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This paper investigates data-driven cooperative output regulation for continuous-time multi-agent systems with unknown network topology. Unlike existing studies that typically assume a known network topology to directly compute controller parameters, a novel approach is proposed that allows for the computation of the parameter without prior knowledge of the topology. A lower bound on the minimum non-zero eigenvalue of the Laplacian matrix is estimated using only edge weight bounds, enabling the output regulation controller design to be independent of global network information. Additionally, the common need for state derivative measurements is eliminated, reducing the amount of data requirements. Furthermore, necessary and sufficient conditions are established to ensure that the data are informative for cooperative output regulation, leading to the design of a distributed output regulation controller. For the case with noisy data, the bound of the output error is provided, which is positively correlated with the noise bound, and a distributed controller is constructed for the approximate cooperative output regulation. Finally, the effectiveness of the proposed methods is verified through numerical simulations.

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.

This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed feedback information. Specifically, each agent in the game is assumed to be informed a sequence of local cost functions and constraint functions, which are known to the agent with time-varying delays subsequent to decision-making at each round. The objective of each agent within a cluster is to collaboratively optimize the cluster's cost function, subject to time-varying coupled inequality constraints and local feasible set constraints over time. Additionally, it is assumed that each agent is required to estimate the decisions of all other agents through interactions with its neighbors, rather than directly accessing the decisions of all agents, i.e., each agent needs to make decision under partial-decision information. To solve such a challenging problem, a novel distributed online delay-tolerant GNE learning algorithm is developed based upon the primal-dual algorithm with an aggregation gradient mechanism. The system-wise regret and the constraint violation are formulated to measure the performance of the algorithm, demonstrating sublinear growth with respect to time under certain conditions. Finally, numerical results are presented to verify the effectiveness of the proposed algorithm.

In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos., Comment: accepted to CS&F

Uncovering higher-order spatiotemporal dependencies within human mobility networks offers valuable insights into the analysis of urban structures. In most existing studies, human mobility networks are typically constructed by aggregating all trips without distinguishing who takes which specific trip. Instead, we claim individual mobility motifs, higher-order structures generated by daily trips of people, as fundamental units of human mobility networks. In this paper, we propose two network construction frameworks at the level of mobility motifs in characterizing regional importance in cities. Firstly, we enhance the structural dependencies within mobility motifs and proceed to construct mobility networks based on the enhanced mobility motifs. Secondly, taking inspiration from PageRank, we speculate that people would allocate values of importance to destinations according to their trip intentions. A motif-wise network construction framework is proposed based on the established mechanism. Leveraging large-scale metro data across cities, we construct three types of human mobility networks and characterize the regional importance by node importance indicators. Our comparison results suggest that the motif-based mobility network outperforms the classic mobility network, thus highlighting the efficacy of the introduced human mobility motifs. Finally, we demonstrate that the performance in characterizing the regional importance is significantly improved by our motif-wise framework.

Blockchain technology is a breakthrough in changing the ways of business and organization operations, in which the consensus problem is challenging with practical constraints, such as computational power and consensus standard. In this paper, a novel consensus mechanism named Proof-of-Prospect-Theory (PoPT) is designed from the view of game theory, where the game prospect value is considered as an important election criterion of the block-recorder. PoPT portrays the popularity of a node in the network as an attribute, which is constituted by the subjective sensibilities of nodes. Furthermore, the performances of the PoPT and the willingness of ordinary nodes to participate in the consensus are analyzed, exploring fairness, decentralization, credibility, and the motivating ability of the consensus mechanism. Finally, numerical simulations with optimization of the PoPT consensus mechanism are demonstrated in the scenario of a smart grid system to illustrate the effectiveness of the PoPT.

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., Comment: 10 pages, 7 figures, 14 pages Supplementary Information

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., Comment: 12 pages

Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the dataset; that is, establishing the integrated taxonomic relation among points, lines and simplices. Here, the simplicial network composed of all-order simplices in a simplicial complex is essential. Because the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values, a method based on the concept of critical simplices can be developed by searching all-order spanning trees. Employing this new method, not only the Morse function values with the theoretical minimum number of critical simplices can be obtained, but also the Betti numbers and composition of all-order cavities in the simplicial network can be calculated quickly. Finally, this method is used to analyze some examples and compared with other methods, showing its effectiveness and feasibility., Comment: 12 pages, 6 figures, 5 tables

The Roamn domination problem is one important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security, considering backups in the face of a dynamic network security requirement. In this paper, firstly, we propose a Roman domination game (RDG) and prove that every Nash equilibrium (NE) of the game corresponds to a strong minimal Roman dominating function (S-RDF), as well as a Pareto-optimal solution. Secondly, we show that RDG is an exact potential game, which guarantees the existence of an NE. Thirdly, we design a game-based synchronous algorithm (GSA), which can be implemented distributively and converge to an NE in $O(n)$ rounds, where $n$ is the number of vertices. In GSA, all players make decisions depending on the local information. Furthermore, we enhance GSA to be enhanced GSA (EGSA), which converges to a better NE in $O(n^2)$ rounds. Finally, we present numerical simulations to demonstrate that EGSA can obtain a better approximate solution in promising computation time compared with state-of-the-art algorithms.

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.

Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM), picture fuzzy interactional weighted Bonferroni mean (PFIWBM), and picture fuzzy interactional normalized weighted Bonferroni mean (PFINWBM) operators. We prove the monotonicity, idempotency, boundedness, and commutativity for the PFIBM and PFINWBM operators. We also establish a novel multi-criteria decision making (MCDM) method under the picture fuzzy environment by applying the PFINWBM operator. Furthermore, we apply our MCDM method to the enterprise resource planning (ERP) systems selection. The comparative results for our MCDM method induced by six classes of well-known triangular norms ensure that the best selection is always the same ERP system. Therefore, our MCDM method is effective for dealing with the picture fuzzy MCDM problems., Comment: This paper has been accepted by IEEE Transactions on Fuzzy Systems

It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher-order nonpairwise relations among nodes, i.e., interactions between among than two nodes at a time. This simplicial structure can be described by simplicial complexes and has an important effect on topological and dynamical properties of networks involving such group interactions. In this paper, we study analytically resistance distances in iteratively growing networks with higher-order interactions characterized by the simplicial structure that is controlled by a parameter q. We derive exact formulas for interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance, which have found applications in various areas elsewhere. We show that the average resistance distance tends to a q-dependent constant, indicating the impact of simplicial organization on the structural robustness measured by average resistance distance., Comment: accepted by The Computer Journal

Despite many distributed resource allocation (DRA) algorithms have been reported in literature, it is still unknown how to allocate the resource optimally over multiple interacting coalitions. One major challenge in solving such a problem is that, the relevance of the decision on resource allocation in a coalition to the benefit of others may lead to conflicts of interest among these coalitions. Under this context, a new type of multi-coalition game is formulated in this paper, termed as resource allocation game, where each coalition contains multiple agents that cooperate to maximize the coalition-level benefit while subject to the resource constraint described by a coupled equality. Inspired by techniques such as variable replacement, gradient tracking and leader-following consensus, two new kinds of DRA algorithms are developed respectively for the scenarios where the individual benefit of each agent explicitly depends on the states of itself and some agents in other coalitions, and on the states of all the game participants. It is shown that the proposed algorithms can converge linearly to the Nash equilibrium (NE) of the multi-coalition game while satisfying the resource constraint during the whole NE-seeking process. Finally, the validity of the present allocation algorithms is verified by numerical simulations.

Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the structure of the associated \textit{functional graph} of Chebyshev permutation polynomials over a ring $\mathbb{Z}_{p^k}$, with $p$ being a prime number greater than three, where every number in the ring is considered as a vertex and the existing mapping relation between two vertices is regarded as a directed edge. Based on some new properties of Chebyshev polynomials and their derivatives, we disclose how the basic structure of the functional graph evolves with respect to parameter $k$. First, we present a complete and explicit form of the length of a path starting from any given vertex. Then, we show that the strong patterns of the functional graph that the number of cycles of any given length always remains constant as $k$ increases. Moreover, we rigorously prove the rules on the elegant structure of the functional graph and verify them experimentally. Our results could be useful for studying the emergence of the complexity of a nonlinear map in digital computers and security analysis of its cryptographic applications., Comment: 15 pages, 2 figures

Being a pair of dual concepts, the normalized distance and similarity measures are very important tools for decision-making and pattern recognition under intuitionistic fuzzy sets framework. To be more effective for decision-making and pattern recognition applications, a good normalized distance measure should ensure that its dual similarity measure satisfies the axiomatic definition. In this paper, we first construct some examples to illustrate that the dual similarity measures of two nonlinear distance measures introduced in [A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems, \emph{IEEE Trans. Syst., Man, Cybern., Syst.}, vol.~51, no.~6, pp. 3980--3992, 2021] and [Intuitionistic fuzzy sets: spherical representation and distances, \emph{Int. J. Intell. Syst.}, vol.~24, no.~4, pp. 399--420, 2009] do not meet the axiomatic definition of intuitionistic fuzzy similarity measure. We show that (1) they cannot effectively distinguish some intuitionistic fuzzy values (IFVs) with obvious size relationship; (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance 1 can be achieved under these two distances; leading to counter-intuitive results. To overcome these drawbacks, we introduce the concepts of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. We prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is completely superior to the existing ones., Comment: Please replace the first version, because the first version lacks copyright description and has some errors

In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical higher-dimensional dynamics. A necessary and sufficient condition on the discernibility of topological variations is derived, in terms of the eigenspaces of the original and the modified network configuarations. By taking the specific network structures into consideration, some lower-dimensional conditions are derived, which reveal how the network topologies, sensor locations, node-system dynamics and output, as well as inner interactions altogether affect the discernibility. Furthermore, the output discernibility of topological changes for networked multi-agent systems is revisited, showing that some criterion reported in the literature does not hold. Consequently, a modified necessary and sufficient condition is established. The effectiveness of the results is demonstrated through several examples.

This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise covariance, a variational Bayesian method and a fixed-point iteration method are utilized to jointly estimate the posterior state vector and the unknown noise covariances under a stochastic event-triggered mechanism. The proposed algorithm ensures low communication loads and excellent estimation performances for a wide range of unknown noise covariances. Finally, the performance of the proposed algorithm is demonstrated by tracking simulations of a vehicle.

All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect the choices of positive ideal-points and negative ideal-points, and construction of admissible distance/similarity measures; (2) the distance/similarity measure, which is closely related to the values of the relative closeness degrees and determines the accuracy and rationality of decision-making. For the order structure, many efforts are devoted to constructing some score functions, which can strictly distinguish different intuitionistic fuzzy values (IFVs) and preserve the natural partial order for IFVs.This paper proves that such a score function does not exist, namely the application of a single monotonous and continuous function does not distinguish all IFVs. For the distance or similarity measure, some examples are given to show that classical similarity measures based on the normalized Euclidean distance and normalized Minkowski distance do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. Moreover,some illustrative examples are given to show that classical intuitionistic fuzzy TOPSIS methods do not ensure the monotonicity with the natural partial order or linear orders, which may yield some counter-intuitive results. To overcome the limitation of non-monotonicity, we propose a novel intuitionistic fuzzy TOPSIS method,using three new admissible distances with the linear orders measured by a score degree/similarity function and accuracy degree, or two aggregation functions, and prove that the proposed TOPSIS method is monotonous under these three linear orders.} This is the first result with a strict mathematical proof on the monotonicity with the linear orders for the intuitionistic fuzzy TOPSIS method.

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., Comment: 12 pages, 10 figures. IEEE Trans. Cybern. 2022

This paper investigates sensor scheduling for state estimation of complex networks over shared transmission channels. For a complex network of dynamical systems, referred to as nodes, a sensor network is adopted to measure and estimate the system states in a distributed way, where a sensor is used to measure a node. The estimates are transmitted from sensors to the associated nodes, in the presence of one-step time delay and subject to packet loss. Due to limited transmission capability, only a portion of sensors are allowed to send information at each time step. The goal of this paper is to seek an optimal sensor scheduling policy minimizing the overall estimation errors. Under a distributed state estimation framework, this problem is reformulated as a Markov decision process, where the one-stage reward for each node is strongly coupled. The feasibility of the problem reformulation is ensured. In addition, an easy-to-check condition is established to guarantee the existence of an optimal deterministic and stationary policy. Moreover, it is found that the optimal policies have a threshold, which can be used to reduce the computational complexity in obtaining these policies. Finally, the effectiveness of the theoretical results is illustrated by several simulation examples.

Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large number of communication and storage systems. By exploiting the iterative demapping and decoding (ID), the BICM is able to approach capacity limits of coded modulation over various channels. In recent years, protograph low-density parity-check (PLDPC) codes and their spatially-coupled (SC) variants have emerged to be a pragmatic forward-error-correction (FEC) solution for BICM systems due to their tremendous error-correction capability and simple structures, and found widespread applications such as deep-space communication, satellite communication, wireless communication, optical communication, and data storage. This article offers a comprehensive survey on the state-of-the-art development of PLDPC-BICM and its innovative SC variants over a variety of channel models, e.g., additive white Gaussian noise (AWGN) channels, fading channels, Poisson pulse position modulation (PPM) channels, and flash-memory channels. Of particular interest is code construction, constellation shaping, as well as bit-mapper design, where the receiver is formulated as a serially-concatenated decoding framework consisting of a soft-decision demapper and a belief-propagation decoder. Finally, several promising research directions are discussed, which have not been adequately addressed in the current literature.

For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence of the estimation error covariance matrix of each sensor is guaranteed under a collective observability condition. In particular, the steady-state covariance matrix can be simplified as the solution to a discrete-time Lyapunov equation. Moreover, the performance degradation induced by reduced fusion frequency is obtained in closed form, which establishes an analytical relation between the performance of the CMDF with finite fusion steps and that of centralized filtering. Meanwhile, it provides a trade-off between the filtering performance and the communication cost. Furthermore, it is shown that the steady-state estimation error covariance matrix exponentially converges to the centralized optimal steady-state matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments.

In network science, the null model is typically used to generate a series of graphs based on randomization as a term of comparison to verify whether a network in question displays some non-trivial features such as community structure. Since such non-trivial features play a significant role in graph classification, the null model could be useful for network data augmentation to enhance classification performance. In this paper, we propose a novel technique that combines the null model with data augmentation for graph classification. Moreover, we propose four standard null model-based augmentation methods and four approximate null model-based augmentation methods to verify and improve the performance of our graph classification technique. Our experiments demonstrate that the proposed augmentation technique has significantly achieved general improvement on the tested datasets. In addition, we find that the standard null model-based augmentation methods always outperform the approximate ones, depending on the design mechanisms of the null models. Our results indicate that the choice of non-trivial features is significant for increasing the performance of augmentation models for different network structures, which also provides a new perspective of data augmentation for studying various graph classification methods.

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.

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.

The conventional LoRa system is not able to sustain long-range communication over fading channels. To resolve the challenging issue, this paper investigates a two-hop opportunistic amplify-and-forward relaying LoRa system. Based on the best relay-selection protocol, the analytical and asymptotic bit error rate (BER), achievable diversity order, coverage probability, and throughput of the proposed system are derived over the Nakagamim fading channel. Simulative and numerical results show that although the proposed system reduces the throughput compared to the conventional LoRa system, it can significantly improve BER and coverage probability. Hence, the proposed system can be considered as a promising platform for low-power, long-range and highly reliable wireless-communication applications., Comment: 7 pages, 6 figures, conference

With the rapid development of artificial intelligence, a number of machine learning algorithms, such as graph neural networks have been proposed to facilitate network analysis or graph data mining. Although effective, recent studies show that these advanced methods may suffer from adversarial attacks, i.e., they may lose effectiveness when only a small fraction of links are unexpectedly changed. This paper investigates three well-known adversarial attack methods, i.e., Nettack, Meta Attack, and GradArgmax. It is found that different attack methods have their specific attack preferences on changing the target network structures. Such attack pattern are further verified by experimental results on some real-world networks, revealing that generally the top four most important network attributes on detecting adversarial samples suffice to explain the preference of an attack method. Based on these findings, the network attributes are utilized to design machine learning models for adversarial sample detection and attack method recognition with outstanding performance.

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., Comment: 10 pages, 11figures

Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information processing. However, existing research focuses on the basic statistics of certain motifs, largely ignoring the connection patterns among them. Recently, a subgraph network (SGN) model is proposed to study the potential structure among motifs, and it was found that the integration of SGN can enhance a series of graph classification methods. However, SGN model lacks diversity and is of quite high time complexity, making it difficult to widely apply in practice. In this paper, we introduce sampling strategies into SGN, and design a novel sampling subgraph network model, which is scale-controllable and of higher diversity. We also present a hierarchical feature fusion framework to integrate the structural features of diverse sampling SGNs, so as to improve the performance of graph classification. Extensive experiments demonstrate that, by comparing with the SGN model, our new model indeed has much lower time complexity (reduced by two orders of magnitude) and can better enhance a series of graph classification methods (doubling the performance enhancement).

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, ignoring those second, third, and higher-order neighbors, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinion is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective., Comment: accepted by Data Mining and Knowledge Discovery

A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In generally, they are simultaneously sparse, scale-free, small-world, and loopy. In this paper, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherence $H_{\rm SO}$ characterized in terms of the $\mathcal{H}_2$-norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherence $H_{\rm SO}$ scales sublinearly with the vertex number $N$. We then study analytically $H_{\rm SO}$ for a class of iteratively growing networks -- pseudofractal scale-free webs (PSFWs), and obtain an exact solution to $H_{\rm SO}$, which also increases sublinearly in $N$, with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally study $H_{\rm SO}$ for Sierpin\'ski gaskets, for which $H_{\rm SO}$ grows superlinearly in $N$, with a power exponent much larger than 1. Sierpin\'ski gaskets have the same number of vertices and edges as the PSFWs, but do not display the scale-free and small-world properties. We thus conclude that the scale-free and small-world, and loopy topologies are jointly responsible for the observed sublinear scaling of $H_{\rm SO}$.

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., Comment: 20 pages, 4+2 figures, 3+3 tables

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.

Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a malicious attack. A framework of hierarchical attack is proposed, by means of edge- or node-removal attacks. Edges (or nodes) in a target network are classified hierarchically into categories, with different priorities to attack. The category of critical edges (or nodes) has the highest priority to be selected for attack. Extensive experiments on nine synthetic networks and nine real-world networks show the effectiveness of the proposed hierarchical attack strategies for destructing the network controllability. From the protection point of view, this study suggests that the critical edges and nodes should be hidden from the attackers. This finding helps better understand the network controllability and better design robust networks., Comment: 10 pages,10 figures

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., Comment: 11 pages, 9 figures. arXiv admin note: text overlap with arXiv:2009.09863

This article briefly introduces the generalized Lorenz systems family, which includes the classical Lorenz system and the relatively new Chen system as special cases, with infinitely many related but not topologically equivalent chaotic systems in between., Comment: 14 pages, 7 figures, 2 tables

In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not the convolution of $t$-norms on $[0, 1]$, is obtained. These results negatively answer two open problems posed by Walker and Walker in [15]., Comment: arXiv admin note: text overlap with arXiv:2003.11953 and arXiv:1908.10532