Chenhao Jin

Chenhao Jin, Hehu Xie

This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the framework of Yee's scheme to eliminate null space and enable matrix-free, GPU-accelerated operations via 3D discrete Fourier transform. Furthermore, we propose a novel discretization for permittivity tensor containing off-diagonal entries and prove that the resulting matrix is Hermitian positive definite, which ensures the correctness of the kernel compensation technique. Numerical experiments on several benchmark examples are demonstrated to validate the robustness and accuracy of our scheme.

Zhenyu Gu, Chenhao Jin, Zhanxun Dong et al.

Today, eye trackers are extensively used in user interface evaluations. However, it's still hard to analyze and interpret eye tracking data from the aesthetic point of view. To find quantitative links between eye movements and aesthetic experience, we tracked 30 observers' initial landings for 40 web pages (each displayed for 3 seconds). The web pages were also rated based on the observers' subjective aesthetic judgments. Shannon entropy was introduced to analyze the eye-tracking data. The result shows that the heatmap entropy (visual attention entropy, VAE) is highly correlated with the observers' aesthetic judgements of the web pages. Its improved version, relative VAE (rVAE), has a more significant correlation with the perceived aesthetics. (r=-0.65, F= 26.84, P$<$0.0001). This single metric alone can distinguish between good- and bad-looking pages with an approximate 85\% accuracy. Further investigation reveals that the performance of both VAE and rVAE became stable after 1 second. The curves indicate that their performances could be better, if the tracking time was extended beyond 3 seconds.