Driver Nodes Research Articles

A controllability method on the social Internet of Things (SIoT) network

In recent years, one type of complex network called the Social Internet of Things (SIoT) has attracted the attention of researchers. Controllability is one of the important problems in complex networks and it has essential applications in social, biological, and technical networks. Applying this problem can also play an important role in the control of social smart cities, but it has not yet been defined as a specific problem on SIoT, and no solution has been provided for it. This paper addresses the controllability problem of the temporal SIoT network. In this regard, first, a definition for the temporal SIoT network is provided. Then, the unique relationships of this network are defined and modeled formally. In the following, the Controllability problem is applied to the temporal SIoT network (CSIoT) to identify the Minimum Driver nodes Set (MDS). Then proposed CSIoT is compared with the state-of-the-art methods for performance analysis. In the obtained results, the heterogeneity (different types, brands, and models) has been investigated. Also, 69.80 % of the SIoT sub-graphs nodes have been identified as critical driver nodes in 152 different sets. The proposed controllability deals with network control in a distributed manner.

HATZFS predicts pancreatic cancer driver biomarkers by hierarchical reinforcement learning and zero-forcing set

The search for cancer biomarkers is of great significance for the early diagnosis and clinical treatment planning of pancreatic cancer. RNA transcription networks can effectively represent the interactions between RNA molecules, and the irregular perturbations in these interactions can lead to pathological states, making them commonly used for identifying cancer biomarkers. However, traditional network-based methods for identifying cancer biomarkers often rely on prior information and mutation data. Furthermore, most network controllability-based methods face the limitation of high computational complexity, preventing their integration with deep learning methods. In this paper, we propose a novel deep learning framework, called HATZFS, for identifying driver biomarkers in pancreatic cancer using RNA differential expression data. The proposed model combines hierarchical deep Q-network (HDQN), graph attention network (GAT), and zero-forcing set (ZFS). Firstly, a pancreatic cancer RNA transcription regulatory network is constructed to embed the complex relationship among Long non-coding RNA (lncRNA), microRNA (miRNA) and messenger RNA (mRNA). Then, we transform it into multiple subgraphs using graph sampling method, and apply GAT to learn the node features of the subgraphs. Finally, the HATZFS performs HDQN to select subgraphs and identify important RNA as driver nodes, and determining the controllability of the subgraphs based on ZFS. More important, the paper theoretically proves that when all subgraphs are controllable, the original graph is also controllable, and the union of the driver node sets of all subgraphs is equal to the driver node set of the original graph. To confirm the effectiveness of the proposed model, comprehensive experiments are conducted on the benchmark dataset consisting of 14 databases, comparing it with eight other algorithms. The experimental results demonstrate that the proposed model outperforms other methods. Overall, HATZFS not only provides the importance of all RNA molecules in the pancreatic cancer RNA regulatory network, but also identifies the driver node set of the network as driver biomarkers. Source code can be accessed at https://github.com/HongJieTongXue/HATZFS.

A practically efficient algorithm for identifying critical control proteins in directed probabilistic biological networks

Network controllability is unifying the traditional control theory with the structural network information rooted in many large-scale biological systems of interest, from intracellular networks in molecular biology to brain neuronal networks. In controllability approaches, the set of minimum driver nodes is not unique, and critical nodes are the most important control elements because they appear in all possible solution sets. On the other hand, a common but largely unexplored feature in network control approaches is the probabilistic failure of edges or the uncertainty in the determination of interactions between molecules. This is particularly true when directed probabilistic interactions are considered. Until now, no efficient algorithm existed to determine critical nodes in probabilistic directed networks. Here we present a probabilistic control model based on a minimum dominating set framework that integrates the probabilistic nature of directed edges between molecules and determines the critical control nodes that drive the entire network functionality. The proposed algorithm, combined with the developed mathematical tools, offers practical efficiency in determining critical control nodes in large probabilistic networks. The method is then applied to the human intracellular signal transduction network revealing that critical control nodes are associated with important biological features and perturbed sets of genes in human diseases, including SARS-CoV-2 target proteins and rare disorders. We believe that the proposed methodology can be useful to investigate multiple biological systems in which directed edges are probabilistic in nature, both in natural systems or when determined with large uncertainties in-silico.

Detection of minimal extended driver nodes in energetic costs reduction.

Structures of complex networks are fundamental to system dynamics, where node state and connectivity patterns determine the cost of a control system, a key aspect in unraveling complexity. However, minimizing the energy required to control a system with the fewest input nodes remains an open problem. This study investigates the relationship between the structure of closed-connected function modules and control energy. We discovered that small structural adjustments, such as adding a few extended driver nodes, can significantly reduce control energy. Thus, we propose MInimal extended driver nodes in Energetic costs Reduction (MIER). Next, we transform the detection of MIER into a multi-objective optimization problem and choose an NSGA-II algorithm to solve it. Compared with the baseline methods, NSGA-II can approximate the optimal solution to the greatest extent. Through experiments using synthetic and real data, we validate that MIER can exponentially decrease control energy. Furthermore, random perturbation tests confirm the stability of MIER. Subsequently, we applied MIER to three representative scenarios: regulation of differential expression genes affected by cancer mutations in the human protein-protein interaction network, trade relations among developed countries in the world trade network, and regulation of body-wall muscle cells by motor neurons in Caenorhabditis elegans nervous network. The results reveal that the involvement of MIER significantly reduces control energy required for these original modules from a topological perspective. Additionally, MIER nodes enhance functionality, supplement key nodes, and uncover potential mechanisms. Overall, our work provides practical computational tools for understanding and presenting control strategies in biological, social, and neural systems.

Target control of linear directed networks based on the path cover problem

Securing complete control of complex systems comprised of tens of thousands of interconnected nodes holds immense significance across various fields, spanning from cell biology and brain science to human-engineered systems. However, depending on specific functional requirements, it can be more practical and efficient to focus on a pre-defined subset of nodes for control, a concept known as target control. While some methods have been proposed to find the smallest driver node set for target control, they either rely on heuristic approaches based on k-walk theory, lacking a guarantee of optimal solutions, or they are overly complex and challenging to implement in real-world networks. To address this challenge, we introduce a simple and elegant algorithm, inspired by the path cover problem, which efficiently identifies the nodes required to control a target node set within polynomial time. To practically apply the algorithm in real-world systems, we have selected several networks in which a specific set of nodes with functional significance can be designated as a target control set. The analysed systems include the complete connectome of the nematode worm C. elegans, the recently disclosed connectome of the Drosophila larval brain, as well as dozens of genome-wide metabolic networks spanning major plant lineages. The target control analysis shed light on distinctions between neural systems in nematode worms and larval brain insects, particularly concerning the number of nodes necessary to regulate specific functional systems. Furthermore, our analysis uncovers evolutionary trends within plant lineages, notably when examining the proportion of nodes required to control functional pathways.

A bridge between influence models and control methods

Understanding how influence is seeded and spreads through social networks is an increasingly important study area. While there are many methods to identify seed nodes that are used to initialize a spread of influence, the idea of using methods for selecting driver nodes from the control field in the context of seed selection has not been explored yet. In this work, we present the first study of using control approaches as seed selection methods. We employ a Minimum Dominating Set to develop a candidate set of driver nodes. We propose methods based upon driver nodes (i.e. Driver-Random, Driver-Degree, Driver-Closeness, Driver-Betweenness, Driver-Degree-Closeness-Betweenness, Driver-Kempe, Driver-Ranked) for selecting seeds from this set. These methods make use of centrality measures to rank the driver nodes in terms of their potential as seed nodes. We compare proposed methods to existing approaches using the Linear Threshold model on both real and synthetic networks. Our experiment results show that the proposed methods consistently outperform the benchmarks. We conclude that using driver nodes as seeds in the influence spread results in faster and thus more effective spread than when applying traditional methods.

Knowledge-embedded constrained multiobjective evolutionary algorithm based on structural network control principles for personalized drug targets recognition in cancer

The structural network control principle for identifying personalized drug targets (SNCPDTs) is a kind of constrained multiobjective optimization (CMO) problem with NP-hard features, which makes traditional mathematical methods difficult to adopt. Therefore, this study designs a knowledge-embedded multitasking constrained multiobjective evolutionary algorithm (KMCEA) to solve the SNCPDTs by mining relevant knowledge. Specifically, the relationships between two optimization objectives (minimizing the number of driver nodes and maximizing prior-known drug-target information) and constraints (guaranteeing network control) are analyzed from the perspective of CMO. We find that two objectives are difficult to optimize; thus two single-objective auxiliary tasks are created to optimize two objectives respectively, so as to maintain diversity along the Pareto front. Furthermore, we find that two optimization objectives have a complex reverse relation and a simple positive relation with constraints, respectively; thus, a population initialization method and a local auxiliary task are designed for two single-objective auxiliary tasks, respectively, so as to improve the performance of the algorithm on two objective functions. Finally, KMCEA is used to solve two kinds of models with three kinds of datasets. Compared with various methods, KMCEA can not only effectively discover clinical combinatorial drugs but also better solve the SNCPDTs regarding convergence and diversity.

On the minimum driver node set of k-uniform linear hypertree networks

The exact controllability research framework of complex networks points out that the controllability of the network has a great relationship with the minimum number of driver nodes. It is generally believed that the smaller the minimum number of driver nodes and the lower the cost of external control of the whole network to achieve the ideal state, the better the controllability of networks. In this paper, the minimum driver node problem of a hypernetwork is transformed into the maximum multiplicative problem of the eigenvalue of its 2-section graph. The minimum driver node numbers of two types of typical k-uniform hypertree networks are described, and their bounds are also given. By designing an algorithm, the method of characterizing the driver node set is obtained, and it is found that the selection of the minimum driver nodes of the network tends to the nodes with low hyperdegree. In addition, the paper verifies the minimum driver node set and the theoretical analysis results of controllability by simulation analysis.

Dynamic relationship between the XRP price and correlation tensor spectra of transaction networks

The emergence of cryptoassets has sparked a paradigm shift in the world of finance and investment, ushering in a new era of digital assets with profound implications for the future of currency and asset management. A recent study showed that during the bubble period around the year, 2018, the price of cryptoasset, XRP has a strong anti correlation with the largest singular values of the correlation tensors obtained from the weekly XRP transaction networks. In this study, we provide a detailed analysis of the method of correlation tensor spectra for XRP transaction networks. We calculate and compare the distribution of the largest singular values of the correlation tensor using the random matrix theory with the largest singular values of the empirical correlation tensor. We investigate the correlation between the XRP price and the largest singular values for a period spanning two years. We also uncover the distinct dependence between the XRP price and the singular values for bubble and non-bubble periods. The significance of the time evolution of singular values is shown by comparison with the evolution of singular values of the reshuffled correlation tensor. Furthermore, we identify a set of driver nodes in the transaction networks that drives the market during the bubble period using singular vectors.

Improving the efficiency of network controllability processes on temporal networks

The controllability of temporal networks has become an important issue for researchers in recent years. In temporal networks, the controllability is achieved through the control of dynamics. Existing studies take only some dynamics into account when controlling such networks, e.g., only adding links, and ignore the rest. Besides, conventional controllability methods on temporal networks suffer from time complexity and data overhead. In this paper, a dynamic controllability method is proposed which considers all dynamics of temporal networks to fully control the network, including adding and removing nodes and links. The proposed controllability method finds all the minimum driver nodes sets (MDSs) of a temporal network in a polynomial time. In this regard, to maintain and track the network changes, a new tree-based model, named Controllable Dynamics Temporal Network (CDTN), is proposed by which the control process is executed with high speed and low overhead. The experimental results show that the proposed controllability method outperforms state-of-the-art methods in terms of speed (47% improvement), overhead (33% improvement), and the size of MDS (38% improvement).

Measuring criticality in control of complex biological networks

Recent controllability analyses have demonstrated that driver nodes tend to be associated to genes related to important biological functions as well as human diseases. While researchers have focused on identifying critical nodes, intermittent nodes have received much less attention. Here, we propose a new efficient algorithm based on the Hamming distance for computing the importance of intermittent nodes using a Minimum Dominating Set (MDS)-based control model. We refer to this metric as criticality. The application of the proposed algorithm to compute criticality under the MDS control framework allows us to unveil the biological importance and roles of the intermittent nodes in different network systems, from cellular level such as signaling pathways and cell-cell interactions such as cytokine networks, to the complete nervous system of the nematode worm C. elegans. Taken together, the developed computational tools may open new avenues for investigating the role of intermittent nodes in many biological systems of interest in the context of network control.

Structural Controllability of Multiplex Networks with the Minimum Number of Driver Nodes

Structural Controllability of Multiplex Networks with the Minimum Number of Driver Nodes

Gene co‐expression network analyses in Mild cognitive impairment

AbstractBackgroundMultiomic data analysis has been extensively developed in recent years. Particularly, microarray data can be used as biomarkers of disease of progression specially in pathologies as cancer, autoimmunity and others. (Dahinden et al., 2010; Soleimani Zakeri et al., 2020). This modality of data analysis can also be employed in other multifactorial diseases as Alzheimer’s disease including the progression from normal cognition to mild cognitive impairment and finally to dementia. These genes work in intricate relationship with each other. The establishment of computational gene interaction networks shows the intricacy of the biological systems but increases the complexity of the analysis, for this reason, the removal of redundant edges leaves a network backbone revealing important driver nodes that are essential for the observed interactions, reducing the number of genes of interest and narrowing potential diagnostic or therapeutic targets. (Gates et al., 2021)MethodsWe used data from the ImaGENE study and the Weighted gene co‐expression network analysis (WGCNA) pipeline to analyze gene‐gene interactions of mRNA transcripts obtaining hierarchical clustering of genes and eigengenes in a sample of 160 individuals (Table 1). The backbones were obtained using the shortest path computation. (Gates et al., 2021; Simas et al., 2021). Gene ontology was used to classify processes associated with these genes.ResultsWe identified 42 hubs of differentially expressed genes and we analyzed the top 5 groups with the strongest association with amnestic mild cognitive impairment (MCI) phenotype (pfdr<0.0001). This cluster consisting of 46 genes was further classified according to function and interactions with other nodes in the backbone identifying processes like calcium signaling, nucleotide excision repair, fatty acid metabolism among others.ConclusionThere is an identifiable difference in gene expression in individuals with MCI compared to normal controls. The analysis of the backbone of the gene hubs allowed to reduce the number of genes of interest. This approach can help to elucidate important biological interactions, potential therapeutic targets and could eventually be used as risk factors markers for the development of MCI and AD.

The recoverability of network controllability with respect to node additions

Network controllability is a critical attribute of dynamic networked systems. Investigating methods to restore network controllability after network degradation is crucial for enhancing system resilience. In this study, we develop an analytical method based on degree distributions to estimate the minimum fraction of required driver nodes for network controllability under random node additions after the random removal of a subset of nodes. The outcomes of our method closely align with numerical simulation results for both synthetic and real-world networks. Additionally, we compare the efficacy of various node recovery strategies across directed Erdös–Rényi (ER) networks, swarm signaling networks (SSNs), and directed Barabàsi Albert (BA) networks. Our findings indicate that the most efficient recovery strategy for directed ER networks and SSNs is the greedy strategy, which considers node betweenness centrality. Similarly, for directed BA networks, the greedy strategy focusing on node degree centrality emerges as the most efficient. These strategies outperform recovery approaches based on degree centrality or betweenness centrality, as well as the strategy involving random node additions.

Control of misbehaving multiagent networks using driver and observer nodes

While applying control signals to every node is typically considered in multiagent networks to mitigate the adverse effects of misbehaving nodes, this control strategy may not always be possible due to physical constraints and/or economical limitations. Motivated by this standpoint, we have recently focused on how to control misbehaving multiagent networks through sending control signals to a subset of nodes (i.e. driver nodes) for suppressing the adverse effects of misbehaving nodes in the overall multiagent network, where the driver nodes only use their own state information to generate their control signals. To address the open problem where the driver nodes cannot obtain their own state information, the main contribution of this paper is that we now take into account that these nodes need to generate their control signals using the state information received from other subset of nodes (i.e. observer nodes). We characterise which nodes in the network behave as desired based on the selection of driver nodes and observer nodes in control of misbehaving multiagent networks. In addition, we provide numerical examples to illustrate the effectiveness of the proposed approach as well as the importance of the selection of driver and observer nodes for maximising the number of nodes that exhibit the desired responses.

Detecting the driver nodes of temporal networks

Detecting the driver nodes of complex networks has garnered significant attention recently to control complex systems to desired behaviors, where nodes represent system components and edges encode their interactions. Driver nodes, which are directly controlled by external inputs, play a crucial role in controlling all network nodes. While many approaches have been proposed to identify driver nodes of static networks, we still lack an effective algorithm to control ubiquitous temporal networks, where network structures evolve over time. Here we propose an effective online time-accelerated heuristic algorithm (OTaHa) to detect driver nodes of temporal networks. Together with theoretical analysis and numerical simulations on synthetic and empirical temporal networks, we show that OTaHa offers multiple sets of driver nodes, and noticeably outperforms existing methods in terms of accuracy and execution time. We further report that most edges are redundant in controlling temporal networks although the complete instantaneous signal-carrying edges cannot be guaranteed. Moreover, removing edges with high edge betweenness (the number of all-pairs shortest paths passing through the edge) significantly impedes the overall controllability. Our work provides an effective algorithm and paves the way for subsequent explorations on achieving the ultimate control of temporal networks.

Target control of complex networks: How to save control energy.

Controlling complex networks has received much attention in the past two decades. In order to control complex networks in practice, recent progress is mainly focused on the control energy required to drive the associated system from an initial state to any final state within finite time. However, one of the major challenges when controlling complex networks is that the amount of control energy is usually prohibitively expensive. Previous explorations on reducing the control energy often rely on adding more driver nodes to be controlled directly by external control inputs, or reducing the number of target nodes required to be controlled. Here we show that the required control energy can be reduced exponentially by appropriately setting the initial states of uncontrollable nodes for achieving the target control of complex networks. We further present the energy-optimal initial states and theoretically prove their existence for any structure of network. Moreover, we demonstrate that the control energy could be saved by reducing the distance between the energy-optimal states set and the initial states of uncontrollable nodes. Finally, we propose a strategy to determine the optimal time to inject the control inputs, which may reduce the control energy exponentially. Our conclusions are all verified numerically, and shed light on saving control energy in practical control.

Controllability analysis of directed networks based on pruning motif isomorph

The current driver nodes search methods are difficult to cope with large networks, and the solution process does not consider the cost of control imposed by the nodes. In order to solve the problem of control input to achieve control synchronization in finite states for networks with different node costs, this paper proposes a pruning and motif isomorph search method for a driver node set. Firstly, we prove the sufficient conditions for the network to be strictly controllable under partial nodes control, then we classify the nodes and prove the equivalence controllability of the pruning network, and then we establish three models of maximum augmenting path search, local pruning and motif matching to form a complete driver node set search algorithm. Finally, the algorithm is validated by three types of experiments: examples, classical networks and real networks. The results show that our method not only guarantees the accuracy of the search results, but also has lower time complexity than other existing methods, which can efficiently handle large networks, and no more than 16.84% of the maximum driver nodes can control the whole network.

Structure-based approach to identify driver nodes in ensembles of biologically inspired Boolean networks

Structure-based approach to identify driver nodes in ensembles of biologically inspired Boolean networks

Control core of undirected complex networks

With the development of complex networks, many researchers have paid greater attention to studying the control of complex networks over the last decade. Although some theoretical breakthroughs allow us to identify all driver nodes, we still lack an efficient method to identify the driver nodes and understand the roles of individual nodes in contributing to the control of a large complex network. Here, we apply a leaf removal process (LRP) to find a substructure of an undirected network, which is considered as the control core of the original network. Based on a strict mathematical proof, the control core obtained by the LRP has the same controllability as the original network, and it contains at least one set of driver nodes. With this method, we systematically investigate the structural property of the control core with respect to different average degrees of the original networks ($\langle k \rangle$). We denote the node density ($n_\text{core}$) and link density ($l_\text{core}$) to characterize the control core when applying the LRP, and we study the impact of $\langle k \rangle$ on $n_\text{core}$ and $l_\text{core}$ in two artificial networks: undirected Erd\"os-R\'enyi (ER) random networks and undirected scale-free (SF) networks. We find that $n_\text{core}$ and $l_\text{core}$ both change nonmonotonously with increasing $\langle k \rangle$ in the two typical undirected networks. With the aid of core percolation theory, we can offer the theoretical predictions for both $n_\text{core}$ and $l_\text{core}$ as a function of $\langle k \rangle$. Then, we recognize that finding the driver nodes in the control core is much more efficient than in the original network by comparing $n_{\text{D}}$, the controllability of the original network, and $n_{\text{core}}$, regardless of how $\langle k \rangle$ increases.