A subelliptic Bourgain-Brezis inequality

We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space $\dot{NL}^{1,Q}$ by $L^{\infty}$ functions, generalizing a result of Bourgain-Brezis \cite{MR2293957}. We then use this to obtain a Gagliardo-Nirenberg inequality for $\bar{\partial}_b$ on the Heisenberg group $\mathbb{H}^n$.Comment: 44 page

Conserved Quantities of harmonic asymptotic initial data sets

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is rather difficult in general. We found a large family of initial data sets on which such a calculation can be carried out effectively. These are initial data sets of harmonic asymptotics, first proposed by Corvino and Schoen to solve the full vacuum constraint equation. In the second half of this article, the new total angular momentum and center of mass for these initial data sets are computed explicitly.Comment: 20 pages. Invited article for the volume "Surveys in Differential Geometry", a Jubilee Volume on General Relativity and Mathematics celebrating 100 Years of General Relativity, edited by L. Bieri and S.T. Ya

Comparison of Nonlinear Phase Noise and Intrachannel Four-Wave-Mixing for RZ-DPSK Signals in Dispersive Transmission Systems

Self-phase modulation induced nonlinear phase noise is reduced with the increase of fiber dispersion but intrachannel four-wave-mixing (IFWM) is increased with dispersion. Both degrading DPSK signals, the standard deviation of nonlinear phase noise induced differential phase is about three times that from IFWM even in highly dispersive transmission systems.Comment: 3 pages, 2 figure

Low-rank semidefinite programming for the MAX2SAT problem

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.Comment: Accepted at AAAI'19. The code can be found at https://github.com/locuslab/mixsa

InfoScrub: Towards Attribute Privacy by Targeted Obfuscation

Personal photos of individuals when shared online, apart from exhibiting a myriad of memorable details, also reveals a wide range of private information and potentially entails privacy risks (e.g., online harassment, tracking). To mitigate such risks, it is crucial to study techniques that allow individuals to limit the private information leaked in visual data. We tackle this problem in a novel image obfuscation framework: to maximize entropy on inferences over targeted privacy attributes, while retaining image fidelity. We approach the problem based on an encoder-decoder style architecture, with two key novelties: (a) introducing a discriminator to perform bi-directional translation simultaneously from multiple unpaired domains; (b) predicting an image interpolation which maximizes uncertainty over a target set of attributes. We find our approach generates obfuscated images faithful to the original input images, and additionally increase uncertainty by 6.2$\times$ (or up to 0.85 bits) over the non-obfuscated counterparts.Comment: 20 pages, 7 figure

Effect of plasma surface pre-treatment on plastic substrate for ZnO TFT

Controlling the surface morphologies of ZnO nanostructures is a critical issue for the fabrication of electronic and photonic devices. This study reports the electrical properties of the ZnO nanostructure grown on the plasma surface pre-treated plastic substrates. The ZnO films were grown by using solution method with zinc nitrate hexahydrate Zn(NO3)2•6H2O and hexamethylenetetramine C12H6N4.as the main solution under various deposition conditions. The films with plasma surface pre-treatment has stronger (100) peak intensity than that without plasma surface pre-treatment. Also, very uniform grain size of the ZnO nanostructures can be seen. The fabricated enhancement mode ZnO thin film transistors (TFTs) exhibiting good transistor behavior with the drain saturation current of 38.1 µA at VGS = 35 V can be achieved. Keywords: ZnO nanostructure, plastic substrate, solution method, plasma, surface pre-treatment, TFT