Recovery Time Constant Depression
Fit log(1−recovered fraction) against recovery interval to estimate exponential recovery tau; this model assumes an asymptotic recovery fraction of one.
Description
A single-exponential recovery model becomes linear in the logarithm of the unrecovered fraction.
A single-exponential recovery model becomes linear in the logarithm of the unrecovered fraction. Its negative slope determines the recovery time constant.
The tool returns recoveryTauMs (recovery tau ms); logDeficitIntercept (log deficit intercept); fitRSquared (fit r squared). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Recovery Time Constant Depression
Use Recovery Time Constant Depression when you already have recoveryIntervalsMs, recoveryFractions and want recoveryTauMs, logDeficitIntercept, fitRSquared. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Recovery Time Constant Depression and understand its results
- Enter recoveryIntervalsMs, recoveryFractions using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read recoveryTauMs, logDeficitIntercept, fitRSquared. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| recoveryIntervalsMs | Recovery intervals ms | list of number | Required |
| recoveryFractions | Recovery fractions | list of number | Required |
Use increasing nonnegative intervals and aligned fractions in [0,1), then fit an intercept in log-deficit space. Require a negative fitted slope.
ln(1−recovery) ≈ intercept+slope×intervalMs; tauMs = −1/slope The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"recoveryIntervalsMs": [
0,
10,
20
],
"recoveryFractions": [
0,
0.6321205588285577,
0.8646647167633873
]
},
"output": {
"recoveryTauMs": 10,
"logDeficitIntercept": 0,
"fitRSquared": 1
}
}Limitations and assumptions
Complete recovery cannot be logged and is rejected. The model has one decay component and does not fit signal-space errors.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Steady State Depression: Summarize the last supplied train responses relative to the first response; a sampled tail is not proof that a true steady state was reached, and facilitation yields negative depression. Ebbinghaus Forgetting Curve: Evaluate a caller-calibrated exponential forgetting approximation with a nonzero floor; elapsed times and tau share one unit, and this is not a universal Ebbinghaus law.
Methodological background: Least squares estimation.1
References
-
Least squares estimation — NIST/SEMATECH
Similar or alternative tools
- Steady State Depression
Summarize the last supplied train responses relative to the first response; a sampled tail is not proof that a true steady state was reached, and facilitation yields negative depression.
- Ebbinghaus Forgetting Curve
Evaluate a caller-calibrated exponential forgetting approximation with a nonzero floor; elapsed times and tau share one unit, and this is not a universal Ebbinghaus law.