CHORD

Circadian Harmonic Oscillation Resolution and Disentanglement

A two-stage statistical framework for detecting 12-hour ultradian rhythms in transcriptomic data and disentangling independent oscillations from circadian harmonic artifacts.

Paper: Fang C. et al. (2026) CHORD: Detecting and Classifying Independent 12-Hour Rhythms from Circadian Harmonics. (under review).

The Problem

Gene expression time-series often show 12-hour periodicity. This can arise from two fundamentally different mechanisms:

• Independent 12h oscillators — driven by dedicated molecular pathways (e.g., IRE1α-XBP1s ER stress cycle)
• Circadian harmonics — mathematical artifacts of non-sinusoidal 24h waveforms

Standard spectral methods (Fourier, Lomb-Scargle, JTK_CYCLE) cannot distinguish between these two cases. CHORD solves this.

How It Works

Stage 1 — Detection: Fuses four complementary methods (parametric F-test, JTK_CYCLE, RAIN, harmonic regression) via the Cauchy Combination Test (CCT), providing robust detection under arbitrary dependence.

Stage 2 — Disentanglement: Evaluates 12 independent lines of evidence — BIC-based Bayes factors, phase freedom F-tests, amplitude ratios, VMD-Hilbert instantaneous frequency, bispectral bicoherence, and more — to classify each detected rhythm as independent or harmonic.

Performance

Synthetic benchmark: 15 scenarios × 50 replicates = 750 genes, 48 timepoints.

On real data (Hughes 2009, 11 datasets), CHORD recovers 60.5% of known 12h genes (F1 = 0.590), outperforming all six comparison methods. BMAL1-KO validation shows 72% reduction in harmonic classification, confirming biological validity.

Installation

pip install chord-rhythm

From source:

git clone https://github.com/chenpg2/CHORD-Circadian-Harmonic-Oscillation-Resolution-and-Disentanglement.git
cd CHORD-Circadian-Harmonic-Oscillation-Resolution-and-Disentanglement
pip install -e ".[dev]"

Optional extras:

pip install chord-rhythm[bayes]   # Bayesian inference (NumPyro/JAX)
pip install chord-rhythm[deep]    # Neural ODE (PyTorch)
pip install chord-rhythm[viz]     # Visualization (matplotlib)
pip install chord-rhythm[full]    # Everything

Quick Start

Single gene

import numpy as np
from chord.bhdt.classifier import classify_gene

t = np.arange(0, 48, 2.0)  # 2h sampling over 48h
y = expression_data          # 1D array

result = classify_gene(t, y)
print(result["classification"])  # 'independent', 'harmonic', 'ambiguous', ...
print(result["confidence"])      # continuous score in [-1, 1]

Batch analysis

from chord.bhdt.classifier import batch_classify

results = batch_classify(t, Y_matrix, gene_names=gene_list)
# Returns DataFrame with classification for each gene

Command line

chord detect expression.csv -t 0,2,4,...,46 -o results.csv

Key Results

• Detection: F1 = 0.957 on synthetic data; 60.5% known 12h gene recovery on real data
• Disentanglement: F1 = 0.939 with perfect specificity (zero false harmonic calls)
• Biological validation: BMAL1-KO harmonic ratio drops 32.1% → 8.9% (72% reduction)
• Cross-species: 100% recovery of 9 conserved 12h genes across 11 datasets
• Robustness: 50% detection at SNR = 0.5; maintains advantage across all sampling resolutions
• Speed: 9.7 ms/gene median; ~3 min for 20,000 genes on single CPU

Project Structure

chord/
├── src/chord/
│   ├── bhdt/                  # Core algorithm
│   │   ├── classifier.py      # Two-stage classifier (main entry point)
│   │   ├── detection/         # Stage 1: CCT-fused detection
│   │   ├── inference.py       # Evidence computation
│   │   ├── models.py          # M0/M1 model fitting
│   │   ├── bispectral.py      # Bispectral bicoherence
│   │   ├── hilbert_if.py      # VMD-Hilbert IF analysis
│   │   └── bootstrap.py       # Parametric bootstrap LRT
│   ├── simulation/            # Synthetic data generation
│   ├── data/                  # Dataset loaders (GEO)
│   └── benchmarks/            # Method comparison framework
├── scripts/                   # Benchmark and analysis scripts
├── tests/                     # Test suite
├── docs/                      # Documentation
└── results/                   # Benchmark results (v9)

Citation

@article{fang2026chord,
  title={CHORD: Detecting and Classifying Independent 12-Hour Rhythms
         from Circadian Harmonics},
  author={Fang, Cong},
  year={2026}
}

License

MIT License. See LICENSE.