Levich Institute and Physics Department, City College of New York, New York, NY 10031.
Theoretical Physics, Eidgenössische Technische Hochschule Zürich, 8093 Zürich, Switzerland.
Proc Natl Acad Sci U S A. 2017 Apr 11;114(15):3849-3854. doi: 10.1073/pnas.1620808114. Epub 2017 Mar 28.
Efficient complex systems have a modular structure, but modularity does not guarantee robustness, because efficiency also requires an ingenious interplay of the interacting modular components. The human brain is the elemental paradigm of an efficient robust modular system interconnected as a network of networks (NoN). Understanding the emergence of robustness in such modular architectures from the interconnections of its parts is a longstanding challenge that has concerned many scientists. Current models of dependencies in NoN inspired by the power grid express interactions among modules with fragile couplings that amplify even small shocks, thus preventing functionality. Therefore, we introduce a model of NoN to shape the pattern of brain activations to form a modular environment that is robust. The model predicts the map of neural collective influencers (NCIs) in the brain, through the optimization of the influence of the minimal set of essential nodes responsible for broadcasting information to the whole-brain NoN. Our results suggest intervention protocols to control brain activity by targeting influential neural nodes predicted by network theory.
高效的复杂系统具有模块化结构，但模块化并不能保证鲁棒性，因为效率还需要相互作用的模块化组件之间的巧妙相互作用。人脑是作为网络的网络（NoN）相互连接的高效稳健模块化系统的基本范例。理解这种模块化架构中鲁棒性的出现，需要从其各个部分的相互连接中找到答案，这是一个长期存在的挑战，引起了许多科学家的关注。受电网启发的 NoN 中依赖关系的当前模型用脆弱的耦合来表达模块之间的相互作用，这些耦合即使在很小的冲击下也会放大，从而阻止了功能的实现。因此，我们引入了一个 NoN 模型来塑造大脑活动的模式，以形成一个稳健的模块化环境。该模型通过优化负责将信息广播到整个大脑 NoN 的最小一组基本节点的影响，预测大脑中的神经集体影响者（NCI）图谱。我们的研究结果表明，通过针对网络理论预测的有影响力的神经节点，可以制定干预方案来控制大脑活动。
