9,955 research outputs found
Structural Target Controllability of Undirected Networks
In this paper, we study the target controllability problem of networked
dynamical systems, in which we are tasked to steer a subset of network states
towards a desired objective. More specifically, we derive necessary and
sufficient conditions for the structural target controllability problem of
linear time-invariant (LTI) systems with symmetric state matrices, such as
undirected dynamical networks with unknown link weights. To achieve our goal,
we first characterize the generic rank of symmetrically structured matrices, as
well as the modes of any numerical realization. Subsequently, we provide a
graph-theoretic necessary and sufficient condition for the structural
controllability of undirected networks with multiple control nodes. Finally, we
derive a graph-theoretic necessary and sufficient condition for structural
target controllability of undirected networks. Remarkably, apart from the
standard reachability condition, only local topological information is needed
for the verification of structural target controllability
Controllability of structural brain networks.
Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function
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