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Effect of threshold disorder on the quorum percolation model
Pascal Monceau1,2, Renaud Renault1, Stéphane Métens1
1Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France.
Physical Review. E
|August 31, 2016
Summary
Disorder in neural network thresholds alters quorum percolation models, shifting transitions and affecting cluster sizes. These effects are predictable using a mean-field approach, even when distinguishing from connectivity disorders is challenging.
Area of Science:
- Computational neuroscience
- Statistical physics
Background:
- The quorum percolation model is crucial for understanding neural network dynamics.
- Investigating the impact of disorder on network behavior is essential for realistic modeling.
Purpose of the Study:
- To analyze how Gaussian threshold variability affects the quorum percolation model on neural networks.
- To develop and validate a mean-field approach for understanding these modifications.
Main Methods:
- Derivation of a mean-field approach.
- Monte Carlo simulations for validation.
- Finite-size analysis of the order parameter.
Main Results:
- Threshold disorder shifts percolation transitions and impacts giant cluster size.
- Disorder-independent fixed points emerge above the critical value.
- The order parameter exhibits weak self-averaging, independent of threshold disorder.
Conclusions:
- Threshold variability significantly modifies quorum percolation dynamics in neural networks.
- The mean-field approach effectively explains observed effects via activation probability.
- Distinguishing between threshold and connectivity disorders in measurements is difficult.
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