Dynamics of transmission in disordered topological insulators

Here we show in simulations of the Haldane model that pulse propagation in disordered topological insulators is robust throughout the central portion of the band gap where localized modes do not arise. Since transmission is robust in topological insulators, the essential field variable is the phase of the transmitted field, or, equivalently, its spectral derivative, which is the transmission time. Except near resonances with bulk localized modes that couple the upper and lower edges of a topological insulator, the transmission time in a topological insulator is proportional to the density of states and to the energy excited within the sample. The average transmission time is enhanced in disordered TIs near the band edge and slightly suppressed in the center of the band gap. The variance of the transmission time at the band edge for a random ensemble with moderate disorder is dominated by fluctuations at resonances with localized states, and initially scales quadratically. When modes are absent, such as in the center of the band gap, the transmission time self-averages and its variance scales linearly. This leads to significant sample-to-sample fluctuations in the transmission time. However, because the transmission time is the sum of contributions from the continuum edge mode, which stretches across the band gap, and far-off-resonance modes near the band edge, there are no sharp features in the spectrum of transmission time in the center of the band gap. As a result, ultrashort, broadband pulses are faithfully transmitted in the center of the band gap of topological insulators with moderate disorder and bent paths. This allows for robust signal propagation in complex topological metawaveguides for applications in high-speed optoelectronics and telecommunications

LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection

The prevalence of location-based services contributes to the explosive growth of individual-level trajectory data and raises public concerns about privacy issues. In this research, we propose a novel LSTM-TrajGAN approach, which is an end-to-end deep learning model to generate privacy-preserving synthetic trajectory data for data sharing and publication. We design a loss metric function TrajLoss to measure the trajectory similarity losses for model training and optimization. The model is evaluated on the trajectory-user-linking task on a real-world semantic trajectory dataset. Compared with other common geomasking methods, our model can better prevent users from being re-identified, and it also preserves essential spatial, temporal, and thematic characteristics of the real trajectory data. The model better balances the effectiveness of trajectory privacy protection and the utility for spatial and temporal analyses, which offers new insights into the GeoAI-powered privacy protection

Transmission Zeros with Topological Symmetry in Complex Systems

Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media, has advanced the understanding and applications of wave interactions. Here we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and by adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss or gain, the transmission zeros appear either singly on the real axis or as conjugate pairs in the complex plane. As the structure is modified, two single zeros and a complex conjugate pair of zeros may interconvert when they meet at a square root singularity in the rate of change of the distance between the transmission zeros in the complex plane with sample deformation. The transmission time is the spectral derivative of the argument of the determinant of the transmission matrix. It is a sum over Lorentzian functions associated with the resonances of the medium, which is the density of states, and with the zeros of the transmission matrix. Transmission vanishes, and the transmission time diverges as zeros are brought near the real axis. Monitoring the transmission and transmission time when two zeros are close may open up new possibilities for ultrasensitive detection