https://skckenneth.github.io/writing/New writing on mathematical thinking, computational experiments and teaching. en Sun, 11 Oct 2026 02:00:00 GMT https://skckenneth.github.io/writing/two-networks-one-spectrum-different-alarms/https://skckenneth.github.io/writing/two-networks-one-spectrum-different-alarms/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.Sun, 11 Oct 2026 02:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/writing/after-a-good-fit-what-to-measure/https://skckenneth.github.io/writing/after-a-good-fit-what-to-measure/A short note on choosing the next observation when several parameter explanations already fit the data.Sun, 11 Oct 2026 00:00:00 GMTdata-aimathematical-thinkingteaching-research-practice https://skckenneth.github.io/writing/choose-the-question-before-the-score/https://skckenneth.github.io/writing/choose-the-question-before-the-score/A small error or an improved average answers only its own question. Event timing and worst-group reliability need their own checks.Sun, 11 Oct 2026 00:00:00 GMTrisk-decisionscities-engineeringdata-ai https://skckenneth.github.io/writing/keep-the-result-that-changes-the-question/https://skckenneth.github.io/writing/keep-the-result-that-changes-the-question/A failed check can narrow a useful question. Two published numerical studies show why the original failure must remain visible.Sun, 11 Oct 2026 00:00:00 GMTteaching-research-practicecomputation-coderisk-decisions https://skckenneth.github.io/writing/how-many-equilibria-did-the-optimizer-miss/https://skckenneth.github.io/writing/how-many-equilibria-did-the-optimizer-miss/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.Sat, 03 Oct 2026 08:20:00 GMTdynamics-networkscomputation-coderisk-decisions https://skckenneth.github.io/writing/what-must-a-traffic-model-remember/https://skckenneth.github.io/writing/what-must-a-traffic-model-remember/A controlled ring-road study separates hidden velocity, projection-induced memory, noisy observation, and numerical sensitivity, asking when a better traffic forecast also gives a better stability diagnosis.Sat, 26 Sep 2026 00:00:00 GMTcities-engineering https://skckenneth.github.io/writing/did-the-hotspot-move-or-did-it-grow/https://skckenneth.github.io/writing/did-the-hotspot-move-or-did-it-grow/Two spatial maps can share a convincing least-cost explanation without revealing the history that produced them. A controlled unbalanced optimal transport study separates endpoint fit, numerical convergence and evidence for movement versus local growth.Sat, 19 Sep 2026 00:00:00 GMTdata-airisk-decisionscities-engineering https://skckenneth.github.io/writing/can-aggregate-observations-bound-an-epidemic/https://skckenneth.github.io/writing/can-aggregate-observations-bound-an-epidemic/Delayed regional totals can support a precise-looking estimate without tightly constraining the hidden state. A six-region synthetic SIR benchmark compares ensemble intervals with validated set bounds, including the cost of bounds that become almost useless.Sat, 12 Sep 2026 00:00:00 GMTdata-airisk-decisionslife-environment https://skckenneth.github.io/writing/when-taking-turns-makes-a-system-unstable/https://skckenneth.github.io/writing/when-taking-turns-makes-a-system-unstable/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.Thu, 10 Sep 2026 00:00:00 GMTdynamics-networks https://skckenneth.github.io/writing/when-early-warnings-cannot-tell-the-difference/https://skckenneth.github.io/writing/when-early-warnings-cannot-tell-the-difference/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.Wed, 09 Sep 2026 00:00:00 GMTdata-ailife-environmentdynamics-networks https://skckenneth.github.io/writing/when-solar-power-changes-fast/https://skckenneth.github.io/writing/when-solar-power-changes-fast/A five-station study asks whether solar prediction intervals remain trustworthy during rapid power changes and missing sensor inputs. Better calibration improves every station, yet the hardest groups still fall far below the intended coverage.Wed, 09 Sep 2026 00:00:00 GMTcities-engineeringrisk-decisionsteaching-research-practice https://skckenneth.github.io/writing/when-starting-over-finds-the-target-faster/https://skckenneth.github.io/writing/when-starting-over-finds-the-target-faster/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.Wed, 09 Sep 2026 00:00:00 GMTrisk-decisionsdynamics-networks https://skckenneth.github.io/writing/assimilating-what-you-can-observe/https://skckenneth.github.io/writing/assimilating-what-you-can-observe/A frozen six-patch EnKF benchmark shows that an explicit aggregate-and-delay observation operator improves synthetic state and peak forecasts, yet undercovers the latent state and therefore earns only a PARTIAL conclusion.Sun, 30 Aug 2026 00:00:00 GMTdata-airisk-decisionslife-environment https://skckenneth.github.io/writing/can-a-mesh-preserve-the-event/https://skckenneth.github.io/writing/can-a-mesh-preserve-the-event/A matched-work experiment asks whether uniform, residual, or goal-oriented finite-element meshes best preserve a growing-domain modal-transition time. In this first smoke test, uniform wins.Sun, 30 Aug 2026 00:00:00 GMTcomputation-codelife-environment https://skckenneth.github.io/writing/from-simulation-to-certificate/https://skckenneth.github.io/writing/from-simulation-to-certificate/A frozen two-compartment positive-system benchmark separates finite spectral checks from verified all-parameter decay bounds and shows a benchmark-specific cost of restricting the quadratic certificate to be diagonal.Sun, 30 Aug 2026 00:00:00 GMTcomputation-coderisk-decisions https://skckenneth.github.io/writing/one-integrator-across-the-fast-slow-boundary/https://skckenneth.github.io/writing/one-integrator-across-the-fast-slow-boundary/A frozen Michaelis-Menten audit separates exact conservation, positivity, and a fixed-step asymptotic limit from accuracy, stiffness failures, and solver-superiority claims.Sun, 30 Aug 2026 00:00:00 GMTcomputation-code https://skckenneth.github.io/writing/random-stress-tests-are-not-certificates/https://skckenneth.github.io/writing/random-stress-tests-are-not-certificates/A deterministic interval benchmark shows exactly what a worst-case certificate contains, and why fixed random, Latin-hypercube, and local-search results remain incumbents.Sun, 30 Aug 2026 00:00:00 GMTrisk-decisionscomputation-code https://skckenneth.github.io/writing/when-a-reduced-ventilation-model-leaves-its-training-regime/https://skckenneth.github.io/writing/when-a-reduced-ventilation-model-leaves-its-training-regime/A frozen synthetic POD and POD-DEIM audit verifies its full-order reference, then stops because both reduced models fail before any declared ventilation shift is applied.Sun, 30 Aug 2026 00:00:00 GMTcities-engineeringcomputation-coderisk-decisions https://skckenneth.github.io/writing/when-a-traffic-solver-invents-a-jam/https://skckenneth.github.io/writing/when-a-traffic-solver-invents-a-jam/A failure-preserving LWR benchmark shows how final shock-grid alignment can make a cell-average norm look exact while threshold arrival and queue accounting remain biased.Sun, 30 Aug 2026 00:00:00 GMTcomputation-codecities-engineering https://skckenneth.github.io/writing/from-pixels-to-patrols/https://skckenneth.github.io/writing/from-pixels-to-patrols/A technical reading of an AI4Nature@AVSS 2026 camera-trap study, tracing how probability calibration reaches a synthetic patrol allocator while keeping programme, evidence, and publication status separate.Sat, 29 Aug 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/writing/how-rare-is-a-flip/https://skckenneth.github.io/writing/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.Sat, 29 Aug 2026 00:00:00 GMTrisk-decisionslife-environmentdynamics-networks https://skckenneth.github.io/writing/when-effective-diffusivity-stops-being-effective/https://skckenneth.github.io/writing/when-effective-diffusivity-stops-being-effective/A verified 24-case synthetic slab benchmark maps where a harmonic effective diffusivity preserves release curves and where finite-cell transients make it miss t50 and t90.Sat, 29 Aug 2026 00:00:00 GMTcomputation-codecities-engineering https://skckenneth.github.io/writing/when-polynomial-chaos-crosses-a-fold/https://skckenneth.github.io/writing/when-polynomial-chaos-crosses-a-fold/A global polynomial and an oracle fold-aligned surrogate receive the same 16 model evaluations on one synthetic CSTR benchmark; the local construction is far more faithful, but the oracle cost is outside the comparison.Sat, 29 Aug 2026 00:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/writing/topology-at-the-edge-of-resolution/https://skckenneth.github.io/writing/topology-at-the-edge-of-resolution/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.Mon, 24 Aug 2026 00:00:00 GMTdata-ailife-environment https://skckenneth.github.io/writing/when-entanglement-expires/https://skckenneth.github.io/writing/when-entanglement-expires/A mathematical-modeling study of how a quantum repeater should trade speed against decoherence when link generation and entanglement swapping are probabilistic.Sun, 09 Aug 2026 00:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/writing/can-adhesion-alone-sort-cells-into-tissues/https://skckenneth.github.io/writing/can-adhesion-alone-sort-cells-into-tissues/A cellular Potts study tests when differential adhesion produces sorting, engulfment, arrested mixtures, or misleadingly similar end states.Sun, 02 Aug 2026 00:00:00 GMTlife-environmentcomputation-code https://skckenneth.github.io/writing/how-much-tail-risk-a-gaussian-model-hides/https://skckenneth.github.io/writing/how-much-tail-risk-a-gaussian-model-hides/A controlled stress test compares Gaussian, Student-t, historical, and extreme-value risk forecasts under volatility clustering, leverage, heavy tails, and jumps.Sun, 02 Aug 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/writing/when-an-american-put-should-be-exercised/https://skckenneth.github.io/writing/when-an-american-put-should-be-exercised/A free-boundary study turns early exercise into an obstacle problem, then audits price, Greeks, convergence, and complementarity across three numerical methods.Sun, 02 Aug 2026 00:00:00 GMTcomputation-coderisk-decisions https://skckenneth.github.io/writing/when-simple-drug-release-laws-stop-being-enough/https://skckenneth.github.io/writing/when-simple-drug-release-laws-stop-being-enough/A hierarchy of empirical and mechanistic dissolution models reveals when a familiar release curve conceals finite-sink transport, parameter trade-offs, and changing regimes.Sun, 02 Aug 2026 00:00:00 GMTdata-aicities-engineering https://skckenneth.github.io/writing/how-noise-flips-a-genetic-switch/https://skckenneth.github.io/writing/how-noise-flips-a-genetic-switch/Deterministic bistability creates two memory states, but finite molecular copy number determines how long a stochastic genetic toggle remains in either one.Thu, 30 Jul 2026 00:00:00 GMTlife-environmentcomputation-codedynamics-networks https://skckenneth.github.io/writing/tracking-mains-noise-without-losing-the-muscle-signal/https://skckenneth.github.io/writing/tracking-mains-noise-without-losing-the-muscle-signal/A reproducible synthetic implementation separates a causal sEMG fast path from a gated frequency tracker, then tests harmonic cancellation, envelope fidelity, and host-Python timing without claiming participant or embedded-device validation.Thu, 30 Jul 2026 00:00:00 GMTdata-ai https://skckenneth.github.io/writing/when-michaelis-menten-stops-being-valid/https://skckenneth.github.io/writing/when-michaelis-menten-stops-being-valid/A 243-case atlas treats Michaelis-Menten kinetics as a testable model reduction and maps where trajectory or event-time errors become important.Thu, 30 Jul 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/writing/when-one-reactor-has-three-temperatures/https://skckenneth.github.io/writing/when-one-reactor-has-three-temperatures/A non-isothermal CSTR can remember its operating path, jump between cold and hot states, and recover ever more slowly before a thermal fold.Thu, 30 Jul 2026 00:00:00 GMTdynamics-networkscities-engineering https://skckenneth.github.io/writing/when-publication-count-selects-the-method/https://skckenneth.github.io/writing/when-publication-count-selects-the-method/A cultural-evolution model shows how publication bias and visible output can select low-effort methods, and when replication audits change that selection pressure.Thu, 30 Jul 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/writing/growing-domain-turing-topology/https://skckenneth.github.io/writing/growing-domain-turing-topology/A verified reaction–diffusion experiment asks when tissue growth preserves a spatial pattern and when it forces peaks to split, merge, or disappear.Tue, 28 Jul 2026 00:00:00 GMTrisk-decisionslife-environmentdynamics-networks https://skckenneth.github.io/writing/heterogeneous-morphoelastic-folding/https://skckenneth.github.io/writing/heterogeneous-morphoelastic-folding/A reduced morphoelastic beam experiment tests whether small spatial changes in stiffness and growth load can steer fold number and location without increasing peak curvature.Mon, 27 Jul 2026 00:00:00 GMTlife-environmentrisk-decisions https://skckenneth.github.io/writing/robust-cstr-safety-envelope/https://skckenneth.github.io/writing/robust-cstr-safety-envelope/A synthetic exothermic-reactor study quantifies how much nominal production is surrendered when a decision must remain below a thermal-risk criterion under uncertain kinetics and heat transfer.Sun, 26 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/writing/positive-conservative-time-stepping/https://skckenneth.github.io/writing/positive-conservative-time-stepping/A stiff transfer-network benchmark compares standard explicit integrators with a linearly implicit update that preserves non-negativity and total mass.Sat, 25 Jul 2026 00:00:00 GMTrisk-decisionsteaching-research-practice https://skckenneth.github.io/writing/scientific-incentives-reliability/https://skckenneth.github.io/writing/scientific-incentives-reliability/An evolutionary agent-based model treats novelty, rigour, and replication credit as competing institutional incentives and maps their discovery–reliability frontier.Fri, 24 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/writing/when-sustainable-harvesting-becomes-a-trap/https://skckenneth.github.io/writing/when-sustainable-harvesting-becomes-a-trap/A stochastic strong-Allee model shows why average sustainable yield can conceal a collapse threshold and why a feedback refuge changes the finite-horizon risk–yield frontier.Fri, 24 Jul 2026 00:00:00 GMTdynamics-networkscomputation-coderisk-decisions https://skckenneth.github.io/writing/rough-volatility-robust-hedging/https://skckenneth.github.io/writing/rough-volatility-robust-hedging/A synthetic hedging experiment freezes one uncertainty-aware no-trade band and tests whether it reduces tail loss and turnover across unseen rough-volatility and cost regimes.Thu, 23 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/writing/intervention-calibrated-neural-odes/https://skckenneth.github.io/writing/intervention-calibrated-neural-odes/A synthetic gene-circuit benchmark compares an unconstrained neural vector field with a sign-structured model under unseen interventions, and finds that feasibility does not guarantee honest uncertainty.Wed, 22 Jul 2026 00:00:00 GMTdata-airisk-decisions https://skckenneth.github.io/writing/when-more-dna-makes-the-wrong-tree-more-certain/https://skckenneth.github.io/writing/when-more-dna-makes-the-wrong-tree-more-certain/A synthetic quartet experiment separates sampling error from model error and shows how a long alignment can give complete bootstrap support to the wrong phylogenetic tree.Wed, 22 Jul 2026 00:00:00 GMTlife-environment https://skckenneth.github.io/writing/dimensional-equation-discovery/https://skckenneth.github.io/writing/dimensional-equation-discovery/A controlled symbolic-regression benchmark asks whether dimensional constraints improve exact equation recovery, shrink the search space, and prevent unit-fragile formulas.Tue, 21 Jul 2026 00:00:00 GMTrisk-decisionsteaching-research-practice https://skckenneth.github.io/writing/sparse-wave-blocking-excitable-media/https://skckenneth.github.io/writing/sparse-wave-blocking-excitable-media/A FitzHugh–Nagumo benchmark freezes an event-triggered local intervention and tests whether it blocks travelling waves under unseen conduction speeds and sensor delays.Mon, 20 Jul 2026 00:00:00 GMTrisk-decisionslife-environment https://skckenneth.github.io/writing/when-randomness-defeats-natural-selection/https://skckenneth.github.io/writing/when-randomness-defeats-natural-selection/A Wright–Fisher experiment shows why a beneficial allele is usually lost when it begins as one copy, how migration can oppose local adaptation, and why a brief bottleneck leaves a lasting genetic deficit.Mon, 20 Jul 2026 00:00:00 GMTlife-environment https://skckenneth.github.io/writing/sequential-nonlinear-model-discrimination/https://skckenneth.github.io/writing/sequential-nonlinear-model-discrimination/A Bayesian sequential-design benchmark chooses forcing experiments that distinguish Van der Pol, Rayleigh, and Duffing mechanisms under a six-experiment budget.Sun, 19 Jul 2026 00:00:00 GMTrisk-decisionsdynamics-networks https://skckenneth.github.io/writing/a-decision-that-survives-the-shift/https://skckenneth.github.io/writing/a-decision-that-survives-the-shift/Distributionally robust optimization asks which decision performs acceptably when the probability model is only approximately known.Thu, 16 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/writing/when-the-fit-is-not-the-model/https://skckenneth.github.io/writing/when-the-fit-is-not-the-model/A close fit can coexist with weak parameter evidence. Identifiability analysis shows when new measurements matter more than another optimizer.Thu, 16 Jul 2026 00:00:00 GMTdata-aidynamics-networks https://skckenneth.github.io/writing/when-treatment-spills-over/https://skckenneth.github.io/writing/when-treatment-spills-over/Network interference changes the meaning of a treatment effect. Exposure mappings connect experimental design, estimands, and defensible causal claims.Thu, 16 Jul 2026 00:00:00 GMTdata-aidynamics-networks https://skckenneth.github.io/writing/when-the-timetable-lies/https://skckenneth.github.io/writing/when-the-timetable-lies/A reproducible classroom experiment on predictive ventilation, unannounced room changes, shared fan limits, and the price of an occupancy buffer.Wed, 15 Jul 2026 00:00:00 GMTcities-engineeringrisk-decisions https://skckenneth.github.io/writing/designing-for-the-missing-sensor/https://skckenneth.github.io/writing/designing-for-the-missing-sensor/An editorial account of a synthetic water-network study that places pressure sensors for useful evidence even after one measurement disappears.Mon, 13 Jul 2026 00:00:00 GMTrisk-decisionscities-engineeringdynamics-networks https://skckenneth.github.io/writing/modeling-workflow/https://skckenneth.github.io/writing/modeling-workflow/A compact workflow for assumptions, model choice, computation, validation, limitations, and communication.Mon, 13 Jul 2026 00:00:00 GMTteaching-research-practice https://skckenneth.github.io/writing/the-alarm-before-the-heat/https://skckenneth.github.io/writing/the-alarm-before-the-heat/Building and stress-testing a graph-aware battery thermal warning model without confusing a synthetic result for a safety claim.Mon, 13 Jul 2026 00:00:00 GMTrisk-decisionsdata-ai https://skckenneth.github.io/writing/climate-driven-dengue/https://skckenneth.github.io/writing/climate-driven-dengue/A guide to what a synthetic reaction–diffusion experiment can—and cannot—show about climate-sensitive transmission.Fri, 26 Dec 2025 00:00:00 GMTlife-environmentrisk-decisions https://skckenneth.github.io/writing/interpolation-guide/https://skckenneth.github.io/writing/interpolation-guide/A topic guide connecting polynomial interpolation, Chebyshev nodes, and the Gibbs phenomenon.Sun, 21 Jul 2024 00:00:00 GMTcomputation-code