.
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Four connected programmes
Research is organized by questions and methods, not only by publication date.
01→02→03→04→
Environmental Modeling
Spatial disease, ecosystems, coastal risk, climate forcing, and energy-environment interactions.
Mathematical Modeling Education
Pathways from an open-ended question to assumptions, computation, critique, and communication.
Reliability and Uncertainty
Sensitivity, calibration, robustness, and decision-making when model inputs or operating conditions are uncertain.
Urban and Mobility Systems
Models of routing, accessibility, traffic stability, fleet operations, and infrastructure trade-offs.
Selected research
Evidence before volume
Only projects with a clear question, reviewed figures, and visible assumptions and limitations appear here.
How Rare Is a Flip?
A reproducible Phase-1 study checks a synthetic low-copy exclusive genetic toggle with an error-bounded finite-state reference and seeded direct SSA.
Topology at the Edge of Resolution
A controlled false-threshold audit of melt-pond connectivity under blur, downsampling, segmentation error, finite windows, and morphology shift.
When Entanglement Expires
A reproducible synthetic study of memory decay, cutoff scheduling, tail latency, and evidence-aware abstention in a four-link quantum repeater chain.
Teaching
From first model to student research
Courses, interactive models, Python laboratories, and mentoring form a path from first assumptions to independent inquiry.
New local teaching resourceMacau School Mathematics Competition ArchiveJunior and Senior Divisions from 2019 to 2025/2026: 214 source-verified solutions, 46 diagrams, and expandable examples.Open the solution archive →Student research milestoneAI4Nature@AVSS 2026 · Paper ID 7A student team I mentored is listed with me as co-author for “From Pixels to Patrols,” scheduled in the workshop's oral programme on 31 August 2026.See the mentoring outcome and official record →