With the development of information technology, the interactions between nodes are no longer restricted to two nodes. Recently, researchers have proposed a higher-order network, which is more suitable to describe the multidimensional interaction relationships in systems. A higher-order network with good robustness can effectively resist natural disasters and deliberate attacks. How to improve the robustness of the higher-order network is worth studying. In this paper, we construct two higher-order networks based on the simplex structure. In addition, we propose a capacity load model that can describe the robustness of higher-order networks. The simulation results show that the robustness of the higher-order network is positively correlated with the size of the high-order network, the larger the size of the higher-order network, the more robust the higher-order network is in two attack strategies. In addition, the robustness of higher-order is related to the number of 2-simplexes in the network. Furthermore, the robustness is affected by the weight coefficients of 1-simplex and 2-simplex interactions. Therefore, we can improve robustness of higher-order networks by controlling the weight coefficients of the 1- and 2-simplex in higher-order networks. We verified the conclusions by two synthetic higher-order networks and a constructed higher-order network based on real data.

Random hyper-network is an important hyper-network structure. Studying the structure and properties of random hyper-networks, which helps researchers to understand the influence of the hyper-network structure on its properties. Currently, studies related to the influence of the internal structure of the hyper-edge on robustness have not been carried out for research on the robustness of hyper-networks. In this paper, we construct three $ k $-uniform random hyper-networks with different structures inside hyper-edges. The nodes inside hyper-edges are connected in the ways randomly connected, preferentially connected and completely connected. Meanwhile, we propose a capacity-load model that can describe the relationship between the internal structure and the robustness of the hyper-edge, based on the idea of capacity-load model. The robustness of the three hyper-networks was obtained by simulation experiments. The results show the variation of the internal structure of hyper-edge has a large influence on the robustness of the $ k $-uniform random hyper-network. In addition, the larger number of ordinary edges $ m_{k} $ inside the hyper-edges and the size of the hyper-network $ k $, the more robust the $ k $-uniform random hyper-network is.

Cascading failures occur frequently in many network systems. In this paper, we propose a hyper-network Capacity Load Model based on hyper-edge degrees load to explore the influence of cascading failures on some K-uniform hyper-networks. In simulation, we attack the hyper-edge which has largest hyper-edge degree. When the hyper-edge fails, its load will be equally distributed to adjacent hyper-edges. Through simulation analysis, we get the relationship between the capacity-load model parameters and the robustness of the k-uniform hyper-network. The results show the robustness of the hyper-networks is enhanced with the increase of its hyper-edge capacity. In addition, simulation result show that the robustness of K-uniform hyper-networks is strongest at α=1.

Hyper-networks tend to perform better in representing multivariate relationships among nodes. Yet, due to the complexity of the hyper-network structure, research in synchronization dynamics is rarely involved. In this paper, a Kuramoto model more suitable for k-uniform hyper-networks is proposed. And the generalized Laplacian matrix expression of the k-uniform hyper-network is present. We use the eigenvalue ratio of the generalized Laplacian matrix to quantify synchronization. And we studied the effects of some important structure parameters on the synchronization of three types of k-uniform hyper-networks. And obtained different relationships between synchronization and these parameters. The results show the synchronization of the k-uniform hyper-networks is related to both structure and parameters. And as the size of the nodes increases, the synchronization ability gradually increases for ER random hyper-network, while that gradually decreases for NW small-world hyper-network and BA scale-free hyper-network. As the uniformity increases, the synchronization ability of all three types of uniform hyper-networks increases. In addition, when the structure and node size are fixed, the synchronization ability increases with the increase of the hyper-clustering coefficient in BA scale-free hyper-network and ER random hyper-network, while it decreases with the increase of the hyper-clustering coefficient in NW small-world hyper-network.

Generative Artificial Intelligence (GenAI) is revolutionizing the field of higher education by leveraging deep learning models to generate human-like content. However, the use of GenAI in education raises ethical concerns such as the potential impact on critical thinking skills and the unethical or dishonest use by students. This paper analyzed the main problems existing in engineering courses in Chinese universities firstly and then proposed corresponding teaching reform measures based on the comprehensive consideration of the benefits and threats of GenAI. We applied the proposed teaching reform measures in the teaching of engineering courses, which greatly improved the teaching quality.

Let G be a graph with n vertices, let $A\left(G\right)$ be an adjacency matrix of G and let $P_A(G,\lambda )$ be the characteristic polynomial of $A\left(G\right)$. The adjacency spectrum of G consists of eigenvalues of $A\left(G\right)$. A graph G is said to be determined by its adjacency spectrum (DS for short) if other graphs with the same adjacency spectrum as G are isomorphic to G. In this paper, we investigate the spectral characterization of unicycle graphs with only two vertices of degree three. We use $G_{21}(s_1,s_2)$ to denote the graph obtained from $Q(s_1,s_2)$ by identifying its pendant vertex and the vertex of degree two of $P_3$, where $Q(s_1,s_2)$ is the graph obtained by identifying a vertex of $C_{s_1}$ and a pendant vertex of $P_{s_2}$. We use $G_{31}(t_1,t_2)$ to denote the graph obtained from circle with the vertices $v_0{v}_1\cdots v_{t_1+t_2+1}$ by adding one pendant edge at vertices $v_0$ and $v_{t_1+1}$, respectively. It is shown that $G_{21}(s_1,s_2)$ ($s_1\ne 4,6$, $s_1\ge 3$, $s_2\ge 3$) and $G_{31}(t_1,t_2)$ ($t_1+t_2\ne 2$, $t_2\ge t_1\ge 1$) are determined by their adjacency spectrum.