Understanding how information propagation affects epidemic dynamics has become an emerging topic of interest. However, the influence of interpersonal relationship heterogeneity on information acquisition and disease transmission has been largely overlooked. In this work, we introduce a hypergraph structure for Cyber-Physical Systems (CPSs) with two distinct layers. The upper layer, referred to as the cyber layer, consists of a mixed hypergraph, capturing both pairwise propagation and higher-order diffusion of epidemic-related information. The lower layer, referred to as the physical layer, employs a Susceptible-Infected-Susceptible (SIS) process to capture epidemic spreading. This work introduces an adaptive perception-protection mechanism based on Jaccard similarity, which accounts for interpersonal heterogeneity. In this mechanism, individuals receive information based on their relationships with neighbors and take protective measures accordingly. We analyze the impact of interpersonal relationships and the adoption of neighborhood-based self-protection strategies on epidemic dynamics. Furthermore, we conduct a theoretical analysis based on the Microscopic Markov Chain Approach (MMCA), analytically derive the outbreak threshold, and confirm the results with extensive Monte Carlo (MC) simulations. The results show that stronger interpersonal relationships can promote information propagation, significantly increase the threshold for epidemic outbreaks, and effectively suppress the scale of the epidemic. The study provides theoretical support for designing epidemic control strategies considering interpersonal heterogeneity and improves the understanding of epidemic spreading on hypergraphs.

Time-series forecasting is considered a critical task with extensive applications across diverse domains. However, effectively capturing both cross-dimension and cross-time dependencies in nonstationary time series remains a significant challenge, particularly due to the confounding effects of environmental factors. These factors often introduce spurious correlations that obscure the learning of meaningful temporal features. In this article, the novel framework Caformer (Causal Transformer) is proposed for time-series forecasting grounded in causal reasoning, the science of identifying causality. The framework consists of four key modules: the dynamic learner, environment learner, temporal learner, and decompose learner. The dynamic learner uncovers dynamic interactions among features to model cross-dimension dependencies, while the temporal learner infers cross-time dependencies under causal constraints. The environment learner, together with the decompose learner, extracts environmental factors and applies a backdoor adjustment to mitigate the confounding effects on the time series. Extensive experiments demonstrate that Caformer achieves the state-of-the-art performance in both long-term and short-term forecasting. It achieves up to a 26.2% mean square error (mse) reduction on the traffic dataset and 21.8% on the electricity dataset compared to PatchTST, with consistent gains across eight long-term benchmarks. On the M4 dataset, Caformer ranks first across all 15 short-term forecasting categories. In addition to strong predictive accuracy, Caformer provides interpretable insights into the learned dependencies.

The rapid spread of fake news on social media has significantly increased the importance of computational detection methods. Graph-based approaches, particularly Graph Neural Networks (GNNs), have emerged as powerful tools for modeling news propagation patterns. Despite their potential, current GNN-based methods still face challenges in robustness and interpretability due to two key shortcomings: they inadequately filter out irrelevant user-induced noise within propagation graphs, and their shallow architectures fail to effectively capture the intricate long-range dependencies characteristic of news propagation. To overcome these limitations, we propose NEGT (Noise-filtering Enhanced Graph Transformer), a novel graph Transformer framework explicitly designed for fake news detection. NEGT introduces a noise-augmented information bottleneck strategy embedded within its self-attention mechanism, effectively identifying and removing task-irrelevant interactions. Additionally, we propose a novel relational propagation graph encoding a strategy that explicitly captures multi-scale user relationships and propagation depth, enabling NEGT to model long-sequence propagation dependencies accurately. Experiments on various benchmark datasets show that NEGT surpasses current methods in accuracy, noise robustness, and interpretability.

Facing climate change, the transformation to renewable energy poses stability challenges for power grids due to their reduced inertia and increased decentralization. Traditional dynamic stability assessments, crucial for safe grid operation with higher renewable shares, are computationally expensive and unsuitable for large-scale grids in the real world. Although multiple proofs in the network science have shown that network measures, which quantify the structural characteristics of networked dynamical systems, have the potential to facilitate basin stability prediction, no studies to date have demonstrated their ability to efficiently generalize to real-world grids. With recent breakthroughs in Graph Neural Networks (GNNs), we are surprised to find that there is still a lack of a common foundation about: Whether network measures can enhance GNNs' capability to predict dynamic stability and how they might help GNNs generalize to realistic grid topologies. In this paper, we conduct, for the first time, a comprehensive analysis of 48 network measures in GNN-based stability assessments, introducing two strategies for their integration into the GNN framework. We uncover that prioritizing measures with consistent distributions across different grids as the input or regarding measures as auxiliary supervised information improves the model's generalization ability to realistic grid topologies, even when models trained on only 20-node synthetic datasets are used. Our empirical results demonstrate a significant enhancement in model generalizability, increasing the$R^{2}$perforsmance from 66% to 83%. When evaluating the probabilistic stability indices on the realistic Texan grid model, GNNs reduce the time needed from 28,950 hours (Monte Carlo sampling) to just 0.06 seconds.

Compressed learning (CL), integrating compressed sensing (CS) and machine learning (ML), enables direct inference from few CS measurements. However, existing CL methods either heavily rely on pre-trained models built upon extremely large-scale datasets or perform only relatively simple tasks on small datasets, restricting their scalability in real-world multimedia scenarios. To address these limitations, we propose an efficient CL framework named HTMA-CL for practical multimedia acquisition and edge intelligent processing. HTMA-CL employs CNN-based learnable sampling to realize block-based CS for high-resolution images, significantly decreasing the transmission bandwidth and storage overhead. A hierarchical tokenization module together with a deep-narrow Transformer module progressively models local and global dependencies within the measurements, enabling accurate inference directly in the compressive domain. Various task heads are constructed for performing diverse multimedia analysis tasks such as image classification and semantic segmentation. Extensive experiments demonstrate that our HTMA-CL achieves state-of-the-art performance compared to other CL methods, and nearly comparable performance to the image domain methods at a CS ratio of 10%. Our method further verifies the strong robustness against external interference in the disturbance-prone IoT multimedia environments. The source code is publicly available at https://github.com/acrlife/HTMA-CL.git .

Understanding how human mobility and information propagation influence the course of an epidemic remains a key challenge in digital epidemiology. In this work, we develop a new awareness-based, event-triggered epidemic model embedded within a networked Cyber-Physical System (CPS). In our framework, disease transmission and the dissemination of epidemic-related information evolve together on two interconnected layers. In detail, the physical layer models dis ease spread through human movement between two types of locations–residences and transfer stations-forming a bipartite metapopulation network. This structure captures the rendezvous effect, which reflects how gatherings in shared locations contribute to infection spread. The cyber layer represents the flow of information through digital communication networks. We introduce an event-triggered migration regulation mechanism, whereby individuals adapt their movement patterns based on local awareness thresholds, leading to a decentralized control process embedded within the network. Using a microscopic Markov chain approach (MMCA), we derive the epidemic threshold analytically and validate our results through extensive Monte Carlo simulations. Our findings show that event-triggered migration effectively suppresses the overall spread of the disease and lowers infection peaks-especially in heterogeneous populations and densely connected gathering points. These results demonstrate the potential of CPS-based epidemic models to enable real-time, awareness-driven interventions and to inform the design of decentralized control strategies that leverage digital communication dynamics.

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the node count remains constant, instead prioritizing node growth. In this work, we depart from the assumptions of node number variation and preferential attachment to present an innovative model that conceptualizes node degree fluctuations as a state-dependent random walk process with stasis and variable diffusion coefficient. We show that this model yields stochastic dynamic networks with stable scale-free properties. Through comprehensive theoretical and numerical analyses, we demonstrate that the degree distribution converges to a power-law distribution, provided that the lowest degree state within the network is not an absorbing state. Furthermore, we investigate the resilience of the fraction of the largest component and the average shortest path length following deliberate attacks on the network. By using three real-world networks, we confirm that the proposed model accurately replicates actual data. The proposed model thus elucidates mechanisms by which networks, devoid of growth and preferential attachment features, can still exhibit power-law distributions and be used to simulate and study the resilience of attacked fixed-size scale-free networks.

Diffusion probabilistic models (DPMs) have recently demonstrated impressive generative capabilities. There is emerging evidence that their sample reconstruction ability can yield meaningful representations for recognition tasks. In this paper, we demonstrate that the objectives underlying generation and representation learning are not perfectly aligned. Through a spectral analysis, we find that minimizing the mean squared error (MSE) between the original graph and its reconstructed counterpart does not necessarily optimize representations for downstream tasks. Instead, focusing on reconstructing a small subset of features, specifically those capturing global information, proves to be more effective for learning powerful representations. Motivated by these insights, we propose a novel framework, the Smooth Diffusion Model for Graphs (SDMG), which introduces a multi-scale smoothing loss and low-frequency information encoders to promote the recovery of global, low-frequency details, while suppressing irrelevant high-frequency noise. Extensive experiments validate the effectiveness of our method, suggesting a promising direction for advancing diffusion models in graph representation learning.

Complex networks serve as abstract models for understanding real-world complex systems and provide frameworks for studying structured dynamical systems. This article addresses limitations in current studies on the exploration of individual birth-death and the development of community structures within dynamic systems. To bridge this gap, we propose a networked evolution model that includes the birth and death of individuals, incorporating reinforcement learning through games among individuals. Each individual has a lifespan following an arbitrary distribution, engages in games with network neighbors, selects actions using Q-learning in reinforcement learning, and moves within a two-dimensional space. The developed theories are validated through extensive experiments. Besides, we observe the evolution of cooperative behaviors and community structures in systems both with and without the birth-death process. The fitting of real-world populations and networks demonstrates the practicality of our model. Furthermore, comprehensive analyses of the model reveal that exploitation rates and payoff parameters determine the emergence of communities, learning rates affect the speed of community formation, discount factors influence stability, and two-dimensional space dimensions dictate community size. Our model offers a novel perspective on real-world community development and provides a valuable framework for studying population dynamics behaviors.

For high-dimensional heterogeneous Kuramoto oscillator networks (HDHKONs) evolving in continuous time, achieving global synchronization can be exceedingly challenging, and in many cases, it may even appear impossible for various network configurations, including Platonic solids and Archimedean solids, or large-scale networks. Herein, a pinning impulsive control approach for HDHKONs is developed to attain global synchronization on the unit sphere without imposing constraints on initial phase distributions. With this approach, the entire network is globally stabilized onto an objective trajectory by impulsively controlling only a small fraction of oscillators. Furthermore, several synchronization criteria are provided to ensure that the global synchronization procedure is successful. These criteria are easily verified and shed light on the interplay among network parameters, the percentage of controlled oscillators, impulsive intensity, and impulsive frequency. Finally, two examples are implemented to validate the theoretical results.

This article aims at the leader-following secure consensus problem of nonlinear multiagent systems (MASs) with switching topologies, where the agents are not only suffered from the aperiodic malicious denial-of-service (DoS) attacks but also affected by instantaneous disturbance from the external environment. Due to the existing challenge of instantaneous disturbance about occurrence time being unknown, the impulsive-based switching network structure is put forward to tackle the impact of external instantaneous disturbance on MASs. Then, a novel hybrid event-triggered and impulsive control protocol is developed to guarantee that nonlinear MASs can resist DoS attacks and achieve the consensus control objective. Contrasted with the methods of continuous control, the developed hybrid event-triggered and impulsive control protocol using the discontinuous sampled state has certain merits saving control resources. Based on the Lyapunov theory, the stability of the closed-loop system is proven, and the Zeno behavior can be excluded successfully. An example is supplied to elicit the availability of the presented methodology.

This article studies the diffusion-source-inference (DSI) problem, whose solution plays an important role in real-world scenarios such as combating misinformation and controlling diffusions of information or disease. The main task of the DSI problem is to optimize an estimator, such that the real source can be more precisely targeted. In this article, we assume that the state of a number of nodes, called observer set, in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the DSI problem. In particular, we find that the conventional error distance metric cannot precisely evaluate the effectiveness of varied DSI approaches in heterogeneous networks, and thus propose a novel and more general measurement, the candidate set, that is formulated to contain the diffusion source for sure. We propose the percolation-based evolutionary framework (PrEF) to optimize the observer set such that the candidate set can be minimized. Hence, one could further conduct more intensive investigation or search on only a few nodes to target the source. To achieve that, we first theoretically show that the size of the candidate set is bounded by the size of the largest component cover, and demonstrate that there are some similarities between the DSI problem and the network immunization problem. We find that, given the associated direction information of the diffusion is known on observers, the minimization of the candidate set is equivalent to the minimization of the order parameter if we view the observer set as the removal node set. Hence, PrEF is developed based on the network percolation and evolutionary algorithm. The effectiveness of the proposed method is validated on both synthetic and empirical networks in regard to varied circumstances. Our results show that the developed approach could achieve much smaller candidate sets compared to the state of the art in almost all cases, e.g., it is better in 26 out of 27 empirical networks and 155 out of 162 cases regarding the critical threshold. Meanwhile, our approach is also more stable, i.e., it works well irrespective of varied infection probabilities, diffusion models, and underlying networks. More importantly, we provide a framework for the analysis of the DSI problem in large-scale networks.

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this article, we introduce a complex network model that considers the stochastic switching of individuals between activated and quiescent states at power-law rates and the corresponding evolutionary dynamics. By using the Markov chain and renewal theory, we discover a homogeneous stationary distribution of activated sizes in the network with power-law activating patterns and infer some statistical characteristics. To better understand the effect of power-law activating patterns, we study the two-person-two-strategy evolutionary game dynamics, demonstrate the absorbability of strategies, and obtain the critical cooperation conditions for prisoner’s dilemmas in homogeneous networks without mutation. The evolutionary dynamics in real networks are also discussed. Our results provide a new perspective to analyze and understand social physics in time-evolving network systems.

In order to investigate how different levels of vigilance affect the spread of a virus and changes in public opinion, this article introduces a network-based susceptible-exposed-infectious-vigilant (SEIV)-Opinion model. The model incorporates vigilance influence functions that depend on infection and recovery rates, which are associated with opinion states. A basic reproduction number dependent on both the viral transmission state and public opinion dynamics is constructed to analyze the conditions for virus eradication or pandemic persistence. These findings indicate that during severe epidemics, people are very concerned about the epidemic, leading to an increased vigilance, thereby significantly slowing the spread of the virus. On the other hand, during milder epidemics, people do not respond adequately to the threat of the epidemic, and thus are less vigilant and have less impact on the spread of the virus. These insights correlate closely with real-world trends. This article uses numerical simulations to demonstrate and confirm these patterns under various conditions.

The rise of social media has intensified fake news risks, prompting a growing focus on leveraging graph learning methods such as graph neural networks (GNNs) to understand post-spread patterns of news. However, existing methods often produce less robust and interpretable results as they assume that all information within the propagation graph is relevant to the news item, without adequately eliminating noise from engaged users. Furthermore, they inadequately capture intricate patterns inherent in long-sequence dependencies of news propagation due to their use of shallow GNNs aimed at avoiding the over-smoothing issue, consequently diminishing their overall accuracy. In this paper, we address these issues by proposing the Propagation Structure-aware Graph Transformer (PSGT). Specifically, to filter out noise from users within propagation graphs, PSGT first designs a noise-reduction self-attention mechanism based on the information bottleneck principle, aiming to minimize or completely remove the noise attention links among task-irrelevant users. Moreover, to capture multi-scale propagation structures while considering long-sequence features, we present a novel relational propagation graph as a position encoding for the graph Transformer, enabling the model to capture both propagation depth and distance relationships of users. Extensive experiments demonstrate the effectiveness, interpretability, and robustness of our PSGT.

Network (or graph) sparsification accelerates many downstream analyses. For graph sparsification, sampling methods derived from local heuristic considerations are common in practice, due to their efficiency in generating sparse subgraphs using only local information. Filtering-based edge sampling is the most typical approach in this respect, yet it heavily depends on an appropriate definition of edge importance. Instead, we propose a generalized node-focused edge sampling framework by preserving scaled/expected local node characteristics. Apart from expected degrees, these local node characteristics include the expected number of triangles and the expected number of non-closed wedges associated with a node. From a technical point of view, we adapt a game-theoretic sampling method from uncertain graph generation to obtain sparse subgraphs that approximate the expected local properties. We include a tolerance threshold for much faster convergence. Within this framework, we provide appropriate algorithmic variants for sparsification. Moreover, we propose a network measure called tri-wedge assortativity for the selection of the most suitable variant when sparsifying a given network. Extensive experimental studies on functional climate, observed real-world, and synthetic networks show the effectiveness of our method in preserving overall structural network properties – on average consistently better than the state of the art.

This article studies the optimized adaptive finite-time consensus control issue for stochastic nonlinear multiagent systems subject to non-affine nonlinear faults. Under the architecture of the adaptive optimized backstepping method, this article develops the neural-network-based simplified reinforcement learning algorithm with an identifier-critic-actor structure, where the identifier, critic and actor are put forward to estimate unknown dynamics, evaluate system performance and implement control behavior, respectively. Then, the Butterworth low-pass filter is introduced to compensate for the adverse effects brought by non-affine nonlinear faults. Furthermore, it is verified by Itô differential equation and the finite-time theory that the closed-loop system is semi-global finite-time stable in probability. Finally, the effectiveness of the control algorithm is illustrated by simulation examples.Note to Practitioners—This paper was motivated by the problem of finite-time convergence is one of significance performance index in many practical application. For systems with high transient performance standards, such as robotic systems, manipulator systems and unmanned aerial systems, finite time convergence is of practical importance. Accordingly, distinguished from the previous investigation results, this article develops the neural-network (NN)-based simplified reinforcement learning (RL) algorithm with an identifier-critic-actor structure, where the identifier, critic and actor are put forward to estimate unknown dynamics, evaluate system performance and implement control behavior, respectively. We believe that the novel research method will bring a research spring for the constrained systems. Preliminary simulation experiments suggest that this approach is feasible. In future research, we will address the fixed time control protocol designs for nonlinear multi-agent systems.

Circuits and systems, such as multidimensional and nonlinear ones, large-scale integration circuits, and power networks, play a significant role in the whole spectrum of science and technology, from basic scientific theories to various real-world applications. With the increasing demand from applications, it is vital to develop circuits and systems with high accuracy, stability, flexibility, and security through efficient learning, design optimization, and integrated implementation. The rapid advancement of artificial intelligence (AI) has fostered a symbiotic relationship between circuits and systems and AI in both theory and applications. On the one hand, research in circuits and systems on efficient learning, design optimization, and integrated implementation aided by AI has recently gained a promising development, where energy-efficient circuits and systems have a very broad range of applications. On the other hand, the utilization of AI in real-world applications has become indispensable for the optimization and implementation of circuits and systems with high efficiency and low-power computation. Overall, through advanced learning, optimization, and implementation driven by AI, efficient circuits and systems running in real-time with low power can be realized for wider applications.

Open data, as an essential element in the sustainable development of the digital economy, is highly valued by many relevant sectors in the implementation process. However, most studies suppose that there are only data providers and users in the open data process and ignore the existence of data regulators. In order to establish long-term green supply relationships between multistakeholders, we hereby introduce data regulators and propose an evolutionary game model to observe the cooperation tendency of multistakeholders (data providers, users, and regulators). The newly proposed game model enables us to intensively study the trading behavior which can be realized as strategies and payoff functions of the data providers, users, and regulators. Besides, a replicator dynamic system is built to study evolutionary stable strategies of multistakeholders. In simulations, we investigate the evolution of the cooperation ratio as time progresses under different parameters, which is proved to be in agreement with our theoretical analysis. Furthermore, we explore the influence of the cost of data users to acquire data, the value of open data, the reward (penalty) from the regulators, and the data mining capability of data users to group strategies and uncover some regular patterns. Some meaningful results are also obtained through simulations, which can guide stakeholders to make better decisions in the future.

In this article, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network of qubits. We construct the unitary transformation for each quantum system to achieve the partial quantum consensus, that is, the directions of the quantum states in the Bloch ball will reach an agreement. A simple case of two-qubit quantum systems is considered first, and a minimum completing time of reaching partial consensus is obtained based on the geometric configuration of each qubit. Furthermore, we extend the approaches to deal with the more general N -qubit networks. Two partial quantum consensus protocols, based on the Lyapunov method for chain graphs and the geometry method for connected graphs, are proposed. The geometry method can be utilized to deal with more general connected graphs, while for the Lyapunov method, the global consensus can be obtained. The numerical simulation over a qubit network is demonstrated to verify the validity and the effectiveness of the theoretical results.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

The psychology of the individual is continuously changing in nature, which has a significant influence on the evolutionary dynamics of populations. To study the influence of the continuously changing psychology of individuals on the behavior of populations, in this article, we consider the game transitions of individuals in evolutionary processes to capture the changing psychology of individuals in reality, where the game that individuals will play shifts as time progresses and is related to the transition rates between different games. Besides, the individual’s reputation is taken into account and utilized to choose a suitable neighbor for the strategy updating of the individual. Within this model, we investigate the statistical number of individuals staying in different game states and the expected number fits well with our theoretical results. Furthermore, we explore the impact of transition rates between different game states, payoff parameters, the reputation mechanism, and different time scales of strategy updates on cooperative behavior, and our findings demonstrate that both the transition rates and reputation mechanism have a remarkable influence on the evolution of cooperation. Additionally, we examine the relationship between network size and cooperation frequency, providing valuable insights into the robustness of the model.

Dynamic processes in complex network are crucial for better understanding collective behavior in human societies, biological systems, and the Internet. In this article, we first focus on the continuous Markov-based modeling of evolving networks with the birth-death of individuals. A new individual arrives at the group by the Poisson process, while new links are established in the network through either uniform connection or preferential attachment. Moreover, an existing individual has a limited lifespan before leaving the network. We determine stationary topological properties of these networks, including their size and mean degree. To address the effect of the birth-death evolution, we further study the information dynamics in the proposed network model from the random drift and natural selection perspective, based on assumptions of total-stochastic and fitness-driven evolution, respectively. In simulations, we analyze the fixation probability of individual information and find that means of new connections affect the random drift process but do not affect the natural selection process.

The neural-approximation-based adaptive nonlinear containment control issue for multiagent systems with full-state constraints is studied by invoking the backstepping approach. First, the barrier Lyapunov functions are established to deal with the state constraining issue in the multiple leaders/followers control scenarios. Then, by introducing the first-order filter, the system communication burden is substantially reduced. Moreover, the event-triggered controller is constructed by utilizing the switching-based mechanism so that the system security, control accuracy, resource consumption, and imposed state constraints are neatly balanced. We prove the output of each follower can converge to the desired hull formulated by leaders under the premise that the imposed state constraints are never violated. Besides, the considered closed-loop signals are uniformly bounded. We finally present a simulation example to show the validity of the developed approach.

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

Autonomous systems possess the features of inferring their own state, understanding their surroundings, and performing autonomous navigation. With the applications of learning systems, like deep learning and reinforcement learning, the visual-based self-state estimation, environment perception, and navigation capabilities of autonomous systems have been efficiently addressed, and many new learning-based algorithms have surfaced with respect to autonomous visual perception and navigation. In this review, we focus on the applications of learning-based monocular approaches in ego-motion perception, environment perception, and navigation in autonomous systems, which is different from previous reviews that discussed traditional methods. First, we delineate the shortcomings of existing classical visual simultaneous localization and mapping (vSLAM) solutions, which demonstrate the necessity to integrate deep learning techniques. Second, we review the visual-based environmental perception and understanding methods based on deep learning, including deep learning-based monocular depth estimation, monocular ego-motion prediction, image enhancement, object detection, semantic segmentation, and their combinations with traditional vSLAM frameworks. Then, we focus on the visual navigation based on learning systems, mainly including reinforcement learning and deep reinforcement learning. Finally, we examine several challenges and promising directions discussed and concluded in related research of learning systems in the era of computer science and robotics.

Ever since the Barabási–Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured with a dynamic evolution including network reduction in addition to network growth. In this article, we propose a novel mechanism for evolving networks from the perspective of vertex degree. We construct a queueing system to describe the increase and decrease of vertex degree, which drives the network evolution. In our mechanism, the degree increase rate is regarded as a function positively correlated to the degree of a vertex, ensuring the PA in a new way. Degree distributions are investigated under two expressions of the degree increase rate, one of which manifests a “long tail,” and another one varies with different values of parameters. In simulations, we compare our theoretical distributions with simulation results and also apply them to real networks, which presents the validity and applicability of our model.

This article investigates the group consensus problem for heterogeneous multiagent systems with time delays via pinning control. Under the designed control protocol, agents in the system could be grouped arbitrarily, and agents in the same subgroup could converge to a constraint position. Meanwhile, the kinetics of agents in the same subgroup could be same or different. Both the fixed and switching topologies are considered. Based on the frequency domain method and stability theory, sufficient conditions for the system achieve group consensus are derived. Finally, several numerical examples are presented to verify the performance of the control protocol.

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with filtering-based edge sampling being the most typical one, heavily relies on an appropriate definition of edge importance. Instead, we propose a different perspective with a generalized local-property-based sampling method, which preserves (scaled) local node characteristics. Apart from degrees, these local node characteristics we use are the expected (scaled) number of wedges and triangles a node belongs to. Through such a preservation, main complex structural properties are preserved implicitly. We adapt a game-theoretic framework from uncertain graph sampling by including a threshold for faster convergence (at least 4 times faster empirically) to approximate solutions. Extensive experimental studies on functional climate networks show the effectiveness of this method in preserving macroscopic to meso-scopic and microscopic network structural properties.

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated.

This paper designs an event-triggering based communication strategy for the global attitude synchronization of a network of rigid bodies. To overcome the topological constraint on the manifold$SO(3)$, the quaternion-based hybrid control strategy is designed using a binary logic variable, relying on the relative measurements of adjacent rigid bodies, to determine the torque orientation. The Zeno-free distributed event-triggering strategies (ETSs) are designed combining with the reset of the binary logic variable to generate discrete communication instants, where only the corresponding parts of the control inputs are updated at those discrete instants. By assuming perfect knowledge of the rigid bodies’ dynamics and considering uncertainties and/or exogenous disturbances simultaneously, nominal and robust cases are analyzed to ensure the global attitude synchronization, respectively. The effectiveness of the main results is demonstrated by considering the attitude synchronization of six miniature quadrotor prototypes.

Deep learning-based methods mymargin have achieved remarkable performance in 3-D sensing since they perceive environments in a biologically inspired manner. Nevertheless, the existing approaches trained by monocular sequences are still prone to fail in dynamic environments. In this work, we mitigate the negative influence of dynamic environments on the joint estimation of depth and visual odometry (VO) through hybrid masks. Since both the VO estimation and view reconstruction process in the joint estimation framework is vulnerable to dynamic environments, we propose the cover mask and the filter mask to alleviate the adverse effects, respectively. As the depth and VO estimation are tightly coupled during training, the improved VO estimation promotes depth estimation as well. Besides, a depth-pose consistency loss is proposed to overcome the scale inconsistency between different training samples of monocular sequences. Experimental results show that both our depth prediction and globally consistent VO estimation are state of the art when evaluated on the KITTI benchmark. We evaluate our depth prediction model on the Make3D dataset to prove the transferability of our method as well.

Evolving networks have always been studied a lot featuring the dynamic properties of real-life networks. Studying the mechanism of the growth and death of a network is of great significance to network modeling. Identical to many models focused on the growing process, in this article, we study the decreasing process thoroughly. A novel evolving network model considering the growing and decreasing process is established based on the queueing system. Focused on the degreasing process, we originally investigate two strategies of vertex deleting that are the brutal strategy and the heritable strategy which characterizes the heritable behavior of “dying” vertices in real networks. On the basis of our model, stochastic properties of the proposed network are analyzed, e.g., the distribution and the expectation of the stationary scale of the network are theoretically obtained. In addition to that, degree distributions with different strategies are demonstrated in simulations, which manifests the power-low distribution. The reliability of the network is also studied by different attacks, sharing the same characteristic with the scale-free network.

Many network analysis tasks like classification over nodes require careful efforts in engineering features used by learning algorithms. Most of recent studies have been made and succeeded in the field of static network representation learning. However, real-world networks are often dynamic and little work has been done on how to describe dynamic networks. In this work, we pose the problem of condensing dynamic networks and introduce SuRep, an encoding-decoding framework which utilizes matrix factorization technique to derive a succinct representation of a dynamic network in any stationary phase. We show that the succinct representation method can uncover the invariant structural properties in the network evolution and derive dense feature representations of the nodes as the byproduct. This method can be easily extended to dynamic attribute networks. For experiments on detecting change points in dynamic networks and network classification with real-world datasets we demonstrate SuRep's potential for capturing latent patterns among nodes.

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.

This article solves the exponential synchronization issue of memristor-based complex-valued neural networks (MCVNNs) with time-varying uncertainties via feedback control. Compared with the traditional control methods, a more practical and general control scheme with the available uncertain information of the parameters is newly developed for MCVNNs. Our approach considers the proposed neural networks as two dynamic real-valued systems. Then, the less conservative exponential synchronization criteria are proposed by incorporating the framework of the Lyapunov method and inequality techniques. Under the proposed algorithm, not only can the stability of MCVNNs be guaranteed but also the behavior of such a system is appropriate for image protection. Meanwhile, the sensitive measure of the encryption and decryption can be converted into synchronization error. When monitoring the secure mechanism as a whole, the influence of error feasible domain on image decryption is analyzed. Simulation examples are provided to verify the efficacy of the proposed synchronization criterion and the results of practical application on image protection.

Semantic segmentation and depth completion are two challenging tasks in scene understanding, and they are widely used in robotics and autonomous driving. Although several studies have been proposed to jointly train these two tasks using some small modifications, such as changing the last layer, the result of one task is not utilized to improve the performance of the other one despite that there are some similarities between these two tasks. In this article, we propose multitask generative adversarial networks (Multitask GANs), which are not only competent in semantic segmentation and depth completion but also improve the accuracy of depth completion through generated semantic images. In addition, we improve the details of generated semantic images based on CycleGAN by introducing multiscale spatial pooling blocks and the structural similarity reconstruction loss. Furthermore, considering the inner consistency between semantic and geometric structures, we develop a semantic-guided smoothness loss to improve depth completion results. Extensive experiments on the Cityscapes data set and the KITTI depth completion benchmark show that the Multitask GANs are capable of achieving competitive performance for both semantic segmentation and depth completion tasks.

Driver fatigue detection is of great significance for guaranteeing traffic safety and further reducing economic as well as societal loss. In this article, a novel complex network (CN) based broad learning system (CNBLS) is proposed to realize an electroencephalogram (EEG)-based fatigue detection. First, a simulated driving experiment was conducted to obtain EEG recordings in alert and fatigue state. Then, the CN theory is applied to facilitate the broad learning system (BLS) for realizing an EEG-based fatigue detection. The results demonstrate that the proposed CNBLS can accurately differentiate the fatigue state from an alert state with high stability. In addition, the performances of the four existing methods are compared with the results of the proposed method. The results indicate that the proposed method outperforms these existing methods. In comparison to directly using EEG signals as the input of BLS, CNBLS can sharply improve the detection results. These results demonstrate that it is feasible to apply BLS in classifying EEG signals by means of CN theory. Also, the proposed method enriches the EEG analysis methods.

Association rule (AR) mining in complex scene has attracted extensive attention of researchers in recent years. Typically, many researchers focused on an algorithm itself and ignored a generalization method to improve the performance of AR mining. Tuna et al., presented a general data structure Speeding-Up AR Structure with Inverted Index Compression (SAII) which could be utilized in most of the existing algorithms to improve their performance IEEE Trans. Cybern. 46(12) (2016) 3059–3072. However, we found that this algorithm consumes a lot of time in re-ordering data because a one-to-one comparison method is used in this process, which is the main reason that the speeding-up structure is difficult to establish when coping with much more large amount of data. To overcome these problems, this paper aims to propose an improved speeding-up AR algorithm based on group similarity and Apache Spark framework to further reduce the memory requirements and runtime. Our simulation results on the police business big dataset make clear that our improved approach performs well and is more suitable for a big data environment.

This study is concerned with probabilistic Boolean control networks (PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs, we resort to a powerful matrix manipulation called semi-tensor product (STP). Because stabilization of networks is of critical importance, the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally, the transient periods (the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.

In this paper, the output feedback set stabilization problem for Boolean control networks (BCNs) is investigated with the help of the semi-tensor product (STP) tool. The concept of output feedback control invariant (OFCI) subset is introduced, and novel methods are developed to obtain the OFCI subsets. Based on the OFCI subsets, a technique, named spanning tree method, is further introduced to calculate all possible output feedback set stabilizers. An example concerning lac operon for the bacterium Escherichia coli is given to illustrate the effectiveness of the proposed method. This technique can also be used to solve the state feedback (set) stabilization problem for BCNs. Compared with the existing results, our method can dramatically reduce the computational cost when designing all possible state feedback stabilizers for BCNs.

This paper is concerned with the consensus issue for a class of multiagent systems with Markovian switching topology under aperiodic sampled data measurements. By constructing a novel piecewise stochastic Lyapunov-Krasovskii functional, some novel conditions with less conservative are established such that the consensus is achieved in the mean square sense. In contrast to some previous publications, the sample period is no longer fixed and the transition probability matrix of Markovian switching topology is uncertain. This issue which is of practical and theoretical significance is further investigated when the sampled data controller of each agent is suffered from distinct time-varying input delay. Quite different with the related studies, a maximally allowable input delay upper bound is replaced by the permissible input delay interval. Furthermore, the corresponding consensus is elegantly obtained in terms of linear matrix inequalities. Finally, the effectiveness and practicability of our consensus criteria are well illustrated by the numerical examples.

There are many target methods that are efficient to tackle the robustness and immunization problem, in particular, to identify the most influential nodes in a certain complex network. Unfortunately, owing to the diversity of networks, none of them could be accounted as a universal approach that works well in a wide variety of networks. Hence, in this paper, from a percolation perspective, we connect the immunization and robustness problem with an evolutionary algorithm, i.e., a framework of an evolutionary algorithm for investigation of influential nodes in complex networks, in which we have developed procedures of selection, mutation, and initialization of population as well as maintaining the diversity of population. To validate the performance of the proposed framework, we conduct intensive experiments on a large number of networks and compare it to several state-of-the-art strategies. The results demonstrate that the proposed method has significant advantages over others, especially on empirical networks in most of which our method has over 10% advantages of both optimal immunization threshold and average giant fraction, even against the most excellent existing strategies. Additionally, our discussion reveals that there might be better solutions with various initial methods.

During the past decades, power-law distributions have played a significant role in analyzing the topology of scale-free networks. However, in the observation of degree distributions in practical networks and other nonuniform distributions such as the wealth distribution, we discover that, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a monotonic decreasing power-law distribution. To better describe the real distributions, in this paper, we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time. By utilizing this distribution, we can precisely describe those distributions commonly existing in the real world, e.g., distributions of degree in social networks and personal wealth. Additionally, we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution, resulting in a better performance of fitness.

This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

The spiking neural network (SNN) is the third generation of neural networks and performs remarkably well in cognitive tasks, such as pattern recognition. The temporal neural encode mechanism found in biological hippocampus enables SNN to possess more powerful computation capability than networks with other encoding schemes. However, this temporal encoding approach requires neurons to process information serially on time, which reduces learning efficiency significantly. To keep the powerful computation capability of the temporal encoding mechanism and to overcome its low efficiency in the training of SNNs, a new training algorithm, the accurate synaptic-efficiency adjustment method is proposed in this paper. Inspired by the selective attention mechanism of the primate visual system, our algorithm selects only the target spike time as attention areas, and ignores voltage states of the untarget ones, resulting in a significant reduction of training time. Besides, our algorithm employs a cost function based on the voltage difference between the potential of the output neuron and the firing threshold of the SNN, instead of the traditional precise firing time distance. A normalized spike-timing-dependent-plasticity learning window is applied to assigning this error to different synapses for instructing their training. Comprehensive simulations are conducted to investigate the learning properties of our algorithm, with input neurons emitting both single spike and multiple spikes. Simulation results indicate that our algorithm possesses higher learning performance than the existing other methods and achieves the state-of-the-art efficiency in the training of SNN.

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

This paper addresses robust multiobjective identification of driver nodes in the neuronal network of a cat's brain, in which uncertainties in determination of driver nodes and control gains are considered. A framework for robust multiobjective controllability is proposed by introducing interval uncertainties and optimization algorithms. By appropriate definitions of robust multiobjective controllability, a robust nondominated sorting adaptive differential evolution (NSJaDE) is presented by means of the nondominated sorting mechanism and the adaptive differential evolution (JaDE). The simulation experimental results illustrate the satisfactory performance of NSJaDE for robust multiobjective controllability, in comparison with six statistical methods and two multiobjective evolutionary algorithms (MOEAs): nondominated sorting genetic algorithms II (NSGA-II) and nondominated sorting composite differential evolution. It is revealed that the existence of uncertainties in choosing driver nodes and designing control gains heavily affects the controllability of neuronal networks. We also unveil that driver nodes play a more drastic role than control gains in robust controllability. The developed NSJaDE and obtained results will shed light on the understanding of robustness in controlling realistic complex networks such as transportation networks, power grid networks, biological networks, etc.

Since the great mathematician Leonhard Euler initiated the study of graph theory, the network has been one of the most significant research subject in multidisciplinary. In recent years, the proposition of the small-world and scale-free properties of complex networks in statistical physics made the network science intriguing again for many researchers. One of the challenges of the network science is to propose rational models for complex networks. In this paper, in order to reveal the influence of the vertex generating mechanism of complex networks, we propose three novel models based on the homogeneous Poisson, nonhomogeneous Poisson and birth death process, respectively, which can be regarded as typical scale-free networks and utilized to simulate practical networks. The degree distribution and exponent are analyzed and explained in mathematics by different approaches. In the simulation, we display the modeling process, the degree distribution of empirical data by statistical methods, and reliability of proposed networks, results show our models follow the features of typical complex networks. Finally, some future challenges for complex systems are discussed.

self-triggered control of networked systems. The system considered here includes parameter uncertainties, packet dropouts, and time delays. The time delay is described in a stochastic way, which takes a value from a given finite set. In order to compensate for the existence of deterministic packet dropouts, a new self-triggered control scheme is proposed. The main feature of the proposed self-triggered control strategy is that the next control task is predicted based on the self-triggered technique, in which the predicted event interval is divided equally for the sake of packet dropouts. The triggered condition is developed to ensure the stability of the uncertain sampled system by utilizing an uncertain algebraic Riccati equation and the comparison principle. Finally, an example of the inverted pendulum of a cart is provided to illustrate the effectiveness of the proposed results.

Communication constraints, which may lead to the degradation of performance, are common and unavoidable in a real-world network. In this paper, two kinds of communication constraints are considered during the process of information transmission in Takagi-Sugeno (TS) fuzzy complex network: 1) partial couplings, where only some part of nodes' state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon; and 2) discrete-time couplings, where the nodes' information are sampled at certain time instants. This is the first time when both communication constraints are simultaneously considered in fuzzy complex networks. Compared with the perfect communication, much less information is available for synchronization. To overcome this difficulty, a regrouping method is employed to reconstruct the fuzzy network. The concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete-time couplings. Simulation examples are also provided to demonstrate the effectiveness of the theoretical results.

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently.

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

In this paper, we investigate the multiobjective identification of controlling areas in the neuronal network of a cat's brain by considering two measures of controllability simultaneously. By utilizing nondominated sorting mechanisms and composite differential evolution (CoDE), a reference-point-based nondominated sorting composite differential evolution (RP-NSCDE) is developed to tackle the multiobjective identification of controlling areas in the neuronal network. The proposed RP-NSCDE shows its promising performance in terms of accuracy and convergence speed, in comparison to nondominated sorting genetic algorithms II. The proposed method is also compared with other representative statistical methods in the complex network theory, single objective, and constraint optimization methods to illustrate its effectiveness and reliability. It is shown that there exists a tradeoff between minimizing two objectives, and therefore pareto fronts (PFs) can be plotted. The developed approaches and findings can also be applied to coordination control of various kinds of real-world complex networks including biological networks and social networks, and so on.

In this paper, the robust synchronization problem of fuzzy complex dynamical networks is investigated. A fuzzy complex dynamical network is an extension to an uncertain complex dynamical network in which all sources of parametric uncertainties are modeled with fuzzy numbers, i.e., all nodes' dynamics are described by fuzzy differential equations (FDEs) that permit a better description of a real process occurring in the presence of inaccuracy. To resolve the synchronization problem, this paper introduces new adaptive and impulsive controllers in which globally exponential synchronization of fuzzy dynamical networks under easily verified conditions is guaranteed. Moreover, we propose an efficient method that helps to find certain suitable nodes to be impulsively controlled via pinning, noting that these nodes, in general, vary at distinct impulsive time instants. Therefore, by using adaptive controllers and applying impulsive controllers to only a small portion of nodes, the whole network will completely be synchronized to a certain objective state. Finally, two numerical examples are given to illustrate the effectiveness of the proposed controllers.

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Controlling regions in cortical networks, which serve as key nodes to control the dynamics of networks to a desired state, can be detected by minimizing the eigenratio R and the maximum imaginary part \sigma of an extended connection matrix. Until now, optimal selection of the set of controlling regions is still an open problem and this paper represents the first attempt to include two measures of controllability into one unified framework. The detection problem of controlling regions in cortical networks is converted into a constrained optimization problem (COP), where the objective function R is minimized and \sigma is regarded as a constraint. Then, the detection of controlling regions of a weighted and directed complex network (e.g., a cortical network of a cat), is thoroughly investigated. The controlling regions of cortical networks are successfully detected by means of an improved dynamic hybrid framework (IDyHF). Our experiments verify that the proposed IDyHF outperforms two recently developed evolutionary computation methods in constrained optimization field and some traditional methods in control theory as well as graph theory. Based on the IDyHF, the controlling regions are detected in a microscopic and macroscopic way. Our results unveil the dependence of controlling regions on the number of driver nodes l and the constraint r. The controlling regions are largely selected from the regions with a large in-degree and a small out-degree. When r=+ \infty, there exists a concave shape of the mean degrees of the driver nodes, i.e., the regions with a large degree are of great importance to the control of the networks when l is small and the regions with a small degree are helpful to control the networks when l increases. When r=0, the mean degrees of the driver nodes increase as a function of l. We find that controlling \sigma is becoming more important in controlling a cortical network with increasing l. The methods and results of detecting controlling regions in this paper would promote the coordination and information consensus of various kinds of real-world complex networks including transportation networks, genetic regulatory networks, and social networks, etc.

Maximizing the controllability of complex networks by selecting appropriate nodes and designing suitable control gains is an effective way to control distributed complex networks. In this paper, some novel particle swarm optimization (PSO) approaches are developed to enhance the controllability of distributed networks. The proposed PSO algorithm is combined with a global search scheme and a modified simulated binary crossover (MSBX). In addition, the node importance-based method is introduced to study the controllability of distributed complex networks. A set of experiments show that the PSO with the global search and the MSBX (PSO-GSBX) can outperform some well-known evolutionary algorithms and pinning schemes. Following the PSO-GSBX approach, some interesting findings about pinned nodes, coupling strengths and the eigenvalues for enhancing the controllability of distributed networks are revealed. The obtained results and methods are applied in unmanned aerial vehicle (UAV) coordination to show their effectiveness. These findings will help to understand controllability of complex networks and can be applied in control science and industrial system.

In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper.

BACKGROUND: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. RESULTS: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. CONCLUSIONS: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.

This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.

BACKGROUND: High complexity is considered a hallmark of living systems. Here we investigate the complexity of temporal gene expression patterns using the concept of Permutation Entropy (PE) first introduced in dynamical systems theory. The analysis of gene expression data has so far focused primarily on the identification of differentially expressed genes, or on the elucidation of pathway and regulatory relationships. We aim to study gene expression time series data from the viewpoint of complexity. RESULTS: Applying the PE complexity metric to abiotic stress response time series data in Arabidopsis thaliana, genes involved in stress response and signaling were found to be associated with the highest complexity not only under stress, but surprisingly, also under reference, non-stress conditions. Genes with house-keeping functions exhibited lower PE complexity. Compared to reference conditions, the PE of temporal gene expression patterns generally increased upon stress exposure. High-complexity genes were found to have longer upstream intergenic regions and more cis-regulatory motifs in their promoter regions indicative of a more complex regulatory apparatus needed to orchestrate their expression, and to be associated with higher correlation network connectivity degree. Arabidopsis genes also present in other plant species were observed to exhibit decreased PE complexity compared to Arabidopsis specific genes. CONCLUSIONS: We show that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.

MOTIVATION: Metabolite profiling aims at an unbiased identification and quantification of all the metabolites present in a biological sample. Based on their pair-wise correlations, the data obtained from metabolomic experiments are organized into metabolic correlation networks and the key challenge is to deduce unknown pathways based on the observed correlations. However, the data generated is fundamentally different from traditional biological measurements and thus the analysis is often restricted to rather pragmatic approaches, such as data mining tools, to discriminate between different metabolic phenotypes. METHODS AND RESULTS: We investigate to what extent the data generated networks reflect the structure of the underlying biochemical pathways. The purpose of this work is 2-fold: Based on the theory of stochastic systems, we first introduce a framework which shows that the emergent correlations can be interpreted as a 'fingerprint' of the underlying biophysical system. This result leads to a systematic relationship between observed correlation networks and the underlying biochemical pathways. In a second step, we investigate to what extent our result is applicable to the problem of reverse engineering, i.e. to recover the underlying enzymatic reaction network from data. The implications of our findings for other bioinformatics approaches are discussed.