Create README.md

Author: qiandaxing

README.md

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+# Structure–Function Coupling/Decoupling (Graph-Spectral Framework)
+
+This repository contains code used in:
+
+**Xing Qian et al. (2026)**  
+Altered salience network structure–function integration underlies the decline in cognitive flexibility during aging  
+PLOS Biology
+
+---
+
+## Overview
+
+This implementation is based on:
+
+Medaglia et al. (2018), Nature Human Behaviour
+
+### Key difference
+
+Instead of selecting a fixed number of eigenmodes, we use a **variance-based criterion** to determine:
+
+- Coupling (alignment; smooth components)
+- Decoupling (liberality; rough components)
+
+This approach:
+- Is data-driven
+- Is robust across parcellations
+- Avoids arbitrary selection of k
+
+---
+
+## Methods
+
+### 1. Component selection (choose_k.m)
+
+Steps:
+
+1. Divide eigenvalues into:
+   - Smooth (positive eigenvalues)
+   - Rough (negative eigenvalues)
+
+2. For each group:
+   - Compute total energy = sum of absolute eigenvalues
+   - Sort eigenvalues (descending)
+   - Compute cumulative energy
+
+3. Define kA and kL as:
+   - Minimum number of eigenvalues explaining 95% energy
+
+4. Average across time → KA, KL
+
+---
+
+### 2. Signal decomposition (signal_decomposition.m)
+
+Structural matrix:
+
+A = V Λ V^T
+
+- V: eigenvectors
+- Λ: eigenvalues
+
+Interpretation:
+- Smooth modes → coherent activity
+- Rough modes → abrupt variation
+
+---
+
+### Graph Fourier Transform
+
+x_hat = V^T x
+
+Reconstruction:
+
+x = V x_hat
+
+---
+
+### Coupling / Decoupling
+
+- Coupling = projection onto smooth modes
+- Decoupling = projection onto rough modes
+
+Use KA and KL to select components.
+
+---
+
+## Notes
+
+- This is NOT SC–FC correlation
+- It is graph spectral decomposition
+
+---
+
+## Citation
+
+Please cite:
+- Qian et al., 2026 (PLOS Biology)
+- Medaglia et al., 2018