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Phase-Response Curve Calibration

Diagnostic estimation — instantiates Decentralized Phase Locking

Maps how much a unit's timing shifts in response to a stimulus delivered at each point in its cycle — including where the same nudge advances versus delays.

Before you can couple oscillators well, you have to know how each one responds. Phase-Response Curve Calibration measures the mapping from when in its cycle a unit receives a stimulus to how much its phase shifts as a result. The point it makes visible, and that no coupling law can assume away, is that the response is not constant: the very same nudge that advances a unit early in its cycle may delay it later, and barely move it in a dead zone between. It is a diagnostic — it characterizes the oscillator against its own uncoupled baseline and hands the resulting curve to whatever mechanism does the correcting. It does not push anything; it tells the pushers how hard, and which way, a push will land.

Example

A traveler crossing six time zones wants to reset their body clock, and light is the lever — but light's effect depends entirely on when it arrives. Bright light in the subjective evening pushes the clock later; the same light near subjective dawn pushes it earlier; around subjective midday it does almost nothing. Calibrating this response (illustratively: a shift of ≈1–2 hours per well-timed exposure, of opposite sign in the two windows, near zero in the dead zone) is exactly what converts a useless instruction like "get more light" into an actionable one: seek light at 7 a.m., avoid it at 11 p.m. The curve, not the raw dose, is the object worth having — and the human light phase-response curve it illustrates is a real, named relationship.

How it works

What distinguishes the calibration from ordinary monitoring:

  • Baseline first. It measures each unit's uncoupled period, drift, and uncertainty; the response is then defined as a deviation from that baseline.
  • Perturb across the whole cycle. A controlled stimulus is applied at systematically varied phases, and the resulting shift recorded at each — producing magnitude and sign as a function of phase.
  • Classify the response shape. Small, smooth curves (weak resetting) behave very differently from large ones that can reset the oscillator outright; the calibration reveals which regime a unit is in.

Tuning parameters

  • Stimulus amplitude — larger probes reveal strong-resetting behavior but risk disrupting the oscillator; smaller stays in the gentle, near-linear regime.
  • Phase resolution — how finely the cycle is sampled; a finer curve costs more trials.
  • Baseline observation length — longer runs pin down drift and uncertainty but spend time.
  • Perturbation fidelity — whether the test stimulus matches the real operational coupling, or only approximates it.
  • Per-unit vs population-average curve — one shared curve is cheap but wrong for every individual when units are heterogeneous.

When it helps, and when it misleads

It earns its place precisely where units respond asymmetrically — where a correction that helps at one phase actively hurts at another. Without the curve, a well-meant nudge applied in the delay window when you wanted an advance will push a unit the wrong way; with it, corrections land where they help.

It misleads when the curve is trusted past its measurement conditions. A response measured at test amplitude may not hold at operating amplitude, and a population-average curve can be wrong for every single member when the population is heterogeneous. The classic misuse is measuring one convenient point and extrapolating an entire curve from it, or reusing a stale curve after the system has changed. The discipline is to re-measure at the amplitude and coupling you actually operate at, and to keep per-unit curves whenever heterogeneity matters.[1]

How it implements the components

  • intrinsic_frequency_and_phase_baseline — the calibration begins by measuring each unit's uncoupled period, drift, and uncertainty; that baseline is the reference the response is measured against.
  • coupling_strength_and_gain_profile — the response curve is the gain profile: how large a shift a given stimulus produces at each phase, and where it flips sign, telling every coupling mechanism how hard and which way to push.

It does not choose a neighbor set or apply the correction — that is Nearest-Neighbor Phase Nudging — nor find the population's capture threshold empirically, which is Weak-Coupling Ramp Trial, though the curve predicts it.

Notes

The curve is a measurement, not a controller. It informs how to couple but holds no phase itself; a beautifully measured response left unconnected to a coupling law changes nothing. Its value is entirely in being consumed by the mechanisms that act.

References

[1] A phase-response curve (or phase-resetting curve) is the established way to characterize how an oscillator's timing shifts as a function of the phase at which a stimulus arrives. Its central lesson — that the same input advances or delays depending on when it lands — is why coupling designed from an average or single-point response can systematically push units the wrong way. ↩