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A sun valve automatically restricts a gas light's supply in daylight and allows it again as illumination falls. In Gustaf Dalén's design, a blackened rod and three polished rods respond differently to sunlight. Their relative thermal expansion operates the gas valve through a membrane; a pilot flame permits relighting. The museum dates this design to 1907.^[ref]

The useful comparison is between two thermal responses. Both kinds of rod expand when warmed; a dark surface can absorb more incident radiant power, so its temperature rises more. Comparing their extensions can reject a common ambient-temperature change while responding to illumination. The mechanism converts light into heat, heat into a difference of length, and that difference into a change of gas flow. Differential thermal model of a sun valve makes those assumptions quantitative.

By Yen-Chi Chen, explicitly named on the lecture page. Authored notes in UW STAT 535: Statistical Machine Learning, Autumn 2026, hosted on the University of Washington faculty website. No separate lecture publication or revision date is established.

Online text: faculty.washington.edu/yenchic/25A_stat535/Lec12_bootstrap.html

Cited passages: The Bootstrap, resampling procedure; High level idea of how bootstrap works, conditional empirical sampling law; Bootstrap and Statistical Functionals, conditional variance and consistency; Failure of the bootstrap, uniform-endpoint counterexample.

Cited passages: equations 10.7–10.20, decay law, half-life, mean lifetime, and activity.

The second, symbol $\mathrm{s}$, is the SI base unit of time. Its definition fixes the unperturbed frequency of the ground-state atomic transition between levels split by hyperfine structure in caesium with mass number $133$ to exactly $9192631770\mathrm{Hz}$. One second therefore corresponds to that many cycles of the specified electromagnetic radiation.^[ref]

A practical atomic clock realizes the reference by interrogating atoms and controlling a reference oscillation. Magnetic fields, motion and environmental effects require corrections: an exact unit definition does not make every physical realization free of measurement uncertainty.

A unit of area used for scattering cross-sections.