Double-Arc Parallel Coordinates and its Axes re-Ordering Methods

The Parallel Coordinates Plot (PCP) is a popular technique for the exploration of high-dimensional data. In many cases, researchers apply it as an effective method to analyze and mine data. However, when today's data volume is getting larger, visual clutter and data clarity become two of the main challenges in parallel coordinates plot. Although Arc Coordinates Plot (ACP) is a popular approach to address these challenges, few optimization and improvement have been made on it. In this paper, we do three main contributions on the state-of-the-art PCP methods. One approach is the improvement of visual method itself. The other two approaches are mainly on the improvement of perceptual scalability when the scale or the dimensions of the data turn to be large in some mobile and wireless practical applications. 1) We present an improved visualization method based on ACP, termed as double arc coordinates plot (DACP). It not only reduces the visual clutter in ACP, but use a dimension-based bundling method with further optimization to deals with the issues of the conventional parallel coordinates plot (PCP). 2）To reduce the clutter caused by the order of the axes and reveal patterns that hidden in the data sets，we propose our first dimensional reordering method，a contribution-based method in DACP, which is based on the singular value decomposition (SVD) algorithm. The approach computes the importance score of attributes (dimensions) of the data using SVD and visualize the dimensions from left to right in DACP according the score in SVD. 3) Moreover, a similarity-based method, which is based on the combination of nonlinear correlation coefficient and SVD algorithm, is proposed as well in the paper. To measure the correlation between two dimensions and explains how the two dimensions interact with each other，we propose a reordering method based on non-linear correlation information measurements. We mainly use mutual information to calculate the partial similarity of dimensions in high-dimensional data visualization, and SVD is used to measure global data. Lastly, we use five case scenarios to evaluate the effectiveness of DACP, and the results show that our approaches not only do well in visualizing multivariate dataset, but also effectively alleviate the visual clutter in the conventional PCP, which bring users a better visual experience

Exploring the Possibilities of Embedding Heterogeneous Data Attributes in Familiar Visualizations

Heterogeneous multi-dimensional data are now sufficiently common that they can be referred to as ubiquitous. The most frequent approach to visualizing these data has been to propose new visualizations for representing these data. These new solutions are often inventive but tend to be unfamiliar. We take a different approach. We explore the possibility of extending well-known and familiar visualizations through including Heterogeneous Embedded Data Attributes (HEDA) in order to make familiar visualizations more powerful. We demonstrate how HEDA is a generic, interactive visualization component that can extend common visualization techniques while respecting the structure of the familiar layout. HEDA is a tabular visualization building block that enables individuals to visually observe, explore, and query their familiar visualizations through manipulation of embedded multivariate data. We describe the design space of HEDA by exploring its application to familiar visualizations in the D3 gallery. We characterize these familiar visualizations by the extent to which HEDA can facilitate data queries based on attribute reordering

Harmonic Splittings of Surfaces

We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic tools like the maximum principle are used to simplify the usual combinatorial topology arguments. Other analytic objects associated to a harmonic map, such as the Hopf differential and the moduli space of harmonic maps, are also introduced as tools for understanding the action of surface groups on trees.Comment: 28 page

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest

Spin transfer and current-induced switching in antiferromagnets

We present theoretical description of the precessional switching processes induced by simultaneous application of spin-polarized current and external magnetic field to antiferromagnetic component of the "pinned" layer. We found stability ranges of different static and dynamic regimes. We showed the possibility of steady current-induced precession of antiferromagnetic vector with frequency that linearly depends on the bias current. Furthermore, we found an optimal duration of current pulse required for switching between different orientations of antiferromagnetic vector and current and field dependence of switching time. Our results reveal the difference between dynamics of ferro- and antiferromagnets subjected to spin transfer torques.Comment: 7 pages, 4 figure

Geodesics on an ellipsoid of revolution

Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems involving geodesics (triangulation, projections, maritime boundaries, and polygonal areas) are investigated.Comment: LaTex, 29 pages, 16 figures. Supplementary material is available at http://geographiclib.sourceforge.net/geod.htm

Generalized Advanced Propeller Analysis System (GAPAS). Volume 2: Computer program user manual

The Generalized Advanced Propeller Analysis System (GAPAS) computer code is described. GAPAS was developed to analyze advanced technology multi-bladed propellers which operate on aircraft with speeds up to Mach 0.8 and altitudes up to 40,000 feet. GAPAS includes technology for analyzing aerodynamic, structural, and acoustic performance of propellers. The computer code was developed for the CDC 7600 computer and is currently available for industrial use on the NASA Langley computer. A description of all the analytical models incorporated in GAPAS is included. Sample calculations are also described as well as users requirements for modifying the analysis system. Computer system core requirements and running times are also discussed