Cascading Dynamics in Modular Networks

多路二维晶格上层叠动力学的临界行为

Critical behaviors of cascading dynamics on multiplex two-dimensional lattices

本研究通过数值模拟分析多路二维晶格中存活簇的临界现象，发现激活级联（CA）与失活级联（CD）过程的巨型存活簇临界行为不同，CA符合单层键渗流、CD符合多路互渗流，并通过鬼场计算磁化率揭示二者生成存活簇的差异。

Robustness and modular structure in networks

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a percolation problem [7-9] or by modeling cascading failures [10-12]. Many complex systems, from power grids and the Internet to the brain and society [13-15], can be modeled using modular networks comprised of small, densely connected groups of nodes [16, 17]. These modules often overlap, with network elements belonging to multiple modules [18, 19]. Yet existing work …

层级间的级联：正则化诱导的特征检测作为深度线性神经网络中的相变

Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks

本文以正则化强度为可调参数，通过解析研究深度线性神经网络玩具模型，揭示了正则化诱导的特征检测相变级联与损失景观几何的关联，为深度学习科学理论提供了研究平台。

Modular networks with hierarchical organization: The dynamical implications of complex structure

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the ne…

无第二网络下的相互依赖网络临界性：$VO_2$中焦耳耦合绝缘体-金属转变的级联崩溃

Interdependent-Network Criticality without a Second Network: Cascading Collapse of the Joule-Coupled Insulator-Metal Transition in $VO_2$

该研究揭示二氧化钒在电驱动下虽为单一结构却表现为相互依赖网络，焦耳耦合引发级联崩溃，实验与模型验证了临界指数，表明单一系统可展现相互依赖网络的灾难性级联行为。

A dynamical model for hierarchy and modular organization: The trajectories en route to the attractor at the transition to chaos

We show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut emergent property. This well-known nonlinear model system combines a simple and precise definition, an intricate nested hierarchical dynamical structure, and emergence of a power-law dynamical property absent in the exponential-law that governs the dynamics within the modules. This classic nonlinear system is put forward as a working example for complex collect…