Guanrong Chen

Lin Wang, Guanrong Chen, Xiaofan Wang et al.

In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: 1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology, quite different from the familiar notion of consensus or formation controllability; 2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; 3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient. For a networked system with single-input/single-output (SISO) LTI nodes, we present precise necessary and sufficient conditions for the controllability of a general network topology.

Zhongkui Li, Zhisheng Duan, Guanrong Chen

This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle,an algorithm is proposed to construct a protocol having an origin-centered disk of radius $δ$ ($0<δ<1$) as its consensus region, where $δ$ has to further satisfy a constraint related to the unstable eigenvalues of a single agent for the case where each agent has a least one eigenvalue outside the unit circle. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.

Yang Lou, Lin Wang, Guanrong Chen

A new complex network model, called q-snapback network, is introduced. Basic topological characteristics of the network, such as degree distribution, average path length, clustering coefficient and Pearson correlation coefficient, are evaluated. The typical 4-motifs of the network are simulated. The robustness of both state and structural controllabilities of the network against targeted and random node- and edge-removal attacks, with comparisons to the multiplex congruence network and the generic scale-free network, are presented. It is shown that the q-snapback network has the strongest robustness of controllabilities due to its advantageous inherent structure with many chain- and loop-motifs.

Yu Zhao, Yongfang Liu, Guanrong Chen

This technical note addresses the distributed fixed-time consensus protocol design problem for multi-agent systems with general linear dynamics over directed communication graphs. By using motion planning approaches, a class of distributed fixed-time consensus algorithms are developed, which rely only on the sampling information at some sampling instants. For linear multi-agent systems, the proposed algorithms solve the fixed-time consensus problem for any directed graph containing a directed spanning tree. In particular, the settling time can be off-line pre-assigned according to task requirements. Compared with the existing results for multi-agent systems, to our best knowledge, it is the first-time to solve fixed-time consensus problems for general linear multi-agent systems over directed graphs having a directed spanning tree. Extensions to the fixed-time formation flying are further studied for multiple satellites described by Hill equations.

Yang Lou, Ruizi Wu, Junli Li et al.

Network robustness is critical for various societal and industrial networks again malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible. In this paper, an improved method for network robustness prediction is developed based on learning feature representation using convolutional neural network (LFR-CNN). In this scheme, higher-dimensional network data are compressed to lower-dimensional representations, and then passed to a CNN to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly lower prediction errors; 2) LFR-CNN is insensitive to the variation of the network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; 4) LFR-CNN not only can accurately predict network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.

Yongfang Liu, Yu Zhao, Wei Ren et al.

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In the context of the fixed-time consensus, we focus on both directed fixed and switching topologies. Under the directed fixed topology, a novel class of distributed algorithms are designed, which guarantee the consensus of the multi-agent system with a fixed settling time if the topology has a directed spanning tree. Under the directed periodically switching topologies, the fixedtime consensus is solved via the proposed algorithms if the topologies jointly have a directed spanning tree. In particular, the fixed settling time can be off-line pre-assigned according to task requirements. Compared with the existing results, to our best knowledge, it is the first time to solve the fixed-time consensus problem for double-integrator systems under directed topologies. Finally, a numerical example is given to illustrate the effectiveness of the analytical results.

Qishao Wang, Zhisheng Duan, Jingyao Wang et al.

The distributed optimal synchronization problem with linear quadratic cost is solved in this paper for multi-agent systems with an undirected communication topology. For the first time, the optimal synchronization problem is formulated as a distributed optimization problem with a linear quadratic cost functional that integrates quadratic synchronization errors and quadratic input signals subject to agent dynamics and synchronization constraints. By introducing auxiliary synchronization state variables and combining the distributed synchronization method with the alternating direction method of multiplier (ADMM), a new distributed control protocol is designed for solving the distributed optimization problem. With this construction, the optimal synchronization control problem is separated into several independent subproblems: a synchronization optimization, an input minimization and a dual optimization. These subproblems are then solved by distributed numerical algorithms based on the Lyapunov method and dynamic programming. Numerical examples for both homogeneous and heterogeneous multi-agent systems are given to demonstrate the effectiveness of the proposed method.

Acong Zhang, Ping Li, Guanrong Chen

In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is distributed discontinuously over the graph. To resolve the discontinuous information transmission problem, we propose a control principle to supervise representation learning by leveraging the prototypes (i.e., class centers) of labeled data. Treating graph learning as a discrete dynamic process and the prototypes of labeled data as "desired" class representations, we borrow the pinning control idea from automatic control theory to design learning feedback controllers for the feature learning process, attempting to minimize the differences between message passing derived features and the class prototypes in every round so as to generate class-relevant features. Specifically, we equip every node with an optimal controller in each round through learning the matching relationships between nodes and the class prototypes, enabling nodes to rectify the aggregated information from incompatible neighbors in a graph with strong heterophily. Our experiments demonstrate that the proposed PCGCN model achieves better performances than deep GNNs and other competitive heterophily-oriented methods, especially when the graph has very few labels and strong heterophily.

Jiayu Lin, Guanrong Chen, Bojun Jin et al.

In this paper we present the results of the AI-Debater 2023 Challenge held by the Chinese Conference on Affect Computing (CCAC 2023), and introduce the related datasets. We organize two tracks to handle the argumentative generation tasks in different scenarios, namely, Counter-Argument Generation (Track 1) and Claim-based Argument Generation (Track 2). Each track is equipped with its distinct dataset and baseline model respectively. In total, 32 competing teams register for the challenge, from which we received 11 successful submissions. In this paper, we will present the results of the challenge and a summary of the systems, highlighting commonalities and innovations among participating systems. Datasets and baseline models of the AI-Debater 2023 Challenge have been already released and can be accessed through the official website of the challenge.

Chengpei Wu, Yang Lou, Lin Wang et al.

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a sequence of values that record the remaining connectivity and controllability after a sequence of node- or edge-removal attacks. For improvement, this paper develops an efficient framework for network robustness prediction, the spatial pyramid pooling convolutional neural network (SPP-CNN). The new framework installs a spatial pyramid pooling layer between the convolutional and fully-connected layers, overcoming the common mismatch issue in the CNN-based prediction approaches and extending its generalizability. Extensive experiments are carried out by comparing SPP-CNN with three state-of-the-art robustness predictors, namely a CNN-based and two graph neural networks-based frameworks. Synthetic and real-world networks, both directed and undirected, are investigated. Experimental results demonstrate that the proposed SPP-CNN achieves better prediction performances and better generalizability to unknown datasets, with significantly lower time-consumption, than its counterparts.

Xinxing Wu, Tao Wang, Qian Liu et al.

We prove that the space of intuitionistic fuzzy values (IFVs) with a linear order based on a score function and an accuracy function has the same algebraic structure as the one induced by a linear order based on a similarity function and an accuracy function. By introducing a new operator for IFVs via the linear order based on a score function and an accuracy function, we show that such an operator is a strong negation on IFVs. Moreover, we observe that the space of IFVs is a complete lattice and a Kleene algebra with the new operator. We also demonstrate that the topological space of IFVs with the order topology induced by the above two linear orders is not separable and metrizable but compact and connected. From some new perspectives,our results partially answer three open problems posed by Atanassov [Intuitionistic Fuzzy Sets: Theory and Applications, Springer, 1999] and [On Intuitionistic Fuzzy Sets Theory, Springer, 2012]. Furthermore, we construct an isomorphism between the spaces of IFVs and q-rung orthopedic fuzzy values (q-ROFVs) under the corresponding linear orders. To this end, we introduce the concept of admissible similarity measures with particular orders for IFSs, extending the existing definition of the similarity measure for IFSs, and construct an admissible similarity measure with a linear order based on a score function and an accuracy function, which is effectively applied to a pattern recognition problem about the classification of building materials.

Hao Wang, Yue Deng, Linyuan Lü et al.

Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention. However, most graph embedding methods have problems such as tedious parameter tuning or poor explanation. This paper presents a simple and hyperparameter-free whole graph embedding method based on the DHC (Degree, H-index, and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The DHC-E can provide a trade-off between simplicity and quality for supervised classification learning tasks involving molecular, social, and brain networks. Moreover, it performs well in lower-dimensional graph visualization. Overall, the DHC-E is simple, hyperparameter-free, and explainable for whole graph embedding with promising potential for exploring graph classification and lower-dimensional graph visualization.

Yong Wang, Zhuo Liu, Leo Yu Zhang et al.

Applying chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems are usually heuristic, without theoretic guarantee for the resultant communication scheme. Among all the primitives for secure communications, it is well-accepted that (pseudo) random numbers are most essential. Taking the well-studied two-dimensional coupled map lattice (2D CML) as an example, this paper performs a theoretical study towards pseudo-random number generation with the 2D CML. In so doing, an analytical expression of the Lyapunov exponent (LE) spectrum of the 2D CML is first derived. Using the LEs, one can configure system parameters to ensure the 2D CML only exhibits complex dynamic behavior, and then collect pseudo-random numbers from the system orbits. Moreover, based on the observation that least significant bit distributes more evenly in the (pseudo) random distribution, an extraction algorithm E is developed with the property that, when applied to the orbits of the 2D CML, it can squeeze uniform bits. In implementation, if fixed-point arithmetic is used in binary format with a precision of $z$ bits after the radix point, E can ensure that the deviation of the squeezed bits is bounded by $2^{-z}$ . Further simulation results demonstrate that the new method not only guide the 2D CML model to exhibit complex dynamic behavior, but also generate uniformly distributed independent bits. In particular, the squeezed pseudo random bits can pass both NIST 800-22 and TestU01 test suites in various settings. This study thereby provides a theoretical basis for effectively applying the 2D CML to secure communications.

Dinghua Shi, Zhifeng Chen, Xiang Sun et al.

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions. Since searching for maximum cliques is an NP-complete problem, we use k-core decomposition to determine the computability of a given network. For a computable network, we design a search method with an implementable algorithm for finding cliques of different orders, obtaining also the Euler characteristic number. Then, we compute the Betti numbers by using the ranks of boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans with data from one typical dataset, and find all of its cliques and some cavities of different orders, providing a basis for further mathematical analysis and computation of its structure and function.

Jiajun Zhou, Jie Shen, Shanqing Yu et al.

Graph classification, which aims to identify the category labels of graphs, plays a significant role in drug classification, toxicity detection, protein analysis etc. However, the limitation of scale in the benchmark datasets makes it easy for graph classification models to fall into over-fitting and undergeneralization. To improve this, we introduce data augmentation on graphs (i.e. graph augmentation) and present four methods:random mapping, vertex-similarity mapping, motif-random mapping and motif-similarity mapping, to generate more weakly labeled data for small-scale benchmark datasets via heuristic transformation of graph structures. Furthermore, we propose a generic model evolution framework, named M-Evolve, which combines graph augmentation, data filtration and model retraining to optimize pre-trained graph classifiers. Experiments on six benchmark datasets demonstrate that the proposed framework helps existing graph classification models alleviate over-fitting and undergeneralization in the training on small-scale benchmark datasets, which successfully yields an average improvement of 3 - 13% accuracy on graph classification tasks.

Yang Lou, Yaodong He, Lin Wang et al.

Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node-removals or edge-removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the network after a sequence of attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this paper, a method to predict the controllability robustness based on machine learning using a convolutional neural network is proposed, motivated by the observations that 1) there is no clear correlation between the topological features and the controllability robustness of a general network, 2) the adjacency matrix of a network can be regarded as a gray-scale image, and 3) the convolutional neural network technique has proved successful in image processing without human intervention. Under the new framework, a fairly large number of training data generated by simulations are used to train a convolutional neural network for predicting the controllability robustness according to the input network-adjacency matrices, without performing conventional attack simulations. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting controllability robustness of different network configurations is accurate and reliable with very low overheads.

Qi Xuan, Jinhuan Wang, Minghao Zhao et al.

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the underlying network. Although such statistics can be used to describe a network model, or even to design some network algorithms, the role of subgraphs in such applications can be further explored so as to improve the results. In this paper, the concept of subgraph network (SGN) is introduced and then applied to network models, with algorithms designed for constructing the 1st-order and 2nd-order SGNs, which can be easily extended to build higher-order ones. Furthermore, these SGNs are used to expand the structural feature space of the underlying network, beneficial for network classification. Numerical experiments demonstrate that the network classification model based on the structural features of the original network together with the 1st-order and 2nd-order SGNs always performs the best as compared to the models based only on one or two of such networks. In other words, the structural features of SGNs can complement that of the original network for better network classification, regardless of the feature extraction method used, such as the handcrafted, network embedding and kernel-based methods.

Yang Lou, Shiu Yin Yuen, Guanrong Chen et al.

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.

Chengqing Li, Shujun Li, Muhammad Asim et al.

This paper studies the security of a recently-proposed chaos-based image encryption scheme, and points out the following problems: 1) there exist a number of invalid keys and weak keys, and some keys are partially equivalent for encryption/decryption; 2) given one chosen plain-image, a subkey $K_{10}$ can be guessed with a smaller computational complexity than that of the simple brute-force attack; 3) given at most 128 chosen plain-images, a chosen-plaintext attack can possibly break the following part of the secret key: $\{K_i\bmod 128\}_{i=4}^{10}$, which works very well when $K_{10}$ is not too large; 4) when $K_{10}$ is relatively small, a known-plaintext attack can be carried out with only one known plain-image to recover some visual information of any other plain-images encrypted by the same key.

Yang Lou, Guanrong Chen, Zhengping Fan et al.

Community structure is essential for social communications, where individuals belonging to the same community are much more actively interacting and communicating with each other than those in different communities within the human society. Naming game, on the other hand, is a social communication model that simulates the process of learning a name of an object within a community of humans, where the individuals can generally reach global consensus asymptotically through iterative pair-wise conversations. The underlying network indicates the relationships among the individuals. In this paper, three typical topologies, namely random-graph, small-world and scale-free networks, are employed, which are embedded with the multi-local-world community structure, to study the naming game. Simulations show that 1) the convergence process to global consensus is getting slower as the community structure becomes more prominent, and eventually might fail; 2) if the inter-community connections are sufficiently dense, neither the number nor the size of the communities affects the convergence process; and 3) for different topologies with the same average node-degree, local clustering of individuals obstruct or prohibit global consensus to take place. The results reveal the role of local communities in a global naming game in social network studies.

Yang Lou, Guanrong Chen, Jianwei Hu

Naming game simulates the process of naming an object by a single word, in which a population of communicating agents can reach global consensus asymptotically through iteratively pair-wise conversations. We propose an extension of the single-word model to a multi-word naming game (MWNG), simulating the case of describing a complex object by a sentence (multiple words). Words are defined in categories, and then organized as sentences by combining them from different categories. We refer to a formatted combination of several words as a pattern. In such an MWNG, through a pair-wise conversation, it requires the hearer to achieve consensus with the speaker with respect to both every single word in the sentence as well as the sentence pattern, so as to guarantee the correct meaning of the saying, otherwise, they fail reaching consensus in the interaction. We validate the model in three typical topologies as the underlying communication network, and employ both conventional and man-designed patterns in performing the MWNG.

Chengqing Li, Bingbing Feng, Shujun Li et al.

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.