30,113 research outputs found
Control of Multilayer Networks
The controllability of a network is a theoretical problem of relevance in a
variety of contexts ranging from financial markets to the brain. Until now,
network controllability has been characterized only on isolated networks, while
the vast majority of complex systems are formed by multilayer networks. Here we
build a theoretical framework for the linear controllability of multilayer
networks by mapping the problem into a combinatorial matching problem. We found
that correlating the external signals in the different layers can significantly
reduce the multiplex network robustness to node removal, as it can be seen in
conjunction with a hybrid phase transition occurring in interacting Poisson
networks. Moreover we observe that multilayer networks can stabilize the fully
controllable multiplex network configuration that can be stable also when the
full controllability of the single network is not stable
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics
Control of nonlinear large-scale dynamical networks, e.g., collective
behavior of agents interacting via a scale-free connection topology, is a
central problem in many scientific and engineering fields. For the linear
version of this problem, the so-called controllability Gramian has played an
important role to quantify how effectively the dynamical states are reachable
by a suitable driving input. In this paper, we first extend the notion of the
controllability Gramian to nonlinear dynamics in terms of the Gibbs
distribution. Next, we show that, when the networks are open to environmental
noise, the newly defined Gramian is equal to the covariance matrix associated
with randomly excited, but uncontrolled, dynamical state trajectories. This
fact theoretically justifies a simple Monte Carlo simulation that can extract
effectively controllable subdynamics in nonlinear complex networks. In
addition, the result provides a novel insight into the relationship between
controllability and statistical mechanics.Comment: 9 pages, 3 figures; to appear in Scientific Report
On controllability of neuronal networks with constraints on the average of control gains
Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently
Nodal dynamics, not degree distributions, determine the structural controllability of complex networks
Structural controllability has been proposed as an analytical framework for
making predictions regarding the control of complex networks across myriad
disciplines in the physical and life sciences (Liu et al.,
Nature:473(7346):167-173, 2011). Although the integration of control theory and
network analysis is important, we argue that the application of the structural
controllability framework to most if not all real-world networks leads to the
conclusion that a single control input, applied to the power dominating set
(PDS), is all that is needed for structural controllability. This result is
consistent with the well-known fact that controllability and its dual
observability are generic properties of systems. We argue that more important
than issues of structural controllability are the questions of whether a system
is almost uncontrollable, whether it is almost unobservable, and whether it
possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page
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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