# gst: dynamics and chaotic properties of the fully disordered Kuramoto model.

<< ️Frustrated random interactions are a key ingredient of spin glasses. From this perspective, (AA) study the dynamics of the Kuramoto model with quenched random couplings: the simplest oscillator ensemble with fully disordered interactions. (AA) answer some open questions by means of extensive numerical simulations and a perturbative calculation (the cavity method). (They) show frequency entrainment is not realized in the thermodynamic limit and that chaotic dynamics are pervasive in parameter space.  >>

<< ️In the weak coupling regime, (AA) find closed formulas for the frequency shift and the dissipativeness of the model. Interestingly, the largest Lyapunov exponent is found to exhibit the same asymptotic dependence on the coupling constant irrespective of the coupling asymmetry, within the numerical accuracy. >>

Iván León, Diego Pazó. Dynamics and chaotic properties of the fully disordered Kuramoto model. arXiv:2507.05168v1 [cond-mat.dis-nn]. Jul 7, 2025.

https://arxiv.org/abs/2507.05168

Also: disorder & fluctuations, weak, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder & fluctuations, weakness, chaos, transitions, volcano transition, slow relaxation, quasientrainment, freezing, nonreciprocity.

# gst: apropos of weakness, weak but influential; nonlinear contributions of structural connectivity to human cognitive abilities and brain functions.

<< Diverse human cognitive abilities are rooted in brain structural connectivity which has weights spanning several orders of magnitude. However, due to false-positive challenges in tractography, weak connectivity has been often treated as noise and ignored - despite its prevalence across mammalian brains. >>

Here AA show << that weak connectivity significantly predicts human cognitive abilities and supports brain functions through amplification of its small weight in a nonlinear manner. >>

AA found that << weak connectivity involves high individual variability and significantly predicts general cognitive ability and memory in individuals, and it is also critical for whole-brain dynamic simulation and structure-function coupling. Importantly, fusing two post-tractography filtering methods of streamlines potentially results in more reliable connectivity that preserves weak links and outperforms conventional thresholding in predicting cognitive abilities and functional connectivity. >>

<< At the network level, weak connectivity expands the operational capacity of brain networks to enhance both global integration and fine-grained segregation, thereby supporting a functional balance essential for cognitive abilities. >>

<< Finally, (AA) identified a specific type of weak connectivity mainly linking visual/motor to limbic areas with negative gene co-expression, which has a disproportionately large impact on cognitive predictions and network dynamics. >>

Rong Wang, Zhao Chang, et al. Weak but influential: Nonlinear contributions of structural connectivity to human cognitive abilities and brain functions. arXiv: 2505.24125v1 [q-bio.NC]. May 30, 2025.

https://arxiv.org/abs/2505.24125

Also: brain, network, weak, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, network, noise,  weakness, weak connectivity,  brain structural connectivity, tractography, multiple tractography algorithms, cognitive ability and memory, individual variability, global integration, fine-grained segregation, limbic areas.