comp-neuro-projects

Computational Neuroscience — from biophysics to information theory
Applied to real EEG signals and epilepsy detection

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Overview

Two interconnected projects exploring the bridge between neural biophysics and information theory, applied to real brain signals.

Hodgkin-Huxley (single neuron)
        ↓
Network of 20 H-H neurons → simulated EEG
        ↓
Complexity metrics (LZC, entropy)
        ↓
Real EEG — motor imagery (EEGBCI) + epilepsy (CHB-MIT)
        ↓
Finding: LZC drops during epileptic seizures

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Notebooks

1. comp_neuro_v1.ipynb — Hodgkin-Huxley + Information Theory

Part 1 — Hodgkin-Huxley model (1952)

Full biophysical simulation of the action potential from scratch using the original 4-ODE system:

$$C_m \frac{dV}{dt} = I_{ext} - g_{Na} m^3 h (V - E_{Na}) - g_K n^4 (V - E_K) - g_L (V - E_L)$$

• Action potential at different input currents (f-I curve)
• Na⁺/K⁺ ionic channel dynamics visualised
• Network of 20 coupled H-H neurons with synapses
• Simulated EEG as emergent mean field

Key finding: The f-I curve directly maps to EEG frequency bands — theta, alpha, beta, and gamma oscillations emerge from neuronal firing rates, not from arbitrary convention.

Part 2 — Information-theoretic complexity metrics

Metric	What it measures
Permutation Entropy	Distribution of ordinal patterns
Sample Entropy	Self-similarity across scales
Lempel-Ziv Complexity (LZC)	Number of unique substrings
Spectral Entropy	Power distribution across frequencies

Applied to:

• Simulated H-H signal (theoretical baseline)
• Real EEG — resting vs motor imagery (EEGBCI, subject 1, channel Cz)
• Real EEG — interictal vs preictal vs ictal (CHB-MIT chb01)

Statistical results (resting vs motor, Mann-Whitney):

Metric	p-value	Significance
Permutation Entropy	0.3759	n.s.
Sample Entropy	0.0043	**
LZC	0.0412	*
Spectral Entropy	0.1666	n.s.

Sample Entropy and LZC significantly distinguish resting from motor imagery — the motor state generates more complex, less predictable signals.

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2. eeg_epilepsy_v1.ipynb — Seizure Detection (CHB-MIT)

Dataset: CHB-MIT Scalp EEG (PhysioNet) — patient chb01, 5 files with annotated seizures

Pipeline:

Raw EEG (256 Hz, 23 channels)
    ↓  Bandpass 0.5–50 Hz + Notch 50 Hz
    ↓  Segment: 10s windows, 50% overlap
    ↓  Features: spectral bands + line length + statistical moments
    ↓  Random Forest / SVM / Gradient Boosting
Interictal / Preictal / Ictal classification

Labels:

• Interictal — ≥1 hour from any seizure
• Preictal — 5 minutes before seizure onset
• Ictal — during seizure

Feature engineering:

• Relative band power: delta, theta, alpha, beta, gamma
• Signal variance and mean absolute amplitude
• Line length — sum of absolute differences between consecutive samples, sensitive to epileptiform spikes

The line length feature is particularly motivated: neurologists visually detect epileptic spikes as sharp, high-amplitude transients. Line length quantifies this morphological property numerically.

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Central Finding

Lempel-Ziv Complexity drops during epileptic seizures.

The brain loses informational complexity when neurons synchronise pathologically. A healthy brain continuously explores its state space — LZC is high. During a seizure, activity collapses into a low-dimensional repetitive cycle — LZC drops.

This connects to Wheeler's It from Bit (1990): the seizure represents a collapse of informational complexity, a reduction in the bits generated per unit time by the neural system.

Implication for detection: LZC can serve as a lightweight, interpretable feature for seizure detection in wearable devices — no spectral decomposition required, computable in real time.

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Datasets

Dataset	Source	Size	Description
EEGBCI	PhysioNet (MNE)	~5 MB/subject	Motor imagery, 109 subjects, 64 channels, 160 Hz
CHB-MIT	PhysioNet	~100 MB/file	Paediatric epilepsy, 23 subjects, annotated seizures

Both datasets download automatically on first run.

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Requirements

pip install mne scikit-learn matplotlib numpy scipy antropy

Library	Version	Purpose
mne	≥1.0	EEG loading, preprocessing, EEGBCI dataset
antropy	≥0.1.6	LZC, permutation entropy, sample entropy
scikit-learn	≥1.0	Classification, cross-validation
scipy	≥1.7	ODE integration (H-H), Welch PSD

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Results

Hodgkin-Huxley action potential

Ionic channel dynamics

f-I curve and frequency spectrum

Network activity (20 neurons)

Complexity metrics — resting vs motor imagery

Feature importance

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Theoretical background

The connection between H-H biophysics and information-theoretic complexity is not arbitrary:

• High LZC → the system generates new information at each instant → high informational complexity → coherence
• Low LZC → the system repeats patterns → collapse to a low-dimensional attractor → incoherence

An epileptic seizure is, in Wheeler's terms, a loss of informational complexity — the brain stops exploring its state space and collapses into a cycle. The same metric that quantifies this collapse in biology quantifies exploration vs exploitation in any dynamical system.

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Related projects

• arc-qrl-peps-solver — Quantum RL agent for ARC-AGI-3
• eeg-epilepsy — Motor imagery BCI: RF → CSP+SVM → EEGNet → VQC

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Built with MNE · antropy · scikit-learn · scipy
Datasets: PhysioNet EEGBCI + CHB-MIT Scalp EEG