The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior such as the spread of information or disease. Recently, a simplicial contagion problem was introduced and considered using a simplicial susceptible-infected-susceptible (SIS) model. Although recent studies have investigated random hypergraphs with a Poisson-type facet degree distribution, hypergraphs in the real world can have a power-law type of facet degree distribution. Here, we consider the SIS contagion problem on scale-free uniform hypergraphs and find that a continuous or hybrid epidemic transition occurs when the hub effect is dominant or weak, respectively. We determine the critical exponents analytically and numerically. We discuss the underlying mechanism of the hybrid epidemic transition.

We have investigated the electronic structure of charged bilayer and trilayer phoshporene using first-principles, density-functional-theory calculations. We find that the effective dielectric constant for an external electric field applied perpendicular to phosphorene layers increases with the charge density and is twice as large as in an undoped system if the electron density is around 5 × 10 13 cm −2 . It is known that if few-layer phosphorene is placed under such an electric field, the electron band gap decreases and if the strength of the electric field is further increased, the band gap closes. We show that the electronic screening due to added charge carriers reduces the amount of this reduction in the band gap and increases the critical strength of the electric field for gap closure. If the electron density is around 4×10 13 cm −2 , for example, this critical field for trilayer phosphorene is 40 % higher than that for a charge-neutral system. The results are directly relevant to experiments on few-layer phosphorene with top and bottom electrical gates and / or with chemical dopants.

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An insufficient supply of effective SARS-CoV-2 vaccine in most countries demands an effective vaccination strategy to minimize the damage caused by the disease. Currently, many countries vaccinate their population in descending order of age to minimize the deaths caused by the disease; however, the effectiveness of this strategy needs to be quantitatively assessed. We employed the susceptible-infected-recovered-dead (SIRD) model to investigate various vaccination strategies. In complex network, the case fatality rate (CFR)-based method was shown to be more effective than the load-based strategy when there is a low supply of vaccine; however, when there is a sufficient quantity of vaccine, the load-based strategy is more effective than the CFR-based strategy. We also constructed a metapopulation model with empirical human contact and CFR data for SARS-CoV-2 and investigated vaccination strategies. We found that the age-based strategy, which is currently employed in many countries, is more effective when the basic reproduction number is high and vaccination supply is low, but the rate-based method outperforms the age-based strategy when there is sufficiently high supply of vaccine. Simulated annealing is performed to find the optimal vaccination strategy. We identified a first-order phase transition in the vaccination strategies which is characterized by discontinuous transition in the optimal strategy and the hysteresis. This phase transition implies that mixing the age-based and rate-based strategy is ineffective in reducing the number of deaths. These conclusions are valid even when the heterogeneous degree distribution of human contact is considered.

Cascading failures in electrical power grids, comprising nodes and links, propagate nonlocally. After a local disturbance, successive resultant can be distant from the source. Since avalanche failures can propagate unexpectedly, care must be taken when formulating a mitigation strategy. Herein, we propose a strategy for mitigating such cascading failures. First, to characterize the impact of each node on the avalanche dynamics, we propose a novel measure, that of Avalanche Centrality (AC). Then, based on the ACs, nodes potentially needing reinforcement are identified and selected for mitigation. Compared with heuristic measures, AC has proven to be efficient at reducing avalanche size; however, due to nonlocal propagation, calculating ACs can be computationally burdensome. To resolve this problem, we use a graph neural network (GNN). We begin by training a GNN using a large number of small networks; then, once trained, the GNN can predict ACs efficiently in large networks and real-world topological power grids in manageable computational time. Thus, under our strategy, mitigation in large networks is achieved by reinforcing nodes with large ACs. The framework developed in this study can be implemented in other complex processes that require longer computational time to simulate large networks.