Hybrid topological photonic crystals.

Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.

An interprovincial cooperative game model for air pollution control in China.

UNLABELLED: The noncooperative air pollution reduction model (NCRM) that is currently adopted in China to manage air pollution reduction of each individual province has inherent drawbacks. In this paper, we propose a cooperative air pollution reduction game model (CRM) that consists of two parts: (1) an optimization model that calculates the optimal pollution reduction quantity for each participating province to meet the joint pollution reduction goal; and (2) a model that distribute the economic benefit of the cooperation (i.e., pollution reduction cost saving) among the provinces in the cooperation based on the Shapley value method. We applied the CRM to the case of SO2 reduction in the Beijing-Tianjin-Hebei region in China. The results, based on the data from 2003-2009, show that cooperation helps lower the overall SO2 pollution reduction cost from 4.58% to 11.29%. Distributed across the participating provinces, such a cost saving from interprovincial cooperation brings significant benefits to each local government and stimulates them for further cooperation in pollution reduction. Finally, sensitivity analysis is performed using the year 2009 data to test the parameters' effects on the pollution reduction cost savings. IMPLICATIONS: China is increasingly facing unprecedented pressure for immediate air pollution control. The current air pollution reduction policy does not allow cooperation and is less efficient. In this paper we developed a cooperative air pollution reduction game model that consists of two parts: (1) an optimization model that calculates the optimal pollution reduction quantity for each participating province to meet the joint pollution reduction goal; and (2) a model that distributes the cooperation gains (i.e., cost reduction) among the provinces in the cooperation based on the Shapley value method. The empirical case shows that such a model can help improve efficiency in air pollution reduction. The result of the model can serve as a reference for Chinese government pollution reduction policy design.