nugap 0.5.0

Vinnicombe nu-gap metric and a pipeline for comparing time-course data across two conditions

nugap

Detect condition-specific changes in dynamics using the Vinnicombe ν-gap metric.

nugap is a lightweight Python implementation of the Vinnicombe ν-gap — a bounded (0–1) distance between linear dynamical systems from robust control theory — together with the model identification and statistics needed to ask a practical question of two-condition time-course data:

Which variables, or which relationships between them, change their dynamical behaviour between conditions?

(for example wild type vs mutant, or untreated vs treated). Comparisons of expression level answer a different question and are blind to changes in timescale, gain or phase. The ν-gap is defined directly on dynamical models, so it is not: two systems close in ν-gap behave the same way under feedback, and a large ν-gap marks a genuine change in dynamics.

Installation

pip install nugap

Requires Python ≥ 3.10. The core and pipelines depend only on NumPy, SciPy and pandas; the plotting helpers additionally use Matplotlib and NetworkX.

Tutorial

A guided, runnable tutorial covers the metric, model fitting, and the two-condition network comparison end to end:

• Open in Colab: https://colab.research.google.com/github/comparativechrono/nugap/blob/main/tutorial_nugap.ipynb
• View on GitHub: tutorial_nugap.ipynb

Quick start

The ν-gap between two systems (coefficients in descending powers of s):

from nugap import tf, nu_gap

P1 = tf([1], [1, 1])     # 1/(s+1)
P2 = tf([1], [1, 3])     # 1/(s+3)
nu_gap(P1, P2)           # -> 0.447   (0 = identical, 1 = maximally different)

Comparing a whole interaction network between two conditions, with replicate-based significance:

from nugap import compare_network

# data_A, data_B: dict {variable_name: array of shape (replicates, timepoints)}
# t: the common time vector
edges = compare_network(data_A, data_B, t, order=1, min_r2=0.5)

edges.query("q_global < 0.1")   # relationships rewired between conditions (FDR < 10%)

What it provides

• nu_gap — the Vinnicombe ν-gap for SISO systems in continuous or discrete time, with an optional frequency-band restriction (band=) and a switchable winding-number test (check_winding=) for oscillatory data.
• Model identification — fit_first_order, fit_model, fit_arx, fit_prony, with simulation-based fit quality and an optional DC-gain floor (min_dc_gain=); plus the dc_gain helper.
• compare_conditions — per-variable comparison of dynamics between two conditions, with a fit-quality reliability flag.
• compare_network — pairwise interaction-network comparison: a low-order model is fitted to every ordered pair of variables in each condition, the ν-gap is taken between conditions, and significance comes from a replicate-derived empirical null with Benjamini–Hochberg FDR control.
• Plotting — nugap.viz (volcano plot, hub network, hub bar plot).

How it works

For each variable or pairwise interaction, nugap fits a low-order linear input–output model under each condition, then measures the ν-gap between the fitted models. Because models are compared on mean-centred trajectories, the metric reflects changes in the relationship — timescale, gain or phase — rather than in absolute level. With biological replicates, the spread of within-condition ν-gaps provides an empirical null and a per-edge noise floor, against which between-condition changes are tested and FDR-controlled.

The models are single-input single-output, so an edge captures a pairwise input–output relationship, not proven causation.

Correctness

The ν-gap implementation is verified by several independent routes — exact closed-form values, an algebraic invariance of the chordal metric, an independent reference implementation, and the Vinnicombe robust-stability theorem — and is cross-checked against MATLAB's gapmetric (Robust Control Toolbox), which it reproduces to within ~10⁻⁶. The scripts are in validation/, with a fast subset run on every commit.

Citing

If you use nugap in your work, please cite the software and the accompanying methods paper:

Hearn, T. J. nugap: condition-specific changes in dynamical relationships via the
Vinnicombe ν-gap. Software archive: Zenodo, DOI: 10.5281/zenodo.XXXXXXX.

<methods paper reference — to be added>

License

Released under the MIT License. Copyright © 2026 Tim Hearn. See LICENSE.