Check the simulator against Q-matrix theory for multi-state mechanisms

[remislp]

test_scsim.py checks the two-state CO mechanism, where the means are 1/alpha and 1/beta. That is the easy case: with one open and one shut state the dwell times are single exponentials, and a simulator can get them right while getting the multi-state case wrong.

These check CH82 and AChR_diamond, where the answer is a Q-matrix expression rather than a reciprocal rate:

• the ideal means, phi_A (-Q_AA)^-1 u and phi_F (-Q_FF)^-1 u;
• P(open) against the equilibrium occupancies;
• and, after a dead time is imposed, the apparent means against scalcslib.exact_mean_open_shut_time.

The last one earns its keep

Nothing else ties the simulator to the missed-events code. test_apparent_means.py checks that code against closed forms and against itself by another route, but never against data. An error of two dead times in the apparent mean open time — exactly what was there until the dARSdS sign was corrected in #20 — is caught here even if every analytic cross-check had been adjusted to agree with it.

Verified by mutation: putting the error back (+ tres → - tres in exact_mean_open_shut_time) makes both mechanisms fail; reverting restores them.

How much power, measured rather than asserted

The sensitivity depends on the dead time as a fraction of the mean open time, so it differs by mechanism. At 400 000 intervals and tres = 25 µs:

mechanism	one t_res	two t_res	actual disagreement
CH82	3.4 SE	6.7 SE	1.3 SE
AChR_diamond	5.6 SE	11.3 SE	1.0 SE

So at the 4 SE tolerance a two-dead-time error is caught on both, and a one-dead-time error on the AChR mechanism but not on CH82, whose open times are a hundred times the dead time.

test_the_apparent_open_time_check_has_power asserts the two-dead-time case everywhere and the one-dead-time case only where the measurement supports it. An earlier draft claimed one dead time everywhere and failed honestly at 100 000 intervals — which is how the numbers above came to be measured rather than guessed. Claiming more than that would make a passing suite mean less than it appears to.

Tolerances

Multiples of the measured standard error rather than fixed percentages, so the tests neither pass by being loose on a sharp quantity nor fail by being tight on a noisy one. Seeds are fixed, so a failure is a real disagreement rather than a bad draw.

Marked slow: 616 passed with them, 598 in 32 s without.

🤖 Generated with Claude Code