Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate spectral methods using rational basis (or modified mapped Gegenbauer functions) for such models in unbounded domains. The main building block of the spectral algorithms is the explicit representations for the Fourier transform and fractional Laplacian of the rational basis, derived from some useful integral identites related to modified Bessel functions. With these at our disposal, we can construct rational spectral-Galerkin and direct collocation schemes by pre-computing the associated fractional differentiation matrices. We obtain optimal error estimates of rational spectral approximation in the fractional Sobolev spaces, and analyze the optimal convergence of the proposed Galerkin scheme. We also provide ample numerical results to show that the rational method outperforms the Hermite function approach

Analytical vectorial structure of non-paraxial four-petal Gaussian beams in the far field

The analytical vectorial structure of non-paraxial four-petal Gaussian beams(FPGBs) in the far field has been studied based on vector angular spectrum method and stationary phase method. In terms of analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are derived in the far field, respectively. According to our investigation, the FPGBs can evolve into a number of small petals in the far field. The number of the petals is determined by the order of input beam. The physical pictures of the FPGBs are well illustrated from the vectorial structure, which is beneficial to strengthen the understanding of vectorial properties of the FPGBs

Your Smart Home Can't Keep a Secret: Towards Automated Fingerprinting of IoT Traffic with Neural Networks

The IoT (Internet of Things) technology has been widely adopted in recent years and has profoundly changed the people's daily lives. However, in the meantime, such a fast-growing technology has also introduced new privacy issues, which need to be better understood and measured. In this work, we look into how private information can be leaked from network traffic generated in the smart home network. Although researchers have proposed techniques to infer IoT device types or user behaviors under clean experiment setup, the effectiveness of such approaches become questionable in the complex but realistic network environment, where common techniques like Network Address and Port Translation (NAPT) and Virtual Private Network (VPN) are enabled. Traffic analysis using traditional methods (e.g., through classical machine-learning models) is much less effective under those settings, as the features picked manually are not distinctive any more. In this work, we propose a traffic analysis framework based on sequence-learning techniques like LSTM and leveraged the temporal relations between packets for the attack of device identification. We evaluated it under different environment settings (e.g., pure-IoT and noisy environment with multiple non-IoT devices). The results showed our framework was able to differentiate device types with a high accuracy. This result suggests IoT network communications pose prominent challenges to users' privacy, even when they are protected by encryption and morphed by the network gateway. As such, new privacy protection methods on IoT traffic need to be developed towards mitigating this new issue