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Item Rendering and Extracting Extremal Features in 3D Fields(The Eurographics Association and John Wiley & Sons Ltd., 2018) Kindlmann, Gordon L.; Chiw, Charisee; Huynh, Tri; Gyulassy, Attila; Reppy, John; Bremer, Peer-Timo; Jeffrey Heer and Heike Leitte and Timo RopinskiVisualizing and extracting three-dimensional features is important for many computational science applications, each with their own feature definitions and data types. While some are simple to state and implement (e.g. isosurfaces), others require more complicated mathematics (e.g. multiple derivatives, curvature, eigenvectors, etc.). Correctly implementing mathematical definitions is difficult, so experimenting with new features requires substantial investments. Furthermore, traditional interpolants rarely support the necessary derivatives, and approximations can reduce numerical stability. Our new approach directly translates mathematical notation into practical visualization and feature extraction, with minimal mental and implementation overhead. Using a mathematically expressive domain-specific language, Diderot, we compute direct volume renderings and particlebased feature samplings for a range of mathematical features. Non-expert users can experiment with feature definitions without any exposure to meshes, interpolants, derivative computation, etc. We demonstrate high-quality results on notoriously difficult features, such as ridges and vortex cores, using working code simple enough to be presented in its entirety.Item Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections(The Eurographics Association and John Wiley & Sons Ltd., 2018) Thiagarajan, Jayaraman J.; Liu, Shusen; Ramamurthy, Karthikeyan Natesan; Bremer, Peer-Timo; Jeffrey Heer and Heike Leitte and Timo RopinskiTwo-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to bivariate relationships. Linear project can be considered as a compromise between complexity and interpretability, as they allow explicit axes labels, yet provide significantly more degrees of freedom compared to axis-aligned projections. Nevertheless, interpreting the axes directions, which are often linear combinations of many non-trivial components, remains difficult. To address this problem we introduce a structure aware decomposition of (multiple) linear projections into sparse sets of axis-aligned projections, which jointly capture all information of the original linear ones. In particular, we use tools from Dempster-Shafer theory to formally define how relevant a given axis-aligned project is to explain the neighborhood relations displayed in some linear projection. Furthermore, we introduce a new approach to discover a diverse set of high quality linear projections and show that in practice the information of k linear projections is often jointly encoded in ~ k axis-aligned plots. We have integrated these ideas into an interactive visualization system that allows users to jointly browse both linear projections and their axis-aligned representatives. Using a number of case studies we show how the resulting plots lead to more intuitive visualizations and new insights.Item Interactive Investigation of Traffic Congestion on Fat-Tree Networks Using TREESCOPE(The Eurographics Association and John Wiley & Sons Ltd., 2018) Bhatia, Harsh; Jain, Nikhil; Bhatele, Abhinav; Livnat, Yarden; Domke, Jens; Pascucci, Valerio; Bremer, Peer-Timo; Jeffrey Heer and Heike Leitte and Timo RopinskiParallel simulation codes often suffer from performance bottlenecks due to network congestion, leaving millions of dollars of investments underutilized. Given a network topology, it is critical to understand how different applications, job placements, routing schemes, etc., are affected by and contribute to network congestion, especially for large and complex networks. Understanding and optimizing communication on large-scale networks is an active area of research. Domain experts often use exploratory tools to develop both intuitive and formal metrics for network health and performance. This paper presents TREESCOPE, an interactive, web-based visualization tool for exploring network traffic on large-scale fat-tree networks. TREESCOPE encodes the network topology using a tailored matrix-based representation and provides detailed visualization of all traffic in the network. We report on the design process of TREESCOPE, which has been received positively by network researchers as well as system administrators. Through case studies of real and simulated data, we demonstrate how TREESCOPE's visual design and interactive support for complex queries on network traffic can provide experts with new insights into the occurrences and causes of congestion in the network.