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arXiv · 2503.20708

Fluctuation-dissipation of the Kuramoto model on fruit-fly connectomes

Géza Ódor·István Papp·Gustavo Deco
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Abstract

We investigate the distance from equilibrium using the Kuramoto model via the degree of fluctuation-dissipation violation as the consequence of different levels of edge weight anisotropies. This is achieved by solving the synchronization equations on the raw, homeostatic weighted and a random inhibitory edge variant of a real full fly (FF) connectome, containing $\simeq 10^5$ neuron cell nodes. We investigate these systems close to their synchronization transition critical points. While the topological(graph) dimension is high: $d \simeq 6$ the spectral dimensions of the variants, relevant in describing the synchronization behavior, are lower than the upper critical dimension: $d_s \simeq 2 < d_c=5$, suggesting relevant fluctuation effects and non mean-field scaling behavior. By measuring the auto-correlations and the auto-response functions for small perturbations we calculate the fluctuation-dissipation ratios (FDR) for the different variants of different anisotropy levels of the FF connectome. Numerical evidence is presented that the FDRs follow the level of anisotropy of these non-equilibrium systems in agreement with the expectations, with increasing temporal oscillations. Numerical values for the aging exponents provide confirmation for the predictions of the generalized time-translational-invariance theory. We compare the non-reciprocal connectome results with those on a symmetric Erd\H os-R\'enyi random graph of similar size and provide estimates for the Kuramoto model aging behavior. We also present a network analysis of the FF connectome and calculate the level of hierarchy, also related to the anisotropy. Finally, we provide some partial results for the periodically forced Shinomoto-Kuramoto model describing fluctuations in the non-resting state. We provide numerical evidence that fluctuations are maximal in the resting state of the critical brain.

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Géza Ódor, István Papp, Gustavo Deco. 2025-03-26. Fluctuation-dissipation of the Kuramoto model on fruit-fly connectomes. https://arxiv.org/abs/2503.20708

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