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Many studies have shown that clustered Wireless Sensor Networks (WSNs) have a better performance in terms of the balance of energy and lifetime. However, due to the harsh environment and open communication, the clustered WSNs are easy to be attacked. The selective forwarding attack is one of the most difficult attacks to be detected. When a malicious sensor node launches the selective forwarding attacks, it drops part of or all the data packets it received. In this paper, we propose a Noise-Based Density Peaks Clustering (NB-DPC) algorithm for detecting selective forwarding attacks. It can detect selective forwarding attacks by clustering the Cumulative Forwarding Rates (CFRs) of all sensor nodes. The NB-DPC algorithm has been improved by defining noise points specifically for identifying malicious behavior and deleting the unnecessary steps in Density Peaks Clustering (DPC) for faster detection speed. The NB-DPC has a low Missed Detection Rate (MDR) and False Detection Rate (FDR) of below 1% according to the simulation results. INDEX TERMS Clustered wireless sensor networks, selective forwarding attacks, cumulative forwarding rate, noise-based density peaks clustering.

Deterministic interface states can be realized in square lattice photonic crystals (PCs) under certain parameters. Using the same parameters, straight lined and circular interface states were constructed by arranging two kinds of sunflower-type PCs in the upper-lower and inner-outer combination structures, respectively. With the condition to generate interface states satisfied, straight lined interface states were proved in the upper-lower combination structures. Sunflowertype PCs do not have translational symmetry in a rectangular coordinate system but they have rotational symmetry, which can be approximately regarded as translational symmetry in polar coordinate system. The transmission spectrum confirms that circular interface states can be realized in sunflower-type PCs by applying parameters consistent with straight lined ones in a rectangular system. By generating circular interface states in a two-dimension system, more applications concerning interface states can be developed.

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