Scalar Wave Equation Modeling with Time-Space Domain Dispersion-Relation-Based Staggered-Grid Finite-Difference Schemes

The staggered-grid finite-difference (SFD) method is widely used in numerical modeling of wave equations. Conventional SFD stencils for spatial derivatives are usually designed in the space domain. However, when they are used to solve wave equations, it becomes difficult to satisfy the dispersion relations exactly. Liu and Sen (2009c) proposed a new SFD scheme for one-dimensional (1D) scalar wave equation based on the time-space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. This new SFD scheme has greater accuracy and better stability than a conventional scheme under the same discretizations. In this paper, we develop this new SFD scheme further for numerical solution of 2D and 3D scalar wave equations. We demonstrate that the modeling accuracy is second order when the conventional 2M-th-order space-domain SFD and the second order time-domain finite-difference stencils are directly used to solve the scalar wave equation. However, under the same discretization, our 1D scheme can reach 2M-th-order accuracy and is always stable; 2D and 3D schemes can reach 2M-th-order accuracy along 8 and 48 directions, respectively, and have better stability. The advantages of the new schemes are also demonstrated with dispersion analysis, stability analysis, and numerical modeling.National Natural Science Foundation of China 41074100Important National Science & Technology Specific Project of China 2008ZX05024-001Institute for Geophysic

Large-Scale Mapping of Human Activity using Geo-Tagged Videos

This paper is the first work to perform spatio-temporal mapping of human activity using the visual content of geo-tagged videos. We utilize a recent deep-learning based video analysis framework, termed hidden two-stream networks, to recognize a range of activities in YouTube videos. This framework is efficient and can run in real time or faster which is important for recognizing events as they occur in streaming video or for reducing latency in analyzing already captured video. This is, in turn, important for using video in smart-city applications. We perform a series of experiments to show our approach is able to accurately map activities both spatially and temporally. We also demonstrate the advantages of using the visual content over the tags/titles.Comment: Accepted at ACM SIGSPATIAL 201

A Note on Noncommutative D-Brane Actions

We use the nonabelian action of N coincident D(-1) branes in constant background fields, in the N $\to \infty$ limit, to construct noncommutative D-brane actions in an arbitrary noncommutative description and comment on tachyon condensation from this perspective.Comment: 11 pages, LaTeX (v2: references added, typos fixed