The Visual Display of Quantitative Information

This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as Web browsing, state-transition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective.

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Graph visualization and navigation in information visualization: A survey

A novel protein superfamily with over 600 members was discovered by iterative profile searches and analyzed with powerful bioinformatics and information visualization methods. Evidence exists that these proteins generate a radical species by reductive cleavage of S-adenosylmethionine (SAM) through an unusual Fe-S center. The superfamily (named here Radical SAM) provides evidence that radical-based catalysis is important in a number of previously well- studied but unresolved biochemical pathways and reflects an ancient conserved mechanistic approach to difficult chemistries. Radical SAM proteins catalyze diverse reactions, including unusual methylations, isomerization, sulfur insertion, ring formation, anaerobic oxidation and protein radical formation. They function in DNA precursor, vitamin, cofactor, antibiotic and herbicide biosynthesis and in biodegradation pathways. One eukaryotic member is interferon-inducible and is considered a candidate drug target for osteoporosis; another is observed to bind the neuronal Cdk5 activator protein. Five defining members not previously recognized as homologs are lysine 2,3-aminomutase, biotin synthase, lipoic acid synthase and the activating enzymes for pyruvate formate-lyase and anaerobic ribonucleotide reductase. Two functional predictions for unknown proteins are made based on integrating other data types such as motif, domain, operon and biochemical pathway into an organized view of similarity relationships.

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Radical SAM, a novel protein superfamily linking unresolved steps in familiar biosynthetic pathways with radical mechanisms: functional characterization using new analysis and information visualization methods

Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament This twist can then significantly alter the dynamics of the filament This paper explores this dynamics via numerical simulation After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)) The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment However this decay is suppressed by uniformly decreasing excitability Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed Results are contrasted with other mechanisms of fibrillation and future prospects are summarized (c)1998 American Institute of Physics

Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation.

We modified the FitzHugh-Nagumo model of an excitable medium so that it describes adequately the dymanics of pulse propagation in the canine myocardium. The modified model is simple enough to be used for intensive 3-dimensional (3D) computations of the whole heart. It simulates the pulse shape and the restitution property of the canine myocardium with good precision.

A simple two-variable model of cardiac excitation

Visualized data often have dubious origins and quality. Different forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and finally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, sonification, and psycho-visual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, flow visualization, and figure animation. We also present a classification of the possibilities in uncertainty visualization, and locate our contributions within this classification.

Approaches to uncertainty visualization

Environmental data have inherent uncertainty which is often ignored in visualization. Meteorological stations and doppler radars, including their time series averages, have a wealth of uncertainty information that traditional vector visualization methods such as meteorological wind barbs and arrow glyphs simply ignore. We have developed a new vector glyph to visualize uncertainty in winds and ocean currents. Our approach is to include uncertainty in direction and magnitude, as well as the mean direction and length, in vector glyph plots. Our glyph shows the variation in uncertainty, and provides fair comparisons of data from instruments, models, and time averages of varying certainty. We also define visualizations that incorporate uncertainty in an unambiguous manner as verity visualization. We use both quantitative and qualitative methods to compare our glyphs to traditional ones. Subjective comparison tests with experts are provided, as well as objective tests, where the information density of our new glyphs and traditional glyphs are compared. The design of the glyph and numerous examples using environmental data are given. We show enhanced visualizations, data together with their uncertainty information, that may improve understanding of environmental vector field data quality.

Glyphs for visualizing uncertainty in vector fields

The paper presents a seed placement strategy for streamlines based on flow features in the dataset. The primary goal of our seeding strategy is to capture flow patterns in the vicinity of critical points in the flow field, even as the density of streamlines is reduced. Secondary goals are to place streamlines such that there is sufficient coverage in non-critical regions, and to vary the streamline placements and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinuities across several streamlines, etc.). The procedure is straightforward and non-iterative. First, critical points are identified. Next, the flow field is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the field using a Poisson disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not image-guided, and hence not view dependent, significant savings are possible when examining flow fields from different viewpoints, especially for 3D flow fields.

A flow-guided streamline seeding strategy

: A multitude of physical and biological processes occur in the ocean over a wide range of temporal and spatial scales. Many of these processes are nonlinear and highly variable, and involve interactions across several scales and oceanic disciplines. For example, sound propagation is infl uenced by physical and biological properties of the water column and by the seabed. From observations and conservation laws, ocean scientists formulate models that aim to explain and predict dynamics of the sea. This formulation is intricate because it is challenging to observe the ocean on a sustained basis and to transform basic laws into generic but usable models. There are imperfections in both data and model estimates. It is important to quantify such uncertainties to understand limitations and identify the research needed to increase accuracies, which will lead to fundamental progress.

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Quantifying Uncertainties in Ocean Predictions

Uncertainty or errors are introduced in fluid flow data as the data is acquired, transformed and rendered. Although researchers are aware of these uncertainties, little has been done to incorporate them in the existing visualization systems for fluid flow. In the absence of integrated presentation of data and its associated uncertainty, the analysis of the visualization is incomplete at best and may lead to inaccurate or incorrect conclusions. The article presents UFLOW-a system for visualizing uncertainty in fluid flow. Although there are several sources of uncertainties in fluid flow data, in this work, we focus on uncertainty arising from the use of different numerical algorithms for computing particle traces in a fluid flow. The techniques that we have employed to visualize uncertainty in fluid flow include uncertainty glyphs, flow envelopes, animations, priority sequences, twirling batons of trace viewpoints, and rakes. These techniques are effective in making the users aware of the effects of different integration methods and their sensitivity, especially near critical points in the flow field.

Alex Pang

Papers

Approaches to uncertainty visualization

Glyphs for visualizing uncertainty in vector fields

A flow-guided streamline seeding strategy

Quantifying Uncertainties in Ocean Predictions

UFLOW: visualizing uncertainty in fluid flow