Controllability Of Networks Research Articles

Robustness of Network Controllability with Respect to Node Removals Based on In-Degree and Out-Degree

Network controllability and its robustness have been widely studied. However, analytical methods to calculate network controllability with respect to node in- and out-degree targeted removals are currently lacking. This paper develops methods, based on generating functions for the in- and out-degree distributions, to approximate the minimum number of driver nodes needed to control directed networks, during node in- and out-degree targeted removals. By validating the proposed methods on synthetic and real-world networks, we show that our methods work reasonably well. Moreover, when the fraction of the removed nodes is below 10% the analytical results of random removals can also be used to predict the results of targeted node removals.

A cloud model-based method for passenger flow control at subway stations: A real-world case study

In the condition of large passenger flow, subway station managers take measures of passenger flow control organization for reducing high safety operation risks at subway stations. The volume of passenger flow in urban railway network operation continues to increase and the Congestion of passenger flow is very high. Passenger flow control measures can greatly give birth to the pressure of transportation and ensure an urban rail transit system’s safe operation. In this paper, we develop a cloud model-based method for passenger flow control, which extends the four-level risk-control grade of a large passenger flow at facilities by considering its fuzzy and stochastic characteristics. Then, an efficient passenger flow control strategy for subway stations is made, where the control time and locations are simultaneously determined. Finally, a station in the Beijing subway is studied to test the validity of the proposed approach. The results show that the time of maximum queuing length is much shorter and the density of passenger flow is lower than existing methods in practice. With the in-depth study of complex network controllability, many studies have applied to control judgment and real network optimization. This paper analyzes the cloud-model-based method for passenger flow control at subway stations and therefore a new method can be incorporated for developing and optimizing control strategies. A few researchers have attempted to find the solution to the problem of crowding risk classification and the passenger flow control strategy. The focus of some studies simultaneously solves the passenger flow control with multiple stations.

Time Parameters Shape the Controllability of Temporally Switching Networks

Based on temporally switching networks, this work studies the influence of time parameters on network controllability. In particular, this work presents a necessary and sufficient condition under which the network controllability must take into account time parameters. For the time parameters that never participate in determining network controllability, a more concise expression of controllability criterion is derived. From the perspective of input matrix formulation, this work also presents a sufficient condition under which the network controllability could avoid the interference of time parameters. By taking control energy as the quantitative measurement, the increase in time parameter would decrease the lower bound of minimum control energy. However, the increase in time parameter may cause an upsurge in the upper bound of minimum control energy. In addition, we find that there exists a statistically significant correlation between time parameter influence level and network characteristic. This work highlights for the first time that subtle changes in time parameters could reshape or even worsen the controllability of temporally switching networks.

Game theoretical approach for critical sizing of energy storage systems for residential prosumers

The integration of Energy Storage Systems (ESS) into the distribution system has resulted in changes in the behavior of energy management systems. The primary objective of ESS management on the consumer side is to minimize operational costs reflected in energy bills, while the main goal for the Distribution System Operator (DSO) is to improve and smooth the aggregated load profile. Utilizing ESSs in distribution systems requires thorough research, as incorrect implementation can reduce controllability of distribution networks. This paper investigates the relationship between energy cost and the load responsiveness index of PV-ESS equipped residential loads using game theoretic approach. Sensitivity analysis is conducted to examine the relationship between load responsiveness and factors such as load profile, PV size, and energy cost. The goal of the paper is to propose a new approach for optimal sizing of ESS.

Structural characteristics in network control of molecular multiplex networks.

Numerous real-world systems can be naturally modeled as multilayer networks, providing an efficient tool to characterize these complex systems. Although recent progress in understanding the controlling of synthetic multiplex networks, how to control real multilayer systems remains poorly understood. Here, we explore the controllability and energy requirement of molecular multiplex networks coupled by transcriptional regulatory network (TRN) and protein-protein interaction (PPI) network from the perspective of network structural characteristics. Our findings reveal that the driver nodes tend to avoid essential or pathogen-related genes. However, imposing external inputs on these essential or pathogen-related genes can remarkably reduce the energy cost, implying their crucial role in network control. Moreover, we find that the minimal driver nodes, as well as the energy required, are associated with disassortative coupling between TRN and PPI networks. Our results provide a comprehensive understanding of the roles of genes in biology and network control across several species.

An adaptive attack model to network controllability

For the ultimate goal of protecting the network controllability and enhancing the controllability robustness, one can learn from how a network can be effectively destructed. In this paper, based on Thompson Sampling, we propose a Probabilistic Adaptive Attack model (PAA) that aims at destructing the network controllability. A set of multiple established attack strategies are employed in PAA, and a probabilistic model is used to adaptively choose the most destructive attack strategy for the current attack. The probabilistic model is updated based on the feedback of the controllability destruction of each single attack strategy. After applying PAA on both synthetic and real-world networks, extensive simulation results not only verify that PAA is more destructive than the single attack strategies, but also show that the probabilistic model can effectively choose the true best-performing attack strategy. Its accuracy reaches 81.96% in synthetic networks and 94.14% in real-world networks. The presented study aims to propose a highly efficient attack scheme and encourage the research of advanced methods to build robust networked systems.

Input node placement restricting the longest control chain in controllability of complex networks

The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is an inherent trade-off between minimizing the number of inputs and control energy. To better understand this trade-off, we study the problem of identifying a minimum set of input nodes such that controllabililty is ensured while restricting the length of the longest control chain. The longest control chain is the maximum distance from input nodes to any network node, and recent work found that reducing its length significantly reduces control energy. We map the longest control chain-constraint minimum input problem to finding a joint maximum matching and minimum dominating set. We show that this graph combinatorial problem is NP-complete, and we introduce and validate a heuristic approximation. Applying this algorithm to a collection of real and model networks, we investigate how network structure affects the minimum number of inputs, revealing, for example, that for many real networks reducing the longest control chain requires only few or no additional inputs, only the rearrangement of the input nodes.

Controllability of Multilayer Snapback Networks

This article studies the controllability of multi-input/multioutput linear time-invariant (LTI) systems in a snapback interlayer coupling framework. Several necessary and sufficient conditions for the controllability of the three-layer snapback networks are established. In addition, controllability conditions about the superposition of the three-layer networks are obtained. These conditions are related to smaller scale factor networks, showing the effects of the interlayer coupling frameworks, intralayer network topologies, node dynamics, inner interactions, and external control inputs on the controllability of the snapback networks. Moreover, controllability conditions of the three-layer snapback networks are extended to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -layer setting. Finally, some examples are presented to illustrate the effectiveness of the controllability conditions.

Linked patterns of symptoms and cognition with brain controllability in major depressive disorder

IntroductionMajor depressive disorder (MDD) is characterized by both clinical symptoms and cognitive deficits. Prior studies have typically examined either symptoms or cognition correlated with brain measures, thus causing a notable paucity of stable brain markers that capture the full characteristics of MDD. Brain controllability derived from newly proposed brain model integrating both metabolism (energy cost) and dynamics from a control perspective has been considered as a sensitive biomarker for characterizing brain function. Thus, identifying such a biomarker of controllability related to both symptoms and cognition may provide a promising state monitor of MDD.ObjectivesTo assess the associations between two multi-dimensional clinical (symptoms and cognition) and brain controllability data of MDD in an integrative model.MethodsSparse canonical correlation analysis (sCCA) was used to investigate the association between brain controllability at a network level and both clinical symptoms and cognition in 99 first-episode medication-naïve patients with MDD. The potential mediation effect of cognition on relationship between controllability and symptoms was also tested.ResultsAverage controllability was significantly correlated with both symptoms and cognition (rmean=0.54, PBonferroni=0.03). Average controllability of dorsal attention network (DAN) (r=0.46) and visual network (r=0.29) had the highest correlation with both symptoms and cognition. Among clinical variables, depressed mood (r =-0.23) , suicide(r =-0.25), work and activities(r =-0.27), gastrointestinal symptoms (r =-0.25) were significantly negatively associated with average controllability, while cognitive flexibility (r=0.29) was most strongly positively correlated with average controllability. Additionally, cognitive flexibility fully mediated the association between average controllability of DAN and depressed mood (indirect effect=-0.11, 95% CI [-0.18, -0.04], P=0.001) in MDD.ConclusionsBrain average controllability was correlated with both clinical symptoms and cognition in first-episode medication-naïve patients with MDD. The results suggest that average controllability of DAN and visual network reached high associations with clinical variates in MDD, thus these brain features may serve as stable biomarkers to control the brain functional states transitions to be relevant to cognitions deficits and clinical symptoms of MDD. Additionally, altered average controllability of DAN in patients could induce impairment of cognitive flexibility, and thus cause severe depressed mood, indicating that controllability of DAN may be a potential intervention target for alleviating depressed mood through improving cognitive flexibility in MDD.Disclosure of InterestNone Declared

Computation of the Distance-Based Bound on Strong Structural Controllability in Networks

In this article, we study the problem of computing a tight lower bound on the dimension of the strong structurally controllable subspace (SSCS) in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing the distances between leaders (nodes with external inputs) and followers (remaining nodes) in the underlying network graph. Such vectors are referred to as the distance-to-leaders vectors. We give exact and approximate algorithms to compute the longest sequences of distance-to-leaders vectors, which directly provide distance-based bounds on the dimension of SSCS. The distance-based bound is known to outperform the other known bounds (for instance, based on zero-forcing sets), especially when the network is partially strong structurally controllable. Using these results, we discuss an application of the distance-based bound in solving the leader selection problem for strong structural controllability. Further, we characterize strong structural controllability in path and cycle graphs with a given set of leader nodes using sequences of distance-to-leaders vectors. Finally, we numerically evaluate our results on various graphs.

WMDS.net: a network control framework for identifying key players in transcriptome programs.

Mammalian cells can be transcriptionally reprogramed to other cellular phenotypes. Controllability of such complex transitions in transcriptional networks underlying cellular phenotypes is an inherent biological characteristic. This network controllability can be interpreted by operating a few key regulators to guide the transcriptional program from one state to another. Finding the key regulators in the transcriptional program can provide key insights into the network state transition underlying cellular phenotypes. To address this challenge, here, we proposed to identify the key regulators in the transcriptional co-expression network as a minimum dominating set (MDS) of driver nodes that can fully control the network state transition. Based on the theory of structural controllability, we developed a weighted MDS network model (WMDS.net) to find the driver nodes of differential gene co-expression networks. The weight of WMDS.net integrates the degree of nodes in the network and the significance of gene co-expression difference between two physiological states into the measurement of node controllability of the transcriptional network. To confirm its validity, we applied WMDS.net to the discovery of cancer driver genes in RNA-seq datasets from The Cancer Genome Atlas. WMDS.net is powerful among various cancer datasets and outperformed the other top-tier tools with a better balance between precision and recall. https://github.com/chaofen123/WMDS.net. Supplementary data are available at Bioinformatics online.

Reachability, Controllability, and Stabilization of Boolean Control Networks With Stochastic Function Perturbations

Robust controllability and stabilization are two fundamental issues in modern control theory. This article investigates the robust controllability and stabilization of Boolean control networks (BCNs) subject to stochastic function perturbations (SFPs). First, by defining the concept of the weighted path and constructing the perturbed position index matrix, the robustness analysis of reachability is divided into two cases. According to these two cases, several criteria are proposed for the robust reachability of BCNs with SFPs. Second, based on the robust reachability, the robust controllability and state-feedback stabilization of BCNs with SFPs are further studied. Finally, the validity of the obtained results is supported by examples.

Network controllability measures of subnetworks: implications for neurosciences

Objective: Recent progress in network sciences has made it possible to apply key findings from control theory to the study of networks. Referred to as network control theory, this framework describes how the interactions between interconnected system elements and external energy sources, potentially constrained by different optimality criteria, result in complex network behavior. A typical example is the quantification of the functional role certain brain regions or symptoms play in shaping the temporal dynamics of brain activity or the clinical course of a disease, a property that is quantified in terms of the so-called controllability metrics. Critically though, contrary to the engineering context in which control theory was originally developed, a mathematical understanding of the network nodes and connections in neurosciences cannot be assumed. For instance, in the case of psychological systems such as those studied to understand psychiatric disorders, a potentially large set of related variables are unknown. As such, while the measures offered by network control theory would be mathematically correct, in that they can be calculated with high precision, they could have little translational values with respect to their putative role suggested by controllability metrics. It is therefore critical to understand if and how the controllability metrics estimated over subnetworks would deviate, if access to the complete set of variables, as is common in neurosciences, cannot be taken for granted. Approach: In this paper, we use a host of simulations based on synthetic as well as structural magnetic resonance imaging (MRI) data to study the potential deviation of controllability metrics in sub- compared to the full networks. Specifically, we estimate average- and modal-controllability, two of the most widely used controllability measures in neurosciences, in a large number of settings where we systematically vary network type, network size, and edge density. Main results: We find out, across all network types we test, that average and modal controllability are systematically, over- or underestimated depending on the number of nodes in the sub- and full network and the edge density. Significance: Finally, we provide formal theoretical proof that our observations generalize to any network type and discuss the ramifications of this systematic bias and potential solutions to alleviate the problem.

Genetic, individual, and familial risk correlates of brain network controllability in major depressive disorder

Many therapeutic interventions in psychiatry can be viewed as attempts to influence the brain’s large-scale, dynamic network state transitions. Building on connectome-based graph analysis and control theory, Network Control Theory is emerging as a powerful tool to quantify network controllability—i.e., the influence of one brain region over others regarding dynamic network state transitions. If and how network controllability is related to mental health remains elusive. Here, from Diffusion Tensor Imaging data, we inferred structural connectivity and inferred calculated network controllability parameters to investigate their association with genetic and familial risk in patients diagnosed with major depressive disorder (MDD, n = 692) and healthy controls (n = 820). First, we establish that controllability measures differ between healthy controls and MDD patients while not varying with current symptom severity or remission status. Second, we show that controllability in MDD patients is associated with polygenic scores for MDD and psychiatric cross-disorder risk. Finally, we provide evidence that controllability varies with familial risk of MDD and bipolar disorder as well as with body mass index. In summary, we show that network controllability is related to genetic, individual, and familial risk in MDD patients. We discuss how these insights into individual variation of network controllability may inform mechanistic models of treatment response prediction and personalized intervention-design in mental health.

Effect of the interdependence between subnets on the structural controllability of complex networks

AbstractControllability is a hot issue in complex networks. In this paper, without changing the number and the positions of the controllers, the effect of interdependence (viz., inter‐coupling relations) between two directed subnets that are controllable or uncontrollable on the structural controllability of complex networks is investigated. According to the Kalman rank criterion and PBH rank criterion, some sufficient conditions and necessary conditions for the structural controllability or uncontrollability of interdependent networks are presented. The results show that (1) if the uncontrollable and controllable nodes in one subnet are inter‐coupled with the controllable and uncontrollable nodes in the other subnet, respectively, and the directions are from controllable nodes to the uncontrollable nodes, then the interdependent network may be controllable; (2) the interdependent network can be obtained structurally controllable if there are simply directed paths covering all the uncontrollable nodes of the two subnets, separately; and (3) the interdependent networks are structurally controllable no matter what kind of inter‐couplings between two controllable subnets. All of these results are adaptive to undirected subnets. The final example verifies the effectiveness and correctness of the results provided in this paper.

Mindful attention promotes control of brain network dynamics for self-regulation and discontinues the past from the present

Mindful attention is characterized by acknowledging the present experience as a transient mental event. Early stages of mindfulness practice may require greater neural effort for later efficiency. Early effort may self-regulate behavior and focalize the present, but this understanding lacks a computational explanation. Here we used network control theory as a model of how external control inputs-operationalizing effort-distribute changes in neural activity evoked during mindful attention across the white matter network. We hypothesized that individuals with greater network controllability, thereby efficiently distributing control inputs, effectively self-regulate behavior. We further hypothesized that brain regions that utilize greater control input exhibit shorter intrinsic timescales of neural activity. Shorter timescales characterize quickly discontinuing past processing to focalize the present. We tested these hypotheses in a randomized controlled study that primed participants to either mindfully respond or naturally react to alcohol cues during fMRI and administered text reminders and measurements of alcohol consumption during 4 wk postscan. We found that participants with greater network controllability moderated alcohol consumption. Mindful regulation of alcohol cues, compared to one's own natural reactions, reduced craving, but craving did not differ from the baseline group. Mindful regulation of alcohol cues, compared to the natural reactions of the baseline group, involved more-effortful control of neural dynamics across cognitive control and attention subnetworks. This effort persisted in the natural reactions of the mindful group compared to the baseline group. More-effortful neural states had shorter timescales than less effortful states, offering an explanation for how mindful attention promotes being present.

Research on system safety in the case of component failure based on degree correlation

Nowadays, complex systems play an irreplaceable role in life, and the security of complex systems has always been the focus of research. In this paper, we focus on the topological characteristics of the network, starting from the degree correlation of the network, and studying the controllability of the network for different network types. For different network datasets, we adopt different security strategies to protect the network. Experiments show that the network controllability of different datasets under different security strategies is very different. Neutral networks and networks with the same configuration have little difference in the performance of each node in the face of network attacks; in the face of network attacks with heterogeneous networks, the security protection strategy of the central node can maintain network security to the greatest extent. Through different security strategies to achieve network controllability, the greatest possible realisation of system security.

Structural Robustness of Complex Networks: A Survey of A Posteriori Measures [Feature

Network robustness is critical for various industrial and social networks against malicious attacks, which has various meanings in different research contexts and here it refers to the ability of a network to sustain its functionality when a fraction of the network fail to work due to attacks. The rapid development of complex networks research indicates special interest and great concern about the network robustness, which is essential for further analyzing and optimizing network structures towards engineering applications. This comprehensive survey distills the important findings and developments of network robustness research, focusing on the a posteriori structural robustness measures for single-layer static networks. Specifically, the a posteriori robustness measures are reviewed from four perspectives: 1) network functionality, including connectivity, controllability and communication ability, as well as their extensions; 2) malicious attacks, including conventional and computation-based attack strategies; 3) robustness estimation methods using either analytical approximation or machine learning-based prediction; 4) network robustness optimization. Based on the existing measures, a practical threshold of network destruction is introduced, with the suggestion that network robustness should be measured only before reaching the threshold of destruction. Then, a posteriori and a priori measures are compared experimentally, revealing the advantages of the a posteriori measures. Finally, prospective research directions with respect to a posteriori robustness measures are recommended.

Effect of methylphenidate on functional controllability: a preliminary study in medication-naïve children with ADHD

Methylphenidate (MPH) is the recommended first-line treatment for attention-deficit/hyperactivity disorder (ADHD). While MPH’s mechanism of action as a dopamine and noradrenaline transporter blocker is well known, how this translates to ADHD-related symptom mitigation is still unclear. As functional connectivity is reliably altered in ADHD, with recent literature indicating dysfunctional connectivity dynamics as well, one possible mechanism is through altering brain network dynamics. In a double-blind, placebo-controlled MPH crossover trial, 19 medication-naïve children with ADHD underwent two functional MRI scanning sessions (one on MPH and one on placebo) that included a resting state scan and two inhibitory control tasks; 27 typically developing (TD) children completed the same protocol without medication. Network control theory, which quantifies how brain activity reacts to system inputs based on underlying connectivity, was used to assess differences in average and modal functional controllability during rest and both tasks between TD children and children with ADHD (on and off MPH) and between children with ADHD on and off MPH. Children with ADHD on placebo exhibited higher average controllability and lower modal controllability of attention, reward, and somatomotor networks than TD children. Children with ADHD on MPH were statistically indistinguishable from TD children on almost all controllability metrics. These findings suggest that MPH may stabilize functional network dynamics in children with ADHD, both reducing reactivity of brain organization and making it easier to achieve brain states necessary for cognitively demanding tasks.

Overview of networked supervisory control with imperfect communication channels

This paper presents an overview of the networked supervisory control frameworks for discrete event systems with imperfect communication networks, which are divided into the centralized setup, the decentralized setup and the distributed setup. The state-of-the-art works on networked supervisory control of discrete-event systems addressing the channel imperfections that are caused by channel delays, data losses or non-FIFO channels are discussed. By presenting the key concepts and main results of each representative work, we analyze the pros and cons of different approaches. Finally, we also provide a summary of the existing works, which roughly follow two different lines of thinking and result in two different verification or synthesis approaches. The first approach utilizes simple, non-networked plant models but relies on the development of sophisticated concepts of network controllability and observability to capture network imperfections, while the second approach embeds relatively complex yet verifiable channel models into the model of the networked plant and adopts the standard concepts of controllability and observability for the (verification and) synthesis of networked supervisors. Some future research topics are also presented.