Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis

We introduce a data-driven approach to complete partial 3D shapes through a combination of volumetric deep neural networks and 3D shape synthesis. From a partially-scanned input shape, our method first infers a low-resolution -- but complete -- output. To this end, we introduce a 3D-Encoder-Predictor Network (3D-EPN) which is composed of 3D convolutional layers. The network is trained to predict and fill in missing data, and operates on an implicit surface representation that encodes both known and unknown space. This allows us to predict global structure in unknown areas at high accuracy. We then correlate these intermediary results with 3D geometry from a shape database at test time. In a final pass, we propose a patch-based 3D shape synthesis method that imposes the 3D geometry from these retrieved shapes as constraints on the coarsely-completed mesh. This synthesis process enables us to reconstruct fine-scale detail and generate high-resolution output while respecting the global mesh structure obtained by the 3D-EPN. Although our 3D-EPN outperforms state-of-the-art completion method, the main contribution in our work lies in the combination of a data-driven shape predictor and analytic 3D shape synthesis. In our results, we show extensive evaluations on a newly-introduced shape completion benchmark for both real-world and synthetic data

An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection

We introduce a new expression for the Z2 topological invariant of band insulators using non- Abelian Berry's connection. Our expression can identify the topological nature of a general band insulator without any of the gauge fixing problems that plague the concrete implementation of previous invariants. The new expression can be derived from the "partner switching" of the Wannier function center during time reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele.Comment: 14 pages, 8 figure

10 to 50 nm Long Quasi Ballistic Carbon Nanotube Devices Obtained Without Complex Lithography

A simple method combining photolithography and shadow (or angle) evaporation is developed to fabricate single-walled carbon nanotube (SWCNT) devices with tube lengths L~10-50 nm between metal contacts. Large numbers of such short devices are obtained without the need of complex tools such as electron beam lithography. Metallic SWCNTs with lengths ~ 10 nm, near the mean free path (mfp) of lop~15 nm for optical phonon scattering, exhibit near-ballistic transport at high biases and can carry unprecedented 100 mA currents per tube. Semiconducting SWCNT field-effect transistors (FETs) with ~ 50 nm channel lengths are routinely produced to achieve quasi-ballistic operations for molecular transistors. The results demonstrate highly length-scaled and high-performance interconnects and transistors realized with SWCNTs.Comment: PNAS, in pres

The Physics of Compressive Sensing and the Gradient-Based Recovery Algorithms

The physics of compressive sensing (CS) and the gradient-based recovery algorithms are presented. First, the different forms for CS are summarized. Second, the physical meanings of coherence and measurement are given. Third, the gradient-based recovery algorithms and their geometry explanations are provided. Finally, we conclude the report and give some suggestion for future work.Comment: 7 pages, 11 Figures. It is a research report which has not been published in any Journal or Conferenc