An approximation scheme for an Eikonal Equation with discontinuous coefficient

We consider the stationary Hamilton-Jacobi equation where the dynamics can vanish at some points, the cost function is strictly positive and is allowed to be discontinuous. More precisely, we consider special class of discontinuities for which the notion of viscosity solution is well-suited. We propose a semi-Lagrangian scheme for the numerical approximation of the viscosity solution in the sense of Ishii and we study its properties. We also prove an a-priori error estimate for the scheme in an integral norm. The last section contains some applications to control and image processing problems

First Results from SPARO: Evidence for Large-Scale Toroidal Magnetic Fields in the Galactic Center

We have observed the linear polarization of 450 micron continuum emission from the Galactic center, using a new polarimetric detector system that is operated on a 2 m telescope at the South Pole. The resulting polarization map extends ~ 170 pc along the Galactic plane and ~ 30 pc in Galactic latitude, and thus covers a significant fraction of the central molecular zone. Our map shows that this region is permeated by large-scale toroidal magnetic fields. We consider our results together with radio observations that show evidence for poloidal fields in the Galactic center, and with Faraday rotation observations. We compare all of these observations with the predictions of a magnetodynamic model for the Galactic center that was proposed in order to explain the Galactic Center Radio Lobe as a magnetically driven gas outflow. We conclude that the observations are basically consistent with the model.Comment: 11 pages, 2 figures, 1 table, submitted to ApJ Let

Anisotropy in the Cosmic Microwave Background at Degree Angular Scales: Python V Results

Observations of the microwave sky using the Python telescope in its fifth season of operation at the Amundsen-Scott South Pole Station in Antarctica are presented. The system consists of a 0.75 m off-axis telescope instrumented with a HEMT amplifier-based radiometer having continuum sensitivity from 37-45 GHz in two frequency bands. With a 0.91 deg x 1.02 deg beam the instrument fully sampled 598 deg^2 of sky, including fields measured during the previous four seasons of Python observations. Interpreting the observed fluctuations as anisotropy in the cosmic microwave background, we place constraints on the angular power spectrum of fluctuations in eight multipole bands up to l ~ 260. The observed spectrum is consistent with both the COBE experiment and previous Python results. There is no significant contamination from known foregrounds. The results show a discernible rise in the angular power spectrum from large (l ~ 40) to small (l ~ 200) angular scales. The shape of the observed power spectrum is not a simple linear rise but has a sharply increasing slope starting at l ~ 150.Comment: 5 page

Dynamics of Social Balance on Networks

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.Comment: 10 pages, 7 figures, 2-column revtex4 forma

Electrochemical pore formation on InP in alkaline solutions

The surface properties of InP electrodes were examined following anodization in (NH4)2S and KOH electrolytes. In both solutions, the observation of current peaks in the cyclic voltammetric curves was attributed to selective etching of the substrate and a film formation process. AFM images of samples anodized in the sulfide solution, revealed surface pitting and TEM micrographs revealed the porous nature of the film formed on top of the pitted substrate. After anodization in the KOH electrolyte, TEM images revealed that a porous layer extending 500 nm into the substrate had been formed. Analysis of the composition of the anodic products indicates the presence of In2S3 in films grown in (NH4)2S and an In2O3 phase within the porous network formed in KOH

An MPEG-7 scheme for semantic content modelling and filtering of digital video

Abstract Part 5 of the MPEG-7 standard specifies Multimedia Description Schemes (MDS); that is, the format multimedia content models should conform to in order to ensure interoperability across multiple platforms and applications. However, the standard does not specify how the content or the associated model may be filtered. This paper proposes an MPEG-7 scheme which can be deployed for digital video content modelling and filtering. The proposed scheme, COSMOS-7, produces rich and multi-faceted semantic content models and supports a content-based filtering approach that only analyses content relating directly to the preferred content requirements of the user. We present details of the scheme, front-end systems used for content modelling and filtering and experiences with a number of users

A Regularized Graph Layout Framework for Dynamic Network Visualization

Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual representation of the network structure at each time step, the sequence should preserve the mental map between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network. In this paper, we propose a framework for dynamic network visualization in the on-line setting where only present and past graph snapshots are available to create the present layout. The proposed framework creates regularized graph layouts by augmenting the cost function of a static graph layout algorithm with a grouping penalty, which discourages nodes from deviating too far from other nodes belonging to the same group, and a temporal penalty, which discourages large node movements between consecutive time steps. The penalties increase the stability of the layout sequence, thus preserving the mental map. We introduce two dynamic layout algorithms within the proposed framework, namely dynamic multidimensional scaling (DMDS) and dynamic graph Laplacian layout (DGLL). We apply these algorithms on several data sets to illustrate the importance of both grouping and temporal regularization for producing interpretable visualizations of dynamic networks.Comment: To appear in Data Mining and Knowledge Discovery, supporting material (animations and MATLAB toolbox) available at http://tbayes.eecs.umich.edu/xukevin/visualization_dmkd_201

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry