Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
复制标题
DOI：
10.1038/s42005-022-01062-3
复制
发表时间：
2022-01
影响因子：
5.5
通讯作者：
Bengi Kilic;D. Taylor
中科院分区：
文献类型：
--
作者：
Bengi Kilic;D. Taylor
网络上的级联（例如，神经雪崩，社会传染和系统故障）通常涉及高阶依赖关系，但理论发展主要集中在两两相互作用模型上。在这里，我们为编码二进、三进和高阶相互作用的简单复合体上的级联建立了一个“简单阈值模型”（STM）。专注于包含短程和远程简单的小世界模型，我们探索了表现为局部和非局部传播之间的挫折的时空模式。我们展示了高阶相互作用和非线性阈值坐标，以鲁棒地引导级联沿着我们称之为“几何通道”的路径的ak维泛化。我们还发现这种协调可以在神经网络的简单-复杂模型（或“神经元复合体”）上增强级联的多样性和效率。我们用分岔理论和基于潜在几何的数据驱动方法支持这些发现。我们的发现为揭示协调非线性级联时空模式的多尺度、多维机制提供了富有成效的方向。
Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades over simplicial complexes that encode dyadic, triadic and higher-order interactions. Focusing on small-world models containing both short- and long-rangek-simplices, we explore spatio-temporal patterns that manifest as a frustration between local and nonlocal propagations. We show that higher-order interactions and nonlinear thresholding coordinate to robustly guide cascades along ak-dimensional generalization of paths that we call ‘geometrical channels’. We also find this coordination to enhance the diversity and efficiency of cascades over a simplicial-complex model for a neuronal network, or ‘neuronal complex’. We support these findings with bifurcation theory and data-driven approaches based on latent geometry. Our findings provide fruitful directions for uncovering the multiscale, multidimensional mechanisms that orchestrate the spatio-temporal patterns of nonlinear cascades.