Dynamic Behavior of Interacting between Epidemics and Cascades on Heterogeneous Networks

Epidemic spreading and cascading failure are two important dynamical processes over complex networks. They have been investigated separately for a long history. But in the real world, these two dynamics sometimes may interact with each other. In this paper, we explore a model combined with SIR epidemic spreading model and local loads sharing cascading failure model. There exists a critical value of tolerance parameter that whether the epidemic with high infection probability can spread out and infect a fraction of the network in this model. When the tolerance parameter is smaller than the critical value, cascading failure cuts off abundant of paths and blocks the spreading of epidemic locally. While the tolerance parameter is larger than the critical value, epidemic spreads out and infects a fraction of the network. A method for estimating the critical value is proposed. In simulation, we verify the effectiveness of this method in Barab\'asi-Albert (BA) networks

A Scale-Free Topology Construction Model for Wireless Sensor Networks

A local-area and energy-efficient (LAEE) evolution model for wireless sensor networks is proposed. The process of topology evolution is divided into two phases. In the first phase, nodes are distributed randomly in a fixed region. In the second phase, according to the spatial structure of wireless sensor networks, topology evolution starts from the sink, grows with an energy-efficient preferential attachment rule in the new node's local-area, and stops until all nodes are connected into network. Both analysis and simulation results show that the degree distribution of LAEE follows the power law. This topology construction model has better tolerance against energy depletion or random failure than other non-scale-free WSN topologies.Comment: 13pages, 3 figure

Microscopic Characteristics and Modelling of Pedestrian Inflow Process with Inactive Persons

Inflow and outflow processes are common phenomena in daily life. Many types of research have been conducted to study the features of the outflow process, especially in scenarios with a single room or a straight corridor. A few scholars have paid attention to the movement characteristics of pedestrian inflow. Further explorations are still under great demand. In this contribution, a set of pre-conducted experiments are used to analyze the characteristics of the pedestrian inflow process with inactive persons. In these experiments, inactive persons were required to randomly cease within the room, leading to intensive detour behavior of pedestrians. The characteristics are carefully investigated using gradient analysis and curl analysis. To mimic the aforementioned inflow process, static global field is constructed to heuristically navigate a social force based microscopic model. The proposed model can reproduce the self-organized phenomena in the experiments. Our work can help understand the field feature of the pedestrian inflow process with inactive persons. High chaos level areas can be marked out providing practical information for managers

Noise assisted quantum coherence protection in hierarchical environment

In this paper, we investigate coherence protection of a quantum system coupled to a hierarchical environment by utilizing noise. As an example, we solve the Jaynes-Cummings (J-C) model in presence of both a classical and a quantized noise. The master equation is derived beyond the Markov approximation, where the influence of memory effects from both noises is taken into account. More importantly, we find that the performance of the coherence protection sensitively depends on the non-Markovian properties of both noises. By analyzing the mathematical mechanism of the coherence protection, we show the decoherence caused by a non-Markovian noise with longer memory time can be suppressed by another Markovian noise with shorter memory time. Last but not least, as an outlook, we try to analyze the connection between the atom-cavity entanglement and the atomic coherence, then discuss the possible clue to search for the required noise. The results presented in this paper show the possibility of protecting coherence by utilizing noise and may open a new path to design noise-assisted coherence protection schemes.Comment: 17 pages, 9 figure

Threshold for the Outbreak of Cascading Failures in Degree-degree Uncorrelated Networks

In complex networks, the failure of one or very few nodes may cause cascading failures. When this dynamical process stops in steady state, the size of the giant component formed by remaining un-failed nodes can be used to measure the severity of cascading failures, which is critically important for estimating the robustness of networks. In this paper, we provide a cascade of overload failure model with local load sharing mechanism, and then explore the threshold of node capacity when the large-scale cascading failures happen and un-failed nodes in steady state cannot connect to each other to form a large connected sub-network. We get the theoretical derivation of this threshold in degree-degree uncorrelated networks, and validate the effectiveness of this method in simulation. This threshold provide us a guidance to improve the network robustness under the premise of limited capacity resource when creating a network and assigning load. Therefore, this threshold is useful and important to analyze the robustness of networks.Comment: 11 pages, 4 figure

A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network

In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advantage of both the least squares structure and the neural network structure of the objective function. By categorizing the weights and biases of the hidden and output layers of the network as nonlinear and linear parameters, respectively, the method iterates back and forth between the nonlinear and linear parameters. The nonlinear parameters are updated by a damped Gauss-Newton method and the linear ones are updated by a linear solver. Moreover, at the Gauss-Newton step, a special form of the Gauss-Newton matrix is derived for the shallow ReLU neural network and is used for efficient iterations. It is shown that the corresponding mass and Gauss-Newton matrices in the respective linear and nonlinear steps are symmetric and positive definite under reasonable assumptions. Thus, the SgGN method naturally produces an effective search direction without the need of additional techniques like shifting in the Levenberg-Marquardt method to achieve invertibility of the Gauss-Newton matrix. The convergence and accuracy of the method are demonstrated numerically for several challenging function approximation problems, especially those with discontinuities or sharp transition layers that pose significant challenges for commonly used training algorithms in machine learning

Lithospheric deformation revealed by teleseismic phases SKS PKS and SKKS splitting in the NE margin of the Tibetan plateau

The NE margin of the Tibetan plateau influenced by multiple blocks, the regional dynamic model and lithospheric deformation characteristics are still controversial. In this study, 15 years data from permanent broadband seismic stations of the seismic network in the study area were adopted for splitting analyses of teleseismic phases XKS (SKS PKS and SKKS, shortly named XKS) using a grid search method, longer observations provided each station with a large number of clear seismic phases. The results show that the fast wave directions of XKS splitting are oriented toward WNW or NW, with reference to the direction of absolute plate motion, the lithospheric deformation is dominantly driven by the asthenosphere, although there are local variations. On both sides of the Haiyuan fault zone, there is a noticeable variation in lithospheric azimuthal anisotropy, further enhances the possibility that it is an extended boundary of the Tibetan plateau. Rheological anisotropic features on the western side of the Ordos block emphasize the obstruction of the rigid Ordos lithosphere. The crust and mantle seem to be coupled below the Qinling orogen, possibly related to the lateral movement of lithospheric material. However, in the Hexi corridor, there may be layered anisotropy within the lithosphere, which is inferred to relate to the subductions of the Alxa block and the Qilian orogen. The thicker lithosphere on the southern margin of the Alxa block may influence the asthenospheric flow. In addition, anisotropy results at the southeastern edge of the Alxa block and the Yinchuan graben reflect the possibility that the lithosphere may be characterized by a combination of horizontal and vertical movements. These results have greatly improved our understanding of the dynamic models and lithospheric deformation characteristics of the northeastern margin of the Tibetan plateau and adjacent areas