{"id":46152431,"url":"https://github.com/secary/belief_simulation","last_synced_at":"2026-03-02T09:02:54.355Z","repository":{"id":319415621,"uuid":"1078637460","full_name":"secary/belief_simulation","owner":"secary","description":"Simulation Code for Belief Dynamics System","archived":false,"fork":false,"pushed_at":"2026-01-25T06:35:14.000Z","size":1328,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-01-25T21:20:58.345Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Jupyter 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Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Belief System Dynamics Simulation Framework\nA modular platform for generating and simulating belief system dynamics on social influence networks, based on:\n\n**Ye et al., IEEE TAC 2020 — \"Consensus and Disagreement of Heterogeneous Belief Systems in Influence Networks\".**\n\nThe framework produces:\n- Social influence matrices $W$\n- Heterogeneous logic matrices $C_i$\n- Initial beliefs $X_0$\n\nand supports exporting, visualization, and downstream simulation.\n\n---\n\n# Model Overview\n\nEach agent $i$ holds an $m$-dimensional belief vector $x_i(t)$.  \nBelief updates follow the extended DeGroot model:\n\n$$\nx_i(t+1) = \\sum_{j=1}^n W_{ij} \\, C_i \\, x_j(t).\n$$\n\n- $W$: row-stochastic influence matrix  \n- $C_i$: logic matrix encoding topic dependencies  \n- Heterogeneity in $C_i$ may lead to consensus or persistent disagreement\n\n---\n\n# Repository Structure\n\n### **1. `social_network.py`**\nGenerates the influence matrix $W$ using ER, WS, BA, or Random-Regular models.  \n- Beta-distributed edge weights  \n- Ensures row-stochasticity  \n- Provides network summary + Gephi export\n\n### **2. `logic_matrix.py`**\nCreates baseline and heterogeneous logic matrices $C_i$.  \n- Lower-triangular structure  \n- Beta-distributed coefficients  \n- Supports sparsity \u0026 heterogeneity  \n- Exports baseline $C_{\\text{base}}$\n\n### **3. `init_belief.py`**\nGenerates initial beliefs $X_0$.  \nModes: `uniform`, `beta`.  \nExports all results into a timestamped folder.\n\n### **4. `belief_simulation.ipynb`**\nInteractive notebook for testing:\n- Component generation\n- Simple belief dynamics\n- Visualizations\n\n\n# Simulation Pipeline\n\n1. Generate $W$, $C_i$, and $X_0$\n2. Update beliefs over time using \n    \n$$\nX(t+1) = \\sum_{j=1}^n W_{ij} \\, C_i \\, x_j(t).\n$$\n\n3. Visualise belief trajectories \n\n\n---\n\n# Reference\n[1] M. Ye, J. Liu, L. Wang, B. D. O. Anderson, and M. Cao,\n“Consensus and Disagreement of Heterogeneous Belief Systems\nin Influence Networks,” IEEE Transactions on Automatic Control,\nvol. 65, no. 11, pp. 4679–4694, Nov. 2020.","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsecary%2Fbelief_simulation","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsecary%2Fbelief_simulation","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsecary%2Fbelief_simulation/lists"}