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Dependence can highly increase the vulnerability of interdependent networks under cascading failure. Recent studies have shown that a constant density of reinforced nodes can prevent catastrophic network collapses. However, the effect of reinforcing dependency links in interdependent networks has rarely been addressed. Here, we develop a percolation model for studying interdependent networks by introducing a fraction of reinforced dependency links. We find that there is a minimum fraction of dependency links that need to be reinforced to prevent the network from abrupt transition, and it can serve as the boundary value to distinguish between the first- and second-order phase transitions of the network. We give both analytical and numerical solutions to the minimum fraction of reinforced dependency links for random and scale-free networks. Interestingly, it is found that the upper bound of this fraction is a constant 0.088 01 for two interdependent random networks regardless of the average degree. In particular, we find that the proposed method has higher reinforcement efficiency compared to the node-reinforced method, and its superiority in scale-free networks becomes more obvious as the coupling strength increases. Moreover, the heterogeneity of the network structure profoundly affects the reinforcement efficiency. These findings may provide several useful suggestions for designing more resilient interdependent networks.

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.

Aiming at the problem that the traditional teaching mode takes teachers as the center, students lack the ability of active learning and flexible application. According to the characteristics of online teaching, this paper applies the BOPPPS model to Rain Class integrating Ding talk, Wechat group and XuetangX platform. The organization methods of bridge-in, learning objective, pre-assessment, participatory-larning, post-assessment, and summary are designed elaborately. The practice shows that under the background of online teaching, the teaching mode proposed in this paper improves the students’ initiative in learning the course of "Systems engineering" and achieves the ideal teaching effect.

Flipped classroom is an effective teaching method to improve teaching efficiency and quality. However, flipped classroom can easily lead to the defects of fragmentation of teaching process and polarization of learning effect, which hinders its effective application in online teaching. Task-driven teaching has the advantages of clear tasks and systematic knowledge, which can make up for the shortcomings of online teaching in flipped classroom. Aiming at the characteristics of online teaching under COVID-19 epidemic, this research carried out the design of task-driven online flipped classroom teaching model and explored practice. Based on the comprehensive use of multi-dimensional information platform, the situational design aroused and motivated the interest of students. The continuously upgrading tasks lead students to realize the conversion of knowledge mastery to ability formation. The effectiveness of online learning is comprehensively evaluated to realize the healthy operation of the teaching process and finally achieve the teaching goals.

Network repair is indispensable for maintaining network security. Conventional static repair is relatively inefficient. In this study, by considering the energy transfer between nodes, a dynamic repair model was established. The fundamental reason for the secondary failure of repaired nodes during the dynamic repair process is the coupling structure of failure networks. A dynamic repair strategy was proposed that can effectively prevent the secondary failure of repair nodes influenced by energy during repair and can cause the redundant capacity of repair nodes to be used reasonably. By turning off the energy transfer function of the link to control the excessive flow of energy into the repair node to avoid the occurrence of secondary failure; on the other hand, by sharing part of the load of the failure node, realize the rational use of the redundant capacity of the repair node to reduce the impact of the failure node on the overall function of the network. The proposed strategy mitigated the effect of failure nodes on network functions and substantially improved the recovery efficiency of network functions. Furthermore, redundant edges, behaving as energy redundant links in a network structure, can considerably improve the robustness of the network by optimizing the removal of redundant edges. Dynamic repair is not only an efficient repair method but also a highly flexible choice for network repair.

Network repair strategies are tactical methods that restore the efficiency of damaged networks; however, unreasonable repair strategies not only waste resources, they are also ineffective for network recovery. Most extant research on network repair focuses on static networks, but results and findings on static networks cannot be applied to evolutionary dynamic networks because, in dynamic models, complex network repair has completely different characteristics. For instance, repaired nodes face more severe challenges, and require strategic repair methods in order to have a significant effect. In this study, we propose the Shell Repair Strategy (SRS) to minimize the risk of secondary node failures due to the cascading effect. Our proposed method includes the identification of a set of vital nodes that have a significant impact on network repair and defense. Our identification of these vital nodes reduces the number of switching nodes that face the risk of secondary failures during the dynamic repair process. This is positively correlated with the size of the average degree 〈 k 〉 and enhances network invulnerability.

Aiming at the direction-of-arrival (DOA) estimation of two-dimensional (2D) coherently distributed (CD) sources which are coherent with each other, we explore the propagator method based on spatial smoothing of a uniform rectangular array (URA). The rotational invariance relationships with respect to the nominal azimuth and nominal elevation are obtained under the small angular spreads assumption. A propagator operator is constructed through spatial smoothing of sample covariance matrices firstly. Then, combination of propagator and identical matrix is divided according to rotational operators, and the nominal angles can be obtained through eigendecomposition lastly. Realizing angle matching automatically, the proposed method can estimate multiple DOAs of 2D coherent CD sources without spectral peak searching and prior knowledge of deterministic angular signal distribution function. Simulations are conducted to verify the effectiveness of the proposed method.

Football course teaching is the key project of college physical education course, which has the nature of unity and entertainment and attracts the interest of college students. However, there are still many problems in football education in our country, so in fact, the football teaching system in university campus is not perfect, which makes students’ interest in sports reduced. Based on this, this paper first analyzes the current situation of football teaching on campus in the world, and then discusses the effective measures to do well in the new environment. So as to provide a reference for people from all walks of life.

This paper presents the pilot-induced oscillation (PIO) problem in the airdrop stage, analyzes the main causes of the PIO in the drop stage, establishes the closed-loop system with the actuator rate limit, and deduces the PIO formula of closed loop system. Based on the synchronization and Neal-Smith pilot model and the different actuator saturation values, the descriptive function method and the GAP criterion are used to predict the PIO trend of a conveyer in the drop stage. The results show that the PIO prediction results are different for different driver models. If the PIO is caused by the driver, the driver can effectively avoid the occurrence of PIO by reducing the manipulated gain. In the reasonable and permissible range, increasing actuator limit value can avoid the occurrence of PIO to a certain extent.

For the pure feedback systems with uncertain actuator nonlinearity and non-differentiable non-affine function, a novel adaptive neural control scheme is proposed. Firstly, the assumption that the non-affine function must be differentiable everywhere with respect to control input has been canceled; in addition, the proposed approach can not only be applicable to actuator input dead zone nonlinearity, but also to backlash nonlinearity without changing the controller. Secondly, the neural network (NN) is used to approximate unknown nonlinear functions of system generated in the process of control design and a nonlinear robust term is introduced to eliminate the actuator nonlinearity modeling error, the NN approximation error and the external disturbances. Semi-globally uniformly ultimately boundedness of all signals in the closed loop system is analytically proved by utilizing Lyapunov theory. Finally, the effectiveness of the designed method is demonstrated via two examples.

“Ca2+ spark” is the elementary event of calcium release through ryanodine receptors (RyRs) from sarcoplasmic reticulum (SR) during the excitation–contraction (EC) coupling process in cardiac myocytes. Questions remain about its underlying physical process, and existing Fick diffusion-based models fail to reproduce the morphology of experimentally recorded Ca2+ sparks, a phenomenon known as the full-width at half maximum (FWHM) paradox. Here we developed an anomalous subdiffusion model involving Ca2+ release from SR, cytosolic diffusion, recycling by SR Ca2+-ATPases, and the interaction with Ca2+-binding sites (including the diffusible Ca2+ indicator). Numerically simulated Ca2+ spark fit perfectly with experimental results in terms of morphology and kinetics, suggesting the anomalous space subdiffusion to be the governing process of Ca2+ diffusion in the cytoplasm. In addition, parameter sensitivity analysis revealed the essential determinants of spark morphology to be the Ca2+ diffusivity, reaction kinetics, and indicator concentration, but the stationary buffers and pumps to a less extent.

The elementary events of excitation-contraction coupling in heart muscle are Ca2+ sparks, which arise from ryanodine receptors in the sarcoplasmic reticulum (SR). Here, an anomalous subdiffusion model is developed to explore Ca2+ spark formation in cardiac myocytes. Numerical simulations reproduce the brightness, the time course, and spatial size of a typical cardiac Ca2+ spark. It is suggested that the diffusion of Ca2+ spark in the cytoplasm may no longer obey Fickian second law, but the anomalous space subdiffusion. The physical reason is perhaps due to the effects of the electric field of the calcium ions and the viscoelasticity of the cytoplasm and its complex structures.