In this paper, we introduce the generalized quasi-variational inequality problem and develop a theory for the existence of solution. This new problem includes as special cases two existing generalizations of the classical variational inequality problem. Relationship with a certain implicit complementarity problem is also studied.

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We study the performance of brain computer interface (BCI) system in a virtual reality (VR) environment and compare it to 2D regular displays. First, we design a headset that consists of three components: a wearable electroencephalography (EEG) device, a VR headset and an interface. Recordings of brain and behavior from human subjects, performing a wide variety of tasks using our device are collected. The tasks consist of object rotation or scaling in VR using either mental commands or facial expression (smile and eyebrow movement). Subjects are asked to repeat similar tasks on regular 2D monitor screens. The performance in 3-D virtual reality environment is considerably higher compared to the to the 2D screen. Particularly, the median number of success rate across trials for VR setting is double of that for the 2D setting (8 successful command in VR setting compared to 4 successful command in 2D screen in 1 minute trials). Our results suggest that the design of future BCI systems can remarkably benefit from the VR setting.

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Non-line-of-sight (NLOS) imaging techniques use light that diffusely reflects off of visible surfaces (e.g., walls) to see around corners. One approach involves using pulsed lasers and ultrafast sensors to measure the travel time of multiply scattered light. Unlike existing NLOS techniques that generally require densely raster scanning points across the entirety of a relay wall, we explore a more efficient form of NLOS scanning that reduces both acquisition times and computational requirements. We propose a circular and confocal non-line-of-sight (C 2 NLOS) scan that involves illuminating and imaging a common point, and scanning this point in a circular path along a wall. We observe that (1) these C 2 NLOS measurements consist of a superposition of sinusoids, which we refer to as a transient sinogram, (2) there exists computationally efficient reconstruction procedures that transform these sinusoidal measurements into 3D positions of hidden scatterers or NLOS images of hidden objects, and (3) despite operating on an order of magnitude fewer measurements than previous approaches, these C 2 NLOS scans provide sufficient information about the hidden scene to solve these different NLOS imaging tasks. We show results from both simulated and real C 2 NLOS scans. 1