Education

Question

How much of an epidemic's transmission history can be recovered from hospital admissions alone?

Method

A SIRS compartmental model with piecewise-constant transmission, fitted to 1,495 days of Dutch COVID-19 hospital admissions. The recovered reproduction number is then compared with RIVM's independently published estimate, which the model never sees during fitting.

Result

At the model's 21-day resolution, the recovered reproduction number correlates 0.804 with RIVM and agrees on the direction of change 81.5% of the time. More flexibility improves the fit to admissions but eventually makes the hidden transmission path worse: the AIC-selected 219-parameter model falls to 0.173 daily correlation.

Artifacts

PageProject summaryPDFPaper41 pp · EN

2026 · Written in English

Question

Can the same theorem be explained once with very little mathematical background and once through a formal proof?

Method

Two treatments built around the same example: a four-page introduction using simulation and an exact exponential example, and a nine-page proof using characteristic functions and Lévy's continuity theorem.

Result

As the sample size grows, the distribution of the mean becomes narrower and less skewed; for exponential data the skewness falls exactly as 2/√n. The short version makes that convergence visible, while the longer version proves why normal convergence occurs in general under the theorem's assumptions.

Artifacts

PageProject summaryPDFGeneral reader4 pp · NLPDFProof9 pp · NL

2026 · Written in Dutch

Question

How does the quadratic map move from a stable fixed point through period doubling into chaotic dynamics?

Method

Analytical derivation of fixed and periodic points and their stability, followed by numerical computation of successive bifurcations and the dynamics beyond the analytically tractable cases.

Result

Successive period-doubling intervals shrink by ratios 4.234, 4.552, 4.646 and 4.664, converging rapidly toward the Feigenbaum constant 4.669202. Beyond the accumulation point, chaotic dynamics coexist with stable periodic windows.

Artifacts

PageProject summaryPDFPaper25 pp · EN

2026 · Written in English