Uniqueness Analysis of Controllability Scores and Their Application to Brain Networks
Kazuhiro Sato, Ryohei Kawamura
备注：
Full version of Uniqueness Analysis of Controllability Scores and Their Application to Brain Networks accepted to IEEE Transactions on Control of Network Systems
发表信息：
IEEE Transactions on Control of Network Systems, 2025
Assessing centrality in network systems is critical for understanding node importance and guiding decision-making processes. In dynamic networks, incorporating a controllability perspective is essential for identifying key nodes. In this paper, we study two control theoretic centrality measures -- the Volumetric Controllability Score (VCS) and Average Energy Controllability Score (AECS) -- to quantify node importance in linear time-invariant network systems. We prove the uniqueness of VCS and AECS for almost all specified terminal times, thereby enhancing their applicability beyond previously recognized cases. This ensures their interpretability, comparability, and reproducibility. Our analysis reveals substantial differences between VCS and AECS in linear systems with symmetric and skew-symmetric transition matrices. We also investigate the dependence of VCS and AECS on the terminal time and prove that when this parameter is extremely small, both scores become essentially uniform. Additionally, we prove that a sequence generated by a projected gradient method for computing VCS and AECS converges linearly to both measures under several assumptions. Finally, evaluations on brain networks modeled via Laplacian dynamics using real data reveal contrasting evaluation tendencies and correlations for VCS and AECS, with AECS favoring brain regions associated with cognitive and motor functions, while VCS emphasizes sensory and emotional regions.
On Structural Controllability of Symmetric (Brain) Networks
University of California at Riverside（加州大学河滨分校）；University of Electronic Science and Technology, Chengdu, China（电子科技大学）；University of Pennsylvania（宾夕法尼亚大学）
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Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Universidade Federal de Pernambuco（伯南布哥联邦大学）；Kuwait University（科威特大学）；Fundação Getúlio Vargas（巴西得恩利奥·瓦加斯基金会）
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The brain is an intricately structured organ responsible for the rich emergent dynamics that support the complex cognitive functions we enjoy as humans. With around $10^{11}$ neurons and $10^{15}$ synapses, understanding how the human brain works has proven to be a daunting endeavor, requiring concerted collaboration across traditional disciplinary boundaries. In some cases, that collaboration has occurred between experimentalists and technicians, who offer new physical tools to measure and manipulate neural function. In other contexts, that collaboration has occurred between experimentalists …
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