Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks

Fiedler, Bernold; Mochizuki, Atsushi; Kurosawa, Gen; Saito, Daisuke

doi:10.1007/s10884-013-9312-7

Cited by 129 publications

(188 citation statements)

References 27 publications

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“…Roughly speaking, (42) is controllable if one can steer it from any point x 0 ∈ M to any other point x 1 ∈ M by choosing u from a set of admissible controls U, which is a subset of functions mapping R + to U. The controllability of nonlinear systems has been extensively studied since the early 1970s (Brockett, 1972;Conte et al, 2007;Elliot, 1970;de Figueiredo and Chen, 1993;Haynes and Hermes, 1970;Hermann and Krener, 1977;Isidori, 1995;Lobry, 1970;Nijmeijer and van der Schaft, 1990;Rugh, 1981;Sontag, 1998;Sussmann and Jurdjevic, 1972). The goal was to derive results of similar reach and generality as obtained for linear time-invariant systems.…”

Section: Controllability Of Nonlinear Systemsmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Section: Controllability Of Nonlinear Systemsmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

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“…In [16], singleton attractors (fixed points) of BNs are characterized from graph structure only. In [52,53], a feedback vertex set of a graph is focused. A feedback vertex set of a graph is a set of vertices whose removal results an acyclic graph.…”

Section: Open Problems In Control Theory Of Probabilistic Boolean Netmentioning

confidence: 99%

“…A minimum feedback vertex set is also not given uniquely. It was shown in [52,53] that in the system given by a differential equation, a certain property of all states can be characterized by analyzing the states relating to a certain feedback vertex set. However, the related results for BNs and PBNs have not been obtained so far.…”

Section: Open Problems In Control Theory Of Probabilistic Boolean Netmentioning

confidence: 99%

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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Abstract:Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs) are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.

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“…Each SCC is itself a maximal subnetwork formed by some nodes and the arcs between them, and any node can reach and be reached by any another node of the same SCC through at least one directed path. Directed cycles are usually abundant in the large SCCs (each of which contains many nodes and arcs), and they cause strong feedback effect and make the information-processing dynamics in the network highly complex [15,16].…”

Section: Introductionmentioning

confidence: 99%

Feedback arcs and node hierarchy in directed networks

Zhao¹,

Zhou²

2017

Chinese Phys. B

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Directed networks such as gene regulation networks and neural networks are connected by arcs (directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which lead to complex information-processing dynamics in the network and make it highly challenging to infer the intrinsic direction of information flow. In this theoretical paper, based on the principle of minimum-feedback, we explore the node hierarchy of directed networks and distinguish feedforward and feedback arcs. Nearly optimal node hierarchy solutions, which minimize the number of feedback arcs from lower-level nodes to higher-level nodes, are constructed by belief-propagation and simulated-annealing methods. For real-world networks, we quantify the extent of feedback scarcity by comparison with the ensemble of direction-randomized networks and identify the most important feedback arcs. Our methods are also useful for visualizing directed networks.

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Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks

Cited by 129 publications

References 27 publications

Control principles of complex systems

Control principles of complex systems

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Feedback arcs and node hierarchy in directed networks

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