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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21605 |
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| _version_ | 1866916849502912512 |
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| author | Zang, Jie Helson, Pascal Liu, Shenquan Kumar, Arvind Mitra, Dhrubaditya |
| author_facet | Zang, Jie Helson, Pascal Liu, Shenquan Kumar, Arvind Mitra, Dhrubaditya |
| contents | Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with a linearized version of the Wilson-Kowan model and introduce a random anisotropy to inter-neuron connection. The resultant model is Edwards-Wilkinson model with a random anisotropic term. Averaging over the quenched randomness with the replica method we obtain a bi-quadratic nonlinearity. We use Wilsonian dynamic renormalization group to analyze this model. We find that, up to one loop order, for dimensions higher than two, the effect of the noise is to change dynamic exponent from two to one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization group analysis of noisy neural field Zang, Jie Helson, Pascal Liu, Shenquan Kumar, Arvind Mitra, Dhrubaditya Disordered Systems and Neural Networks Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with a linearized version of the Wilson-Kowan model and introduce a random anisotropy to inter-neuron connection. The resultant model is Edwards-Wilkinson model with a random anisotropic term. Averaging over the quenched randomness with the replica method we obtain a bi-quadratic nonlinearity. We use Wilsonian dynamic renormalization group to analyze this model. We find that, up to one loop order, for dimensions higher than two, the effect of the noise is to change dynamic exponent from two to one. |
| title | Renormalization group analysis of noisy neural field |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2503.21605 |