Fit the two-process sleep model¶

Question¶

Which sleep-pressure parameters are supported by this record?

See every package-generated example · Read the complete analysis pipeline

When to use¶

Use this after immobility sleep scoring when homeostatic sleep pressure and a circadian threshold are to be modelled without claiming uniquely identified parameters.

Example figure¶

Fit the two-process sleep model output generated by Circadian Workbench

This deterministic example is calculated by the two_process_fit action and drawn by render_two_process_svg, the same renderer used for publication export. Empty or withheld elements are therefore visible exactly as they are in a real result.

import circadian_workbench as cw

cw.call("two_process_fit", sleep_result=sleep_result, period_hours=24, acrophase_hours=4)

Required inputs and controls¶

The public function is the registered action below. settings= is accepted as a friendlier alias for config= by cw.call; the calculation stores the complete normalized config in provenance.

Function reference¶

cw.call("two_process_fit", sleep_result, period_hours=24.0, acrophase_hours=0.0, config=None)

Arguments and parameters¶

Name	Type	Required	Default	Units	Meaning
`sleep_result`	object	yes	—	-	An immobility_sleep result, whole. A record it refused to score is refused here for the same reason rather than re-derived.
`period_hours`	float	no	`24.0`	hours	Fixed cycle of the two-process sleep fit; omitted or null uses the installed reference-cycle default, not a search range.
`acrophase_hours`	number	no	`0.0`	hours	Circadian-term acrophase of the sleep model; omitted or null uses zero on the declared cycle.
`config`	object	no	`null`	-	Partial scientific settings. Omitted or None values use the shared installed defaults; invalid fresh values are rejected. Run describe_config for names, meanings, units, bounds and choices. Explicitly load old saved mappings with load_saved_settings to report compatibility conversions.

Every nested config key, default, allowed value, and purpose is listed in the complete configuration reference.

How it works¶

Sleep pressure rises exponentially while awake and falls exponentially while asleep. Repeated optimisation retains every parameter set that ties the best mismatch, so the result is a family rather than an unjustified single fit.

$$ \frac{dS}{dt}=\frac{U-S}{\tau_w}\ \text{awake},\qquad \frac{dS}{dt}=\frac{L-S}{\tau_s}\ \text{asleep} $$

Implementation: two_process.py::two_process_fit.

Outputs and interpretation¶

The result contains measured and predicted sleep profiles, the tied parameter ensemble and intervals, mismatch, transition coverage, identifiability, convergence, day-to-day scatter, verdict, and notes.

cw.call returns a Result: use .data for calculated values, .warnings for scientific qualifications, .provenance for version and input identity, .script for an equivalent replay script, and .files for saved outputs.

Limitations¶

The public inputs are the complete sleep result, circadian period, acrophase, and config; optimiser bounds and starting values are internal. Inadequate transitions or days are refused, and parameters are reported as ranges when not identifiable.

Example¶

The figure above is a real package result from a seeded, redistributable synthetic dataset. Its editable SVG embeds the exact plotted data and provenance and is included with a rendered preview in the installed help. The separate authoring bundle retains figure_data_two-process-fit.csv, a standalone plot_two-process-fit.py and source hashes; these companion files are not installed application files.

Methods text¶

A two-process sleep model was fitted to the complete immobility-sleep result by repeated bounded optimisation; all parameter sets tying the best mismatch were retained and parameter ranges were reported when the record did not identify a unique fit.