Goal-driven selective attention (GDSA) is a remarkable function that allows the complex dynamical networks of the brain to support coherent perception and cognition. Part I of this two-part article proposes a new control-theoretic framework, termed hierarchical selective recruitment (HSR), to rigorously explain the emergence of GDSA from the brain's network structure and dynamics. This part completes the development of HSR by deriving conditions on the joint structure of the hierarchical subnetworks that guarantee top-down recruitment of the task-relevant part of each subnetwork by the subnetwork at the layer immediately above, while inhibiting the activity of task-irrelevant subnetworks at all the hierarchical layers. To further verify the merit and applicability of this framework, we carry out a comprehensive case study of selective listening in rodents and show that a small network with HSR-based structure can explain the data with remarkable accuracy while satisfying the theoretical stability and timescale separation requirements of HSR. Our technical approach relies on the theory of switched systems and provides a novel converse Lyapunov theorem for state-dependent switched affine systems that is of independent interest.

中文翻译：

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线性阈值脑网络中的分层选择性招募第二部分：多层动态和自上而下的招募


目标驱动选择性注意（GDSA）是一项非凡的功能，它允许大脑复杂的动态网络支持连贯的感知和认知。这篇由两部分组成的文章的第一部分提出了一种新的控制理论框架，称为分层选择性招募（HSR），以严格解释来自大脑网络结构和动力学的 GDSA 的出现。这部分通过推导分层子网的联合结构的条件来完成HSR的开发，保证上一层子网自上而下地招募每个子网的任务相关部分，同时抑制与任务无关的部分的活动所有层级的子网络。为了进一步验证该框架的优点和适用性，我们对啮齿类动物的选择性聆听进行了全面的案例研究，结果表明，基于 HSR 结构的小型网络可以非常准确地解释数据，同时满足理论稳定性和时间尺度分离要求高铁。我们的技术方法依赖于切换系统理论，并为状态相关的切换仿射系统提供了一种新颖的逆李雅普诺夫定理，该定理具有独立意义。