Can a Worm Dance to Chopin?

The project

Biology + Mathematics + Music — two directions

C. elegans has exactly 302 neurons and 96 body wall muscles — the simplest animal with a fully mapped connectome (White et al. 1986). v1.x turns that connectome into a composer: NAML algorithms align the worm's body wave to Chopin's nocturne (best F1 = 0.933). v2.0.0 inverts the pipeline: Chopin's patterns are extracted via RSVD + K-means, ranked by Pearson excitability, and mapped onto 96 muscles — the worm dances to the music in real time in your browser.

302

C. elegans neurons
(complete connectome)

96

body wall muscles
= 96 piano pitches

8

Chopin musical states
(K-means K*=8)

0.933

best musical F1
(v1 Step 9 Worm+Time)

229 s

Chopin nocturne
fully covered (v1 + v2)

7

NAML methods
in v2 pipeline

v2.0.0 — Live demo

The Worm Dances to Chopin

Chopin's Nocturne in C# minor is decomposed into K*=8 recurring patterns via RSVD (Eckart-Young) + K-means (silhouette criterion), ranked by biological Pearson excitability, and mapped to 96 body-wall muscles via least-squares regression. Body wave, neural circuit panel, locomotion trail, and pattern timeline — all live.

Step 1 · L06–L09

RSVD — Eckart-Young

M ∈ ℝ^{56×11711} → U_k Σ_k V_k^T, k=12 (90% variance)

Step 2–3 · L10 · Lab02

K-means + Silhouette

Cluster V_k time frames → K*=8 musical states

Step 4 · AppStat

Pearson Excitability

max|r(V_p[:,i], Z_worm[:,j])| ranks patterns by biological resonance

Step 5 · L07/L09 · Lab03

Least Squares W_nm

lstsq(Z_worm, V_mus) → neural→96-muscle map

Step 6

Synthetic body wave

4 piano modes → synthMusFromVp → locomotion (FORWARD/TURN/HALT)

📊 Full NAML presentation 📓 Notebook 06 ↗ Full-screen demo

Sub-projects

Modules & Presentations

Each module targets a different PoliMi course and a different layer of the pipeline. Presentations open in-browser (Reveal.js · CDN-only · works anywhere). Notebooks open in nbviewer — no install required.

🧠

NAML 2025-26 · Prof. Miglio

PyANNOW

v2.0.0 (inverse): Chopin → RSVD (Eckart-Young, k=12) → K-means (K*=8) → Pearson excitability → lstsq → 96-muscle worm dance. Live browser demo above ↑

v1.x (forward): 10-step Worm→Music journey: SVD → K-means → Ridge → MLP → Adam → L-BFGS → RF → PINN → Worm+Time hybrid MLP (F1=0.933) → full-piece 229 s WAV.

Boyle 4×24 model · 96-cell simulation · Karplus-Strong piano synthesis.

📊 Presentation v2 (live dance) 📊 Presentation v1 📓 NB06 — v2 inverse pipeline 📓 NB03 — v1 full progression 📓 NB05 — Step 9b audio 📓 NB04 — Chopin score net ⬡ Source

📊

AppStat 2026 · Profs. Beraha & Andre

wormuse-analytics

Applied Statistics pipeline for worm-music data:
PCA + t-SNE + UMAP on neural activity → K-means / DBSCAN / GMM clustering of motor states → OLS + Ridge diagnostics (VIF · Breusch-Pagan · Durbin-Watson) → Logistic regression + Random Forest classification → ROC/AUC for onset detection quality → Statistical validation of the NAML pipeline.

📊 AppStat Presentation 📓 NB01 — Lecture audit ⬡ Source

🔧

AMSC · Prof. Formaggia

wormuse-sim

C++ Sibernetic wrapper (RAII · shared-library ABI) → OpenWorm Docker integration (Sibernetic SPH + C302 neural) → MPI distributed parameter search → Azure NC24-A100 GPU acceleration of the PINN training loop → Piano FEM modal synthesis upgrade (Chabassier 2014).

Presentation and notebooks in a future release.

📌 In development — AMSC project (2026) ⬡ Source

Note on audio: The NAML presentation includes HTML5 audio players that stream directly from GitHub Releases v1.0.0 — no download required. To generate the audio locally, run Step 10 in 03_pyannow_naml_progression.ipynb which produces step_outputs/worm_mlp_full.wav and chopin_synth_full.wav. All slides, equations, and code are fully functional online.

Algorithm progression

PyANNOW — 10 NAML Steps

Each step introduces one new method from the NAML course and measures its impact on musical F1 (onset timing accuracy, ±50 ms tolerance). Step 0 deterministic body-wave is the floor; Step 9 Worm+Time MLP is the best.

STEP 0

Body-wave baseline

F1 = 0.217

Deterministic · IOI=0.447

STEP 1a/b · L06/L09

SVD + Procrustes

F1 = 0.095 – 0.186

302-D → k=4 PCs · Eckart-Young theorem

STEP 2 · L08/L10

K-means clustering

F1 = 0.109

Motor primitives · unsupervised

STEP 3 · L07/L11

Ridge regression

F1 = 0.286

▲ first supervised · beats baseline

STEPS 4-6 · L14-22

MLP + Adam + L-BFGS

F1 ≈ 0.25

JAX autodiff · tanh · 2-stage optimiser

STEP 7 · AppStat Lec07

Random Forest

F1 = 0.872

▲▲ 100 trees · OOB=0.829 · huge leap

STEP 8a/b · L14+L27

ODE + PDE PINN

Physics focus

Locomotion ODE · 1D wave eq. along body

STEP 9 · NB04 + AppStat ★

Worm+Time hybrid MLP

F1 = 0.933 ★ BEST

Fourier(27-D) + worm PCA · 10s window
+8.7pp above NB04 time-only ceiling

STEP 9b · L27

Physics-residual MLP

F1 ≈ 0.933

+ ODE residual feature · tied with Step 9

STEP 10 · NB04+Step9b

Full-piece 229s generalization

Full-length WAV 🎵

Train on full piece · t/T∈[0,1] always · no extrapolation

All notebooks

Jupyter Notebooks — v1.x forward + v2.0 inverse

Open in nbviewer (rendered, no install needed) or view directly on GitHub (native .ipynb rendering). Run locally: clone the repo and pip install pyannow && jupyter lab

Notebook	Module	Key topics	Open
06_chopin_patterns_worm_dance_v2 v2.0.0 inverse pipeline · Chopin → worm dance · fully executed	NAML	Piano-roll M∈ℝ^{56×11711} · RSVD (Eckart-Young, k=12) · K-means K*=8 · Pearson excitability · lstsq W_nm · synthetic body wave · worm dance JS viz	nbviewer GitHub
03_pyannow_naml_progression Main PyANNOW notebook · Steps 0-10 · fully executed	NAML	SVD · K-means · Ridge · MLP · Adam · L-BFGS · RF · PINN (ODE+PDE) · Worm+Time MLP · NB04+Step9b full-piece · F1=0.933	nbviewer GitHub
05_pyannow_step9b_audio Step 9b · full 229s Chopin piece · Karplus-Strong piano synthesis	NAML	Step 9b · full-piece (229 s) · Karplus-Strong piano · physics-residual MLP · audio render pipeline · F1=0.933	nbviewer GitHub
04_chopin_score_net NB04 · pure Fourier time-net · F1=0.858 ceiling	NAML	Fourier positional encoding · full-piece training · NB04 recipe · onset detection · worm biology headroom proof	nbviewer GitHub
02_chopin_worm_optimizer Parameter optimiser for the Boyle worm model	NAML	Boyle 4×24 model · ion-channel parameters · Nelder-Mead · Adam · onset loss surface	nbviewer GitHub
01_appstat_lecture_audit AppStat methods applied to worm-music data	AppStat	PCA · t-SNE · UMAP · clustering (K-means/DBSCAN/GMM) · OLS + VIF · RF · ROC/AUC · statistical validation	nbviewer GitHub
scientific_foundation_demo Mathematical foundations · cross-system equivalence	docs	Worm ODE ↔ piano PDE structural correspondence · PINN residual · Boyle model derivation · 20-row equivalence table	nbviewer GitHub