Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-$\theta_6$-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex $s$ to any vertex $t$ whose length is within $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Generation of Realistic Synthetic Raw Radar Data for Automated Driving Applications using Generative Adversarial Networks

The main approaches for simulating FMCW radar are based on ray tracing, which is usually computationally intensive and do not account for background noise. This work proposes a faster method for FMCW radar simulation capable of generating synthetic raw radar data using generative adversarial networks (GAN). The code and pre-trained weights are open-source and available on GitHub. This method generates 16 simultaneous chirps, which allows the generated data to be used for the further development of algorithms for processing radar data (filtering and clustering). This can increase the potential for data augmentation, e.g., by generating data in non-existent or safety-critical scenarios that are not reproducible in real life. In this work, the GAN was trained with radar measurements of a motorcycle and used to generate synthetic raw radar data of a motorcycle traveling in a straight line. For generating this data, the distance of the motorcycle and Gaussian noise are used as input to the neural network. The synthetic generated radar chirps were evaluated using the Frechet Inception Distance (FID). Then, the Range-Azimuth (RA) map is calculated twice: first, based on synthetic data using this GAN and, second, based on real data. Based on these RA maps, an algorithm with adaptive threshold and edge detection is used for object detection. The results have shown that the data is realistic in terms of coherent radar reflections of the motorcycle and background noise based on the comparison of chirps, the RA maps and the object detection results. Thus, the proposed method in this work has shown to minimize the simulation-to-reality gap for the generation of radar data

Probing two-electron multiplets in bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enables to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in a bilayer graphene quantum dot in the single-electron regime. By making use of a highly-tunable double quantum dot device we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of $\approx 65~\mu$eV. Also, we find an upper limit of a potentially disorder-induced mixing of the $K$ and $K'$ states below $20~\mu$eV.Comment: 5 Pages 5 Figure

Exploring Simple Grid Polygons

We investigate the online exploration problem of a shortsighted mobile robot moving in an unknown cellular room without obstacles