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This paper is concerned with the existence and global exponential stability of the periodic solution of delayed Cohen–Grossberg neural networks (CGNNs) with discontinuous activation functions. The activations considered herein are non-decreasing but not required to be Lipschitz or continuous. Based on differential inclusion theory, Lyapunov functional theory and Leary–Schauder alternative theorem, some sufficient criteria are derived to ensure the existence and global exponential stability of the periodic solution. In order to show the superiority of the obtained results, an application and some detailed comparisons between some existing related results and our results are presented. Finally, some numerical examples are also illustrated. [ABSTRACT FROM AUTHOR]

This paper considers the stabilization of stochastic delayed networks with Markovian switching via aperiodically intermittent control (AIC). The concepts of average control ratio and average control period are proposed to characterize the distributions of control and rest intervals of AIC. It should be noted that the averaging technique used here is more general and less restrictive than the quasi-periodicity condition and minimum control ratio condition used in previous works. Then two kinds of stabilization criteria are obtained: (1) the upper bound of time delay should be less than the average control width; (2) the upper bound of time delay has no relationship with the average control width. Finally, the results are applied to studying the stabilization of coupled stochastic neural networks with Markovian switching via AIC. Numerical simulations are provided to show the effectiveness of obtained results. [ABSTRACT FROM AUTHOR]

Sulphuric Acid Anodic Oxide (AAO) film is a common method for corrosion protection of 5083 Al alloys, and cracks may occur in the AAO film due to stress damage. In this study, cracks in the AAO film on 5083 Al alloy were pre-prepared by mechanical tension, and the cracks on the corrosion protection property of AAO film were in-situ investigated by scanning electrochemical microscopy (SECM). The morphology and composition of the AAO film were measured by SEM, XRD and XPS. The results show that the corrosion protection performance of AAO film for 5083 Al alloy decreases with the increase of cracks, which is due to the fact that cracks can act as diffusion channels for corrosive media, resulting in serious corrosion reaction. SECM shows the local current at the cracks of the AAO film first increases and then decreases due to the cracks being gradually repaired by the deposited corrosion products (Al(OH) 3 , Al(OH) 2 Cl, and AlOOH). A repair mechanism of cracks in AAO film on 5083 Al alloys is revealed during the corrosion process. • The corrosion process of the damaged AAO film is observed in situ by SECM. • The cracks of damaged AAO film on Al alloy can be repaired by the corrosion products. • A corrosion model is proposed to reflect the repair mechanism of cracks in AAO on 5083 Al alloys. [ABSTRACT FROM AUTHOR]

The emergence of Internet of Things (IoT) and new manufacturing paradigms have brought greater complexity of massive datasets. Radio frequency identification (RFID), as one of the key IoT technologies, has been used to collect real-time production data to support the manufacturing decision-making in smart factories. The adoption of these technologies results in a large amount of data collection. To extract useful information from this data, this paper utilizes a big data approach to figure out useful insights from RFID-enabled data regarding possible bottlenecks or inefficiencies on the shop floor so as to improve the quality management. Time and quality are the main metrics measured in this paper, where the longest process times, part accuracy percentage, and failure rate are determined for each of the workers (UserIDs) and process types (ProcCodes). Key findings and observations are significant to make advanced decisions in the smart factory by making full use of the RFID captured data. Note to Practitioners— This paper was motivated by a real-life company which has used RFID technology for over ten years. Great myriad of data has been captured from frontline production shop floors where machines, workers, materials, and manufacturing jobs were logically associated. Processing time and quality data are studied in this paper so as to investigate the production performance in the RFID-enabled smart factory. [ABSTRACT FROM AUTHOR]

This paper shows that the generalized eigenvalues of a symmetric positive matrix pair can be computed efficiently under more general hypothesises by the proposed recurrent neural network (RNN) in Liu et al. (2008). More precisely, it is proved that based on more general hypothesises, the state solution of the proposed RNN converges to the generalized eigenvector of symmetric positive pair, and its related generalized eigenvalue depends on the initial point of the state solution. Furthermore, the related largest and smallest generalized eigenvalues can also be obtained by the proposed RNN. Some related numerical experiments are also presented to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the problem of the exponential synchronisation for delayed neutral-type multi-weights complex networks (DNMCNs) with regime-switching jump diffusion under aperiodically intermittent control. Compared with the related works, hybrid time delays and regime-switching jump diffusion are introduced into neutral-type networks which can better simulate more complicated practical applications. The introduction of regime-switching jump diffusion increases the difficulties of synchronisation analysis in comparison with the Markovian jump diffusion. Meanwhile, it is noteworthy that we firstly extend the availability of aperiodically intermittent control scheme to handle the synchronisation issue with DNMCNs. On the basis of a technique that combines the Lyapunov method and graph theory, some sufficient criteria to synchronise DNMCNs via intermittent control are obtained. Finally, an oscillator system is considered as the application, and the corresponding numerical simulations are proposed to validate the applicability of the obtained theorems and show the effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, a recurrent neural network with a new tunable activation is proposed to solve a kind of convex quadratic bilevel programming problem. It is proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov, and the state of the proposed neural network converges to an equilibrium point in finite time. In contrast to the existing related neurodynamic approaches, the proposed neural network in this paper is capable of solving the convex quadratic bilevel programming problem in finite time. Moreover, the finite convergence time can be quantitatively estimated. Finally, two numerical examples are presented to show the effectiveness of the proposed recurrent neural network. [ABSTRACT FROM AUTHOR]

This paper considers a general class of stochastic complex networks with time-varying delays (SCNTVDs). A systematic method of constructing a global Lyapunov function for the complex network is provided by combining graph theory and Lyapunov method. Consequently, some novel and simple sufficient conditions of exponential stability for the SCNTVDs are given. These conditions are presented in terms of the topological structure of networks. In addition, to illustrate the effectiveness and applicability of the proposed theory, a practical model in physics is studied and the numerical simulation is also given. [ABSTRACT FROM AUTHOR]

The trivalent chromium conversion coating (CCC) is prepared on pure zinc, and the corrosion resistance of trivalent CCC is characterized by scanning electron microscopy (SEM), polarization curves and electrochemical impedance spectroscopy (EIS). The local corrosion and self-healing behavior of trivalent CCC at the initial stage of immersion corrosion are investigated in situ by scanning electrochemical microscopy (SECM). The results show that trivalent CCC has higher impedance value and lower corrosion current density as compared to pure zinc, and the coating has excellent corrosion protection for pure zinc. At the initial stage of corrosion (0−12 h), the SECM feedback current of the trivalent CCC does not change significantly; after immersed for 24 h, the local current rises from 0.83 to 0.95, which can be explained that the trivalent CCC cracks locally and occurs local corrosion. In situ analysis of oxygen concentration at the scratch of trivalent CCC indicates that the addition of polyaniline can inhibit the oxygen reduction reaction, which hinders the corrosion process and improves the self-healing ability of trivalent CCC. [Display omitted] • The prepared trivalent CCC has excellent corrosion resistance. • The corrosion process of the trivalent CCC is observed in situ by SECM. • The self-healing behavior of the trivalent CCC is observed in situ by SECM. • Polyaniline enhances the self-healing ability of the trivalent CCC. [ABSTRACT FROM AUTHOR]

Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen-Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results. [ABSTRACT FROM AUTHOR]

An interior regularity criterion of suitable weak solutions is formulated for the Ericksen-Leslie system of liquid crystals. Such a criterion is point-wise, with respect to some appropriate norm of velocity u and the gradient of d, and it can be viewed as a sort of simply sufficient condition on the local regularity of suitable weak solutions. [ABSTRACT FROM AUTHOR]

This paper addresses a stochastic coupled oscillators model. By employing the Lyapunov function method combined with Kirchhoff's Matrix Tree Theorem in graph theory, we establish a sufficient criterion to guarantee the existence of a stationary distribution for stochastic coupled oscillators. Moreover, a numerical example is given to illustrate the effectiveness of our theoretical results. • The problem we considered is the existence of a stationary distribution of a stochastic coupled oscillators model. • By using the Lyapunov method and Kirchhoff's Matrix Tree Theorem. • The approach we employ avoids constructing a Lyapunov function directly. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of a discrete-time multi-patch Beddington–DeAngelis type predator-prey model with time-varying delay, where the dispersal of both predators and prey is considered. A nonstandard finite difference scheme is used to discretize this model. Then, combining the Lyapunov–Krasovskii method with the graph-theoretical technique, a stability criterion is derived, which is closely related to the dispersal topology. And an example with numerical simulation is given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Multi-group models have attracted considerable attention due to their promising potential applications in various fields. In this paper, aperiodically intermittent control is designed to study the exponential stability of fractional-order multi-group models with dispersal. By applying Lyapunov method and graph theory, some sufficient conditions about exponential stability are established. From the theoretical results, we observe that the convergence speed depends on the control gain and the order of fractional derivative. Moreover, to show the practicality of theoretical results, we provide an application of modified fractional-order competitive neural networks. A stability criterion is also given to guarantee the exponential stability of modified fractional-order competitive neural networks. Finally, a numerical example is provided to show the effectiveness of the stated results. Some simulation comparisons are also carried out to illustrate the relationship between the convergence speed and the control gain with the order of fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time stabilization of stochastic coupled systems on networks (SCSNs) is studied. Different from previous research methods, the method used in this paper combines Lyapunov method with graph theory, and some novel sufficient conditions are obtained to ensure finite-time stability for SCSNs. Meanwhile, the convergence time is closely related to topological structure in networks. As a practical application in physics, we address a concrete finite-time stabilization problem of stochastic coupled oscillators through our main results. In addition, a numerical example is presented to illustrate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential bipartite synchronization of a general class of delayed signed networks with multi-links by using an aperiodically intermittent control strategy. The main result is a set of sufficient conditions for bipartite synchronization that depend on the network's topology, control gain, and the maximum proportion of rest time. An application to Chua's circuits is then considered, and some numerical simulation results are presented. [ABSTRACT FROM AUTHOR]

In this paper, by linking Fokker-Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker-Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator-prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem is presented where the conditions of it are based on the coefficients of system. Moreover, to show the practicality of theoretical results, we give two applications to fractional-order chaotic CDNs with multiple links and fractional-order Hindmarsh–Rose neuron systems with multiple links, respectively. Meanwhile, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

With the digital transformation of enterprises, the traditional security defense technology has been unable to meet the security requirements of enterprises, and the data security and privacy protection have brought great challenges to the Internet. Therefore, taking zero trust as the security concept and taking the network boundary as the best practice landing technology architecture, this paper studies the zero trust access authorization and control of network boundary based on cloud big data fuzzy clustering of. Through the network stealth technology, it constructs a virtual boundary for the enterprise, uses the cloud big data fuzzy clustering algorithm to mine the user behavior related data, and designs the trust evaluation mechanism to obtain the user trust level. The dynamic access authorization control mechanism is designed to judge the access requests in and out of the permission boundary. Combined with the user's trust level, the legal requests and illegal requests are distinguished to complete the zero trust access authorization and control of network boundary. Experimental results show that: the method can accurately control the access authorization of the network boundary, improve the success rate of access authorization and control interaction; the interception rate of illegal access is high, and it has high securit. [ABSTRACT FROM AUTHOR]

In previous work, the synchronization of multi-links systems with Lévy noise (MLSLN) has not been fully investigated. Therefore, the synchronization of MLSLN is concerned via feedback discrete-time observations control. Therein, we provide a novel Lyapunov functional for MLSLN. Moreover, the upper bound of the state observations interval duration is obtained. By making use of Lyapunov functional method, some techniques of inequality and graph theory, we derive some sufficient conditions to guarantee the mean-squared asymptotical synchronization of MLSLN. Then, the theoretical results are employed to study the synchronization of single-link robot arms. Meantime, numerical simulations are given to demonstrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

• Traditional glass windows are endowed with electromagnetic wave control capabilities by metasurfaces, which would be applied in 5G/6G communications and smart cities. • The concept of optically transparent meta -window is first proposed for satellite signal reception. • The proposed meta -window is able to achieve high efficiency in the microwave frequency range at the cost of losing about 4% of extremely low optical transparency. Glass window, as a widely used functional unit in architecture and transportation, is a visual bridge connecting the indoor and outdoor world, and also a wireless communication window that is easily overlooked. In order to explore additional possibilities of glass window in the field of wireless communication, we propose to use meta -windows combining traditional window glass with metasurface to manipulate electromagnetic waves in microwave frequency band while ensuring its good optical transparency. Here, the meta -window is constructed by rotated meta -atoms made of fine copper wires printed on glasses to minimize the loss of optical transparency. As a proof of concept, we design and fabricate an optically transparent focusing meta -window for receiving satellite signals. In the experiment of television reception from the ChinaSat 9 satellite, stable high-definition video reception has been verified. The meta -windows endow traditional glass windows with new capabilities in electromagnetic modulations, which may be applied in 5G/6G communications, satellite ground integrations, and smart cities. [ABSTRACT FROM AUTHOR]

In this paper, based on Razumikhin method, stability of stochastic Lévy noise coupled systems with mixed delays (SLCSD) is researched. Here, both mixed delays and Lévy noise are considered into coupled systems for the first time. Then, by combining Razumikhin method with Lyapunov method and graph theory, several stability criteria including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem are given to ensure the pth moment exponential stability of SLCSD. In particular, the stability of a class of coupled oscillators and the stability of single-link robot arms are investigated as practical applications of the obtained results. And some numerical simulations are offered to illustrate the feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the stability and synchronization problems of fractional‐order delayed multilink complex networks with nonlinear hybrid couplings are investigated simultaneously, where discrete time‐varying delays and distributed time‐varying delays are both taken into account. By virtue of graph‐theoretic approach and Lyapunov method, under feedback control, some criteria are established to guarantee that the underlying networks achieve stability and synchronization. The obtained criteria are related to topological structure of subsystems, control gain, and the upper bound of time‐varying delays. Furthermore, in order to show practicality, the obtained results are applied to fractional‐order delayed multilink competitive neural networks with nonlinear hybrid couplings and fractional‐order Lorenz chaotic delayed coupled systems with nonlinear hybrid couplings, respectively. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the exponential synchronisation of second‐order stochastic complex dynamical networks (SOSCDNs) is considered. A novel control called periodically intermittent pinning discrete observations control is proposed, which is based on discrete‐time state observations instead of continuous‐time state observations during the control time. To the authors' knowledge, the above control strategy has rarely been investigated in previous researches. Compared with the existing literature, there are no restrictions on the network topology structure in this study. Furthermore, by employing the Lyapunov method, stochastic analysis techniques, and matrix theory, a synchronisation criterion and a corollary about the exponential synchronisation of the SOSCDNs are presented. In particular, when the duration between two consecutive observations tends to zero, periodically intermittent pinning discrete observations control degenerates into periodically intermittent pinning control, and relevant corollaries are also derived. Finally, they applied theoretical results to single‐link robot arm systems and oscillator systems. Meanwhile, the numerical simulations are performed to demonstrate the effectiveness of their results. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of global Mittag-Leffler synchronization of multi-links impulsive fractional-order complex networks (MIFCNs). A class of feedback control based on discrete-time state observations is first adopted for synchronization of MIFCNs. By combining Lyapunov method with graph-theoretic approach, a synchronization criterion for MIFCNs is derived. In particular, this synchronization criterion is related to the order of fractional derivatives, the parameters of control and the topological structure of networks. Furthermore, as an application of our theoretical results, synchronization of multi-links impulsive fractional-order BAM neural networks is studied in detail and a synchronization criterion is also provided. Finally, a numerical example is presented to illustrate the validity and feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a new neurodynamic approach for solving the constrained pseudoconvex optimization problem based on more general assumptions. The proposed neural network is equipped with a hard comparator function and a piecewise linear function, which make the state solution not only stay in the feasible region, but also converge to an optimal solution of the constrained pseudoconvex optimization problem. Compared with other related existing conclusions, the neurodynamic approach here enjoys global convergence and lower dimension of the solution space. Moreover, the neurodynamic approach does not depend on some additional assumptions, such as the feasible region is bounded, the objective function is lower bounded over the feasible region or the objective function is coercive. Finally, both numerical illustrations and simulation results in support vector regression problem show the well performance and the viability of the proposed neurodynamic approach. [ABSTRACT FROM AUTHOR]

• A novel link prediction method Graph Regularization weighted Nonnegative Matrix Factorization(GWNMF) is proposed. • GWNMF integrates two types of information: local topology information and links weight information. • We derive the multiplicative updating rules to learn the parameter of GWNMF. • Conducting experiments on seven real-world weighted network demonstrates that GWNMF outperforms the state-of-the-arts methods for weighted networks task. In weight networks, both link weights and topological structure are important features for link prediction. Currently, almost all existing weighted network link prediction algorithms only focused on naturally existed link weight but ignored the topological structure information. Therefore, these methods will suffer from the challenge of network sparsity and insufficient topology information. In this paper, we propose a novel Graph Regularization Weighted Nonnegative Matrix Factorization(GWNMF) model to integrate local topology information with link weights information for link prediction. Specifically, this model integrates two types of information: local topology and link weight information, and utilizes the weighted cosine similarity(WCS) method to calculate the weight similarity between local nodes. The WCS score matrix as the indicator weighted matrix to capture more useful link weight information. While graph regularization technology combines WCS score matrix to capture the local information. Besides, we derive the multiplicative updating rules to learn the parameter of this model. Empirically, we conduct the experiments on eight real-world weighted networks demonstrate that GWNMF remarkably outperforms the state-of-the-arts methods for weighted link prediction tasks. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization problem of complex-valued delayed coupled systems on networks with aperiodically on-off coupling is investigated. The on-off coupling is aperiodic, which takes the general on-off coupling as a special case. We analyze the complex-valued system directly by using R -Derivative and Conjugate R -Derivative. Then based on the Lyapunov method and graph theory, we give two kinds of synchronization criteria, which have a close relationship with the switch-on width of the coupling and the topological structure of the underlying network. Specially, when the switch-on width tends to zero, on-off coupling becomes impulsive control. Hence, the corresponding synchronization criteria under impulsive control are given as well. To illustrate the practicability of the main results, we apply the derived results to complex-valued delayed coupled oscillators. Finally, two numerical examples are given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

As the anode material of Al air battery, 2N-purity (99 wt%) Al-based alloy has the disadvantages of low efficiency and low discharge voltage, which is attributed to the impurity of Fe in the 2N Al alloy. In this paper, the 2N Al-based anode with high energy efficiency and discharge voltage is successfully designed by adding Mn, Zn and Ga. The results show that adding Mn separately can inhibit hydrogen evolution corrosion but lead to the exfoliation corrosion of 2N Al. The addition of Ga, Mn and Zn together can suppress hydrogen evolution, decrease the weight loss of 2N Al alloy and significantly increase the output voltage and energy efficiency of an Al-air battery, which makes it possible to use cheap 2N Al as the anode of an Al-air battery. [Display omitted] • Al 6 (Mn,Fe) formed by Mn addition will decrease the self corrosion of 2 N Al. • Addition of Ga alone will lead to obvious intergranular corrosion of Al alloy. • The presence of Zn will rapidly stabilize the voltage of Al anode. • The coordination of Ga, Zn and Mn improves the discharge performance of Al anode. [ABSTRACT FROM AUTHOR]

In this brief, we propose an effective algorithm for synchronization of instantaneously coupled harmonic oscillators by using sampled data which may contain measurement noise. We discuss the convergence of this algorithm for both fixed and switching directed network topologies in the presence or absence of leaders. We also establish sufficient conditions under which the coupled harmonic oscillators could attain synchronized oscillatory motions in the presence of noise. And moreover, it is shown that synchronization can be attained even when the velocity information is exchanged only at discrete-time instants. Finally, we give some numerical examples to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays by using an M-matrix approach. The M-matrix strategy allows many synchronization problems with much relaxed conditions to be considered and can be used to derive sufficient conditions for this new class of NCCNs by pinning control. We also propose an effective way of adapting the coupling strengths of complex networks and give numerical examples to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

• Multiple time-varying delay links are introduced into fractional-order competitive neural networks. • An integral inequality associated with every upper bound of each time-varying delay is proposed. • Based on integral inequality, a generalized fractional-order Halanay inequality is obtained. • The stability criterion is dependent on the topological structure of networks. Competitive neural networks have become increasingly popular since this kind of neural networks can better describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In this paper, we first propose fractional-order competitive neural networks with multiple time-varying-delay links and explore the global asymptotic stability of this class of neural networks. A novel and generalized integral inequality related to every upper bound of each time-varying delay is given. Moreover, based on Lyapunov method and graph theory, we obtain some sufficient conditions with the help of this integral inequality to guarantee the global asymptotic stability. The theoretical results offer a new perspective to show the close relationship between the stability criterion and the topological structure of networks. Finally, an illustrative numerical example is given to demonstrate the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

• Introduce a model to fuse local and global information in directed network. • The model can capture topological structures and robust to sparser networks. • Present an effective update rule to learn model parameters. • Experimental results show that our method is outperforms other indices. The aim of link prediction is to predict missing links in current networks or new links in future networks. Almost all the existing directed link prediction algorithms only take into account the links direction formation but ignored the abundant network topological information such as local and global structures. Therefore, how to preserve both local and global structure information is an important issue for directed link prediction. To solve this problem, in this paper, we are motivated to propose a novel Nonnegative Matrix Factorization via Asymmetric link clustering and PageRank model, namely NMF-AP. Specifically, we utilize the PageRank algorithm to calculate the influence score of the node, which captures the global network structure information. While we employ the asymmetric link clustering method to calculate the link clustering coefficient score, which preserves the local network structure information. By jointly optimizing them in the nonnegative matrix factorization model, our model can preserve both the local and global information at the same time. Besides, we provide an effective the multiplicative updating rules to learn the parameter of NMF-AP. Extensive experiments are conducted on ten real-world directed networks, experiment results demonstrate that the method NMF-AP outperforms state-of-the-art link prediction methods. [ABSTRACT FROM AUTHOR]

The aim of link prediction is to disclose the underlying evolution mechanism of networks, which could be utilized to predict missing links or eliminate spurious links. However, real-world networks data usually encounters challenges,such as missing links, spurious links and random noise, which seriously hamper the prediction accuracy of existing link prediction methods. Therefore, in this paper, we propose a novel Robust Non-negative Matrix Factorization via jointly Manifold regularization and Sparse learning (MS-RNMF) method in link prediction that solves the problems. Compared to existing methods, MS-RNMF has three-fold advantages: First of all, the MS-RNMF employ manifold regularization and k-medoids algorithm jointly to preserve the network local and global topology information. Besides, the MS-RNMF adopts ℓ 2 , 1 -norm to constrain loss function and regularization term, random noise and spurious links could be effectively remove. Finally, we employ multiplicative updating rules to learn the model parameter and prove the convergence of the algorithm. Extensive experiments results performed on eleven real-world networks demonstrate that the MS-RNMF outperforms the state-of-the-arts methods in predicting missing links , identifying spurious links and eliminating random noise. • Introduce a nonnegative matrix factorization based model for link prediction. • The model integrates two types of information: local and global information. • We employ ℓ 2 , 1 -norm regularizer to eliminate random noise and identify spurious links. • Experimental results demonstrate that our method is outperforms the other methods. [ABSTRACT FROM AUTHOR]

The existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated. In terms of model, feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching. In terms of method, graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching. And some sufficient conditions are given based on Lyapunov method connected with the graph theory and the M-matrix method to ensure the existence of stationary distribution, which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance, feedback control and coupling strength. Furthermore, the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results. Finally, a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution. • Feedback control is considered in the study of stationary distribution. • The existing area is affected by feedback control. • The theoretical results are applied to coupled oscillators. [ABSTRACT FROM AUTHOR]