Pinning Control of Multiplex Dynamical Networks Using Spectral Graph Theory.

Pinning control has been attracting wide attention for the study of various complex networks for decades. This article explores grounded theory on the pinning synchronization of the emerging multiplex dynamical networks. The multiplex dynamical networks under study can describe many real-world scenarios, in which different layers have distinct individual dynamics of node. In this work, we build the bridge between multiplex structures and network dynamics by using the Lyapunov stability theory and the spectral graph theory. Furthermore, by analyzing spectral properties of the grounded super-Laplacian matrices, we set up several graph-based synchronization criteria for multiplex networks via pinning control. In addition, we overcome the difficulties induced by distinct node dynamics in different layers, and find that interlayer coupling strengths promote intralayer synchronization of multiplex networks. Finally, a collection of numerical simulations verifies the effectiveness of theoretical results.

Dynamical vaccination behavior with risk perception and vaccination rewards.

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

Adaptive Fuzzy Tracking Control With Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems.

For strict-feedback systems with mismatched uncertainties, adaptive fuzzy control techniques are developed to provide global prescribed performance with prescribed-time convergence. First, a class of prescribed-time prescribed performance functions are designed to quantify the performance constraints of the tracking error. Additionally, a novel error transformation function is provided to eliminate the initial value limitations and resolve the singularity issue in previous research. To ensure the convergence of the tracking error into a prescribed bounded region within a prescribed time and satisfactory transient performance, controllers with or without approximating structures are established. Notably, the settling time and initial condition of the prescribed performance function are completely independent of the initial tracking error and system parameters, thereby improving upon existing results. Furthermore, the disadvantage of the semi-global boundedness of tracking error induced by dynamic surface control can be eliminated through the use of a novel Lyapunov-like energy function. Finally, the effectiveness of the proposed strategies is validated through numerical simulations performed on practical examples.

Constructing In2S3/CdS/N-rGO Hybrid Nanosheets via One-Pot Pyrolysis for Boosting and Stabilizing Visible Light-Driven Hydrogen Evolution.

The construction of hybrid junctions remains challenging for the rational design of visible light-driven photocatalysts. Herein, In2S3/CdS/N-rGO hybrid nanosheets were successfully prepared via a one-step pyrolysis method using deep eutectic solvents as precursors. Benefiting from the surfactant-free pyrolysis method, the obtained ultrathin hybrid nanosheets assemble into stable three-dimensional self-standing superstructures. The tremella-like structure of hybrid In2S3/N-rGO exhibits excellent photocatalytic hydrogen production performance. The hydrogen evolution rate is 10.9 mmol·g-1·h-1, which is greatly superior to CdS/N-rGO (3.7 mmol·g-1·h-1) and In2S3/N-rGO (2.6 mmol·g-1·h-1). This work provides more opportunities for the rational design and fabrication of hybrid ultrathin nanosheets for broad catalytic applications in sustainable energy and the environment.

Critical behaviors of nonlinear contagion models with recurrent mobility patterns.

Recently, there has been a lot of discussion about the nonlinearity property of contagion processes in epidemic spreading on social networks with various structures. In this paper, we propose a nonlinear contagion model in networked metapopulations to investigate the critical behavior of epidemics with recurrent mobility patterns. First, we build up a discrete-time Markovian chain model to formulate the spreading of susceptible-infected-susceptible-like diseases. Additionally, we develop a practicable framework to analyze the impact of mobility on the epidemic threshold and derive the theoretical condition for the transition of an epidemic from a local to a global scale. This transition is associated with multiple discontinuous phase changes. We validate our analytical results through extensive numerical simulations on both regular and heterogeneous networks. Our findings offer a useful tool to discuss the implementation of prevention strategies such as quarantine and lockdown.

Improving insulin self-injection accuracy in patients with diabetes mellitus through a nursing project.

BACKGROUND: Non-standardized insulin injection has an impact on the efficacy of glucose control. OBJECTIVES: The aim of the study was to explore the effectiveness of a nursing project in improving the insulin self-injection accuracy of diabetes mellitus patients. MATERIAL AND METHODS: A total of 200 type 2 diabetes patients who received insulin therapy with an insulin pen were recruited at the First Affiliated Hospital of Army Medical University (Chongqing, China). Patients were randomly assigned to a control (n = 100) or intervention (n = 100) group. Conventional health education was conducted in the control group, while a nursing project and conventional health education were undertaken in the intervention group. The following parameters were analyzed between the 2 groups: standardized insulin pen use at admission and discharge, glycosylated hemoglobin (HbA1c), time in range (TIR), and adipose hyperplasia incidence rate 6 months after discharge. RESULTS: Concerning standardized insulin self-injection, the intervention group was superior to the control group, and the difference between the 2 groups was statistically significant (p < 0.05). The HbA1c levels (p = 0.000), TIR (p = 0.005) and adipose hyperplasia incidence rate 6 months after discharge (p = 0.000) all improved in the intervention group compared to the control group. CONCLUSIONS: The application of the nursing project effectively improved the efficacy of glucose control in diabetes mellitus patients.

Identification of disease propagation paths in two-layer networks.

To determine the path of disease in different types of networks, a new method based on compressive sensing is proposed for identifying the disease propagation paths in two-layer networks. If a limited amount of data from network nodes is collected, according to the principle of compressive sensing, it is feasible to accurately identify the path of disease propagation in a multilayer network. Experimental results show that the method can be applied to various networks, such as scale-free networks, small-world networks, and random networks. The impact of network density on identification accuracy is explored. The method could be used to aid in the prevention of disease spread.

Occurrence of super-diffusion in two-layer networks.

Super-diffusion is a phenomenon that can be observed in multilayer networks, which describes that the diffusion in a multilayer network is faster than that in the fastest individual layer. In most studies of super-diffusion on two-layer networks, many researchers have focused on the overlap of edges in the two layers and the mode of interlayer connectivity. We discover that the occurrence of super-diffusion in two-layer networks is not necessarily related to the overlap degree. In particular, in a two-layer network, sparse topological structures of individual layers are more beneficial to the occurrence of super-diffusion than dense topological structures. Additionally, similar diffusion abilities of both layers favor super-diffusion. The density of interlayer edges and interlayer connection patterns also influence the occurrence of super-diffusion. This paper offers suggestions to improve the diffusion ability in two-layer networks, which can facilitate the selection of practical information transmission paths between different systems and optimize the design of the internal framework of a company composed of multiple departments.

Predefined-Time Bounded Consensus of Multiagent Systems With Unknown Nonlinearity via Distributed Adaptive Fuzzy Control.

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

The Event-Triggered Impulsive Controls for Quasisynchronization of the Leader-Following Heterogeneous Dynamical Networks.

The time-triggered impulsive controls were widely used to study the collective behavior of homogeneous dynamical networks due to their low control cost, which was a bit conservative in the occupation of communication channels. This article addresses designing the event-triggered impulsive controls for the quasisynchronization, namely, a weak cooperative behavior with the synchronization error no more than a positive constant in the leader-following heterogeneous dynamical network, which thus can reduce the occupation of resources significantly. The centralized and distributed impulsive controls are designed to lead the followers to synchronize approximately to the leader within a nonzero bound, where the impulsive instants are triggered, respectively, by the global or local state-dependent conditions. Numerical results are put forward to verify the effectiveness of the proposed methods.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs.

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Indirect transmission and disinfection strategies on heterogeneous networks.

Besides direct contacts of individuals, indirect contacts with environments being the medium is another route of epidemic transmission, which most previous studies have ignored. Disinfection is one of the most effective and commonly used measures to prevent and control epidemic spreading. In this paper, we propose a metapopulationlike model incorporating direct and indirect transmissions for susceptible-infected-susceptible-like epidemics on heterogeneous networks. Furthermore, we explore the epidemic spreading process with heterogeneous disinfection on both spatial and time dimensions. Specifically, we put forward three types of disinfection strategies, namely, the static disinfection strategy, the random time disinfection strategy, and the event-triggered disinfection strategy. Comparative analysis of the three strategies suggests that managers should prioritize disinfection resource allocation to large-flow environments, especially when disinfection resources are limited. In addition, timely disinfection of environments with infected visitors is an effective and economical strategy. Our model sheds light on the interplay dynamics of indirect transmission and disinfection and the results provide theoretical support for governors to select proper disinfection strategies in practical scenarios.

Identifying partial topology of simplicial complexes.

This paper investigates partial topology identification of simplicial complexes based on adaptive synchronization. For the nodes of interest, the interactions that they participate in can be accurately reconstructed by designing adaptive controllers and parameter estimators. Particularly, not only pairwise interactions but a higher-order structure can be effectively recovered by our method. Moreover, a new linear independence condition with a rigorous definition is established for parameter estimators to converge asymptotically to the true values. Numerical simulations on a general two-dimensional simplicial complex as well as a real-world structure are provided to show the validity of the result and discuss the influence of different parameters on the identification process.

Maximizing synchronizability of networks with community structure based on node similarity.

In reality, numerous networks have a community structure characterized by dense intra-community connections and sparse inter-community connections. In this article, strategies are proposed to enhance synchronizability of such networks by rewiring a certain number of inter-community links, where the research scope is complete synchronization on undirected and diffusively coupled dynamic networks. First, we explore the effect of adding links between unconnected nodes with different similarity levels on network synchronizability and find that preferentially adding links between nodes with lower similarity can improve network synchronizability more than that with higher similarity, where node similarity is measured by our improved Asymmetric Katz (AKatz) and Asymmetric Leicht-Holme-Newman (ALHNII) methods from the perspective of link prediction. Additional simulations demonstrate that the node similarity-based link-addition strategy is more effective in enhancing network synchronizability than the node centrality-based methods. Furthermore, we apply the node similarity-based link-addition or deletion strategy as the valid criteria to the rewiring process of inter-community links and then propose a Node Similarity-Based Rewiring Optimization (NSBRO) algorithm, where the optimization process is realized by a modified simulated annealing technique. Simulations show that our proposed method performs better in optimizing synchronization of such networks compared with other centrality-based heuristic methods. Finally, simulations on the Rössler system indicate that the network structure optimized by the NSBRO algorithm also leads to better synchronizability of coupled oscillators.

Semiquantitative assessment of 99mTc-MIBI uptake in parathyroids of secondary hyperparathyroidism patients with chronic renal failure.

Objective: To explore the valuably influential factors and improve the diagnostic accuracy and efficiency of 99mTc-methoxyisobutylisonitrile (MIBI) uptake in parathyroids of secondary hyperparathyroidism (SHPT) patients with chronic renal failure (CRF). Methods: The correlation analysis was performed between clinical indices related to CRF and 99mTc-MIBI uptake intensity TBR (the gray value mean ratio between the parathyroid target and the bilateral neck background, semiquantitatively calculated with ImageJ software). All clinical indices and TBRs were compared by a three- or two-level grouping method of MIBI uptake, which was visually qualitatively assessed. The three-level grouping method comprised slight, medium, and high groups with little, faint, and distinct MIBI concentration in parathyroids, respectively. The two-level grouping method comprised insignificant and significant groups with TBR greater than or less than 0.49-0.71, respectively. Results: MIBI uptake was significantly positively related to patient age, CRF course, hemodialysis vintage, serum parathyroid hormone (PTH), and alkaline phosphatase (AKP) but was significantly negatively related to serum uric acid (UA). MIBI washout was significantly positively related to patient age but was significantly negatively related to serum phosphorus (P) and calcium (Ca) × P. Oral administration of calcitriol and calcium could significantly reduce the MIBI uptake. MIBI uptake tendency might alter. Such seven indices, namely the MIBI uptake, CRF course, hemodialysis vintage, serum AKP, calcium, cysteine proteinase inhibitor C, and PTH, were comparable between the slight and medium groups but were significantly different between the slight and high groups or between the medium and high groups. The above seven indices plus blood urea nitrogen/creatinine were all significantly different between the insignificant and significant groups. All above significances were with P < 0.05. Conclusions: Patient age, CRF course, hemodialysis vintage, serum PTH, AKP, UA, phosphorus, Ca × P, oral administration of calcitriol and calcium, and parathyroids themselves can significantly influence MIBI uptake in parathyroids of SHPT patients with CRF. The two-level grouping method of MIBI intensity should be adopted to qualitatively diagnose the MIBI uptake.

A model for analyzing competitive dynamics on triplex networks.

This paper studies the evolution process of competitive dynamics on triplex complex networks. We propose a new triplex network model in which the state of the node in each layer is affected by its neighbors as well as inter-layer competition. Through this model, we combine the opinion diffusion model, the Ising model, and the signed network and extend their application from single-layer to multi-layer networks. We derive the evolution process and dynamical equations of the model and carry out a series of numerical simulations to discuss the influence of several factors on the evolution process and the competitiveness of the network. First, we find that the increase of global transition threshold p or the proportion of initial active nodes will lead to more surviving layers and more active nodes in each layer. In addition, we summarize the similarities and differences of the evolution curves under different conditions. Second, we discuss the influence of initial active nodes and the average degree on the competitiveness of the network and find the correlations between them. Finally, we study the relationship between network topology and network competitiveness and conclude the conditions for the best competitiveness of the network. Based on the simulation results, we give specific suggestions on how to improve the competitiveness of the platform in reality.

Fixed-Time Synchronization of Complex Dynamical Networks: A Novel and Economical Mechanism.

Fixed-time synchronization of complex networks is investigated in this article. First, a completely novel lemma is introduced to prove the fixed-time stability of the equilibrium of a general ordinary differential system, which is less conservative and has a simpler form than those in the existing literature. Then, sufficient conditions are presented to realize synchronization of a complex network (with a target system) within a settling time via three different kinds of simple controllers. In general, controllers designed to achieve fixed-time stability consist of three terms and are discontinuous. However, in our mechanisms, the controllers only contain two terms or even one term and are continuous. Thus, our controllers are simpler and of more practical applicability. Finally, three examples are provided to illustrate the correctness and effectiveness of our results.

Synchronizability of two-layer correlation networks.

This study investigates the synchronizability of a typical type of two-layer correlation networks formed by two regular networks interconnected with two interlayer linking patterns, namely, positive correlation (PC) and negative correlation (NC). To analyze the network's stability, we consider the analytical expressions of the smallest non-zero and largest eigenvalues of the (weighted) Laplacian matrix as well as the linking strength and the network size for two linking patterns. According to the master stability function, the linking patterns, the linking strength, and the network size associated with two typical synchronized regions exhibit a profound influence on the synchronizability of the two-layer networks. The NC linking pattern displays better synchronizability than the PC linking pattern with the same set of parameters. Furthermore, for the two classical synchronized regions, the networks have optimal intralayer and interlayer linking strengths that maximize the synchronizability while minimizing the required cost. Finally, numerical results verify the validity of the theoretical analyses. The findings based on the representative two-layer correlation networks provide the basis for maximizing the synchronizability of general multiplex correlation networks.

Synchronizability of double-layer dumbbell networks.

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers. Furthermore, the largest and smallest nonzero eigenvalues of the Laplacian matrix are calculated analytically and numerically for the single-link coupling pattern and also obtained numerically for the two-link coupling pattern so as to characterize the synchronizability of double-layer dumbbell networks. It is shown that interlayer coupling patterns have a significant impact on the synchronizability of multiplex systems. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis. Our findings can facilitate company managers to select optimal interlayer coupling patterns and to assign proper parameters in terms of improving the efficiency and reducing losses of the whole team.

Topology identification of fractional-order complex dynamical networks based on auxiliary-system approach.

Many practical systems can be well described by various fractional-order equations. This paper focuses on identifying the topology of the response layer of a drive-response fractional-order complex dynamical network using the auxiliary-system approach. Specifically, the response layer and the auxiliary layer receive the same input signals from the drive layer. By a designed adaptive control law, the unknown topology of the response layer is successfully identified. Moreover, the proposed method is effective even if the drive layer is made up of isolated nodes. The correctness of the theoretical results is demonstrated by numerical simulations.