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A new material interface reconstruction method for volume fraction data is presented. Our method is comprised of two components: first, we generate initial interface topology; then, using a combination of smoothing and volumetric forces within an active interface model, we iteratively transform the initial material interfaces into high-quality surfaces that accurately approximate the problem's volume fractions. Unlike all previous work, our new method produces material interfaces that are smooth, continuous across cell boundaries, and segment cells into regions with proper volume. These properties are critical during visualization and analysis. Generating high-quality mesh representations of material interfaces is required for accurate calculations of interface statistics, and dramatically increases the utility of material boundary visualizations.

Driven by the ability to generate ever-larger, increasingly complex data, there is an urgent need in the scientific community for scalable analysis methods that can rapidly identify salient trends in scientific data. Query-Driven Visualization (QDV) strategies are among the small subset of techniques that can address both large and highly complex datasets. This paper extends the utility of QDV strategies with a statistics-based framework that integrates non-parametric distribution estimation techniques with a new segmentation strategy to visually identify statistically significant trends and features within the solution space of a query. In this framework, query distribution estimates help users to interactively explore their query's solution and visually identify the regions where the combined behavior of constrained variables is most important, statistically, to their inquiry. Our new segmentation strategy extends the distribution estimation analysis by visually conveying the individual importance of each variable to these regions of high statistical significance. We demonstrate the analysis benefits these two strategies provide and show how they may be used to facilitate the refinement of constraints over variables expressed in a user's query. We apply our method to datasets from two different scientific domains to demonstrate its broad applicability.

While the scientific visualization community is comfortable with isosurfacing and volume rendering of scalar fields, data from simulations and sensors often have additional constraints or dimensions that are not easily handled by these algorithms. In the first part of this dissertation we consider volume fraction data and the material interface reconstruction problem, for which existing isosurfacing and segmentation methods do not produce satisfactory results. Optimization-based methods are introduced that produce accurate multi-material segmenting surfaces through volume fraction data. In the second part, we discuss visualization techniques for function fields. A dimension reduction approach based upon probing and range-space segmentation is introduced, allowing function fields to be analyzed with traditional visualization algorithms. Finally, queries are considered for explicit feature extraction.

We present a dimension reduction and feature extraction method for the visualization and analysis of function field data. Function fields are a class of high-dimensional, multi-variate data in which data samples are one-dimensional scalar functions. Our approach focuses upon the creation of high-dimensional range-space segmentations, from which we can generate meaningful visualizations and extract separating surfaces between features. We demonstrate our approach on high-dimensional spectral imagery, and particulate pollution data from air quality simulations.

One fundamental element of scientific inquiry is discovering relationships, particularly the interactions between different variables in observed or simulated phenomena. Building upon our prior work in the field of Query-Driven Visualization, where visual data analysis processing is focused on subsets of large data deemed to be "scientifically interesting," this new work focuses on a novel knowledge discovery capability suitable for use with petascale class datasets. It enables visual presentation of the presence or absence of relationships (correlations) between variables in data subsets produced by Query-Driven methodologies. This technique holds great potential for enabling knowledge discovery from large and complex datasets currently emerging from SciDAC and INCITE projects. It is sufficiently generally to be applicable to any time of complex, time-varying, multivariate data from structured, unstructured or adaptive grids.

Material interface reconstruction (MIR) is the task of constructing boundary interfaces between regions of homogeneous material, while satisfying volume constraints, over a structured or unstructured spatial domain. In this paper, we present a discrete approach to MIR based upon optimizing the labeling of fractional volume elements within a discretization of the problem's original domain. We detail how to construct and initially label a discretization, and introduce a \emph{volume conservative swap} move for optimization. Furthermore, we discuss methods for extracting and visualizing material interfaces from the discretization. Our technique has significant advantages over previous methods: we produce interfaces between multiple materials that are continuous across cell boundaries for time-varying and static data in arbitrary dimension with bounded error.

We present an unbiased method for generating caustic lighting using importance sampled Path Tracing with {\em Caustic Forecasting}. Our technique is part of a straightforward rendering scheme which extends the \emph{Illumination by Weak Singularities} method to allow for fully unbiased global illumination with rapid convergence. A photon shooting preprocess, similar to that used in Photon Mapping, generates photons that interact with specular geometry. These photons are then clustered, effectively dividing the scene into regions which will contribute similar amounts of caustic lighting to the image. Finally, the photons are stored into spatial data structures associated with each cluster, and the clusters themselves are organized into a spatial data structure for fast searching. During rendering we use clusters to decide the caustic energy importance of a region, and use the local photons to aid in importance sampling, effectively reducing the number of samples required to capture caustic lighting.

We present interactive techniques for identifying and extracting features in function fields. Function fields map points in $n$-dimensional Euclidean space to 1-dimensional scalar functions. Visual feature identification is accomplished by interactively rendering scalar distance fields, constructed by applying a function-space distance metric over the function field. Combining visual exploration with feature extraction queries, formulated as a set of function-space constraints, facilitates quantitative analysis and annotation. Numerous application domains give rise to function fields. We present results for two-dimensional hyperspectral images, and a simulated time-varying, three-dimensional air quality dataset.

Our capability to generate increasingly large and more complex datasets has established the need for scalable methods that can provide insight into important variable trends. Query-driven methods are among the small subset of techniques that are able to address both large and highly complex data sets. This paper presents a new method in which coherent and meaningful visualizations are constructed to convey relational information about the trends that exist \emph{between} variables in a query. Correlation fields are created between pairs of variables and used in conjunction with the cumulative distribution function of each of the query's variables to reveal, both visually and statistically, trends in variable behavior and interactions. We illustrate our concepts by discussing interactions between variables in two flame-front simulations.

We present a higher-order approach to the extraction of isosurfaces from unstructured meshes. Existing methods use linear interpolation along each mesh edge to find isosurface intersections. In contrast, our method determines intersections by performing barycentric interpolation over diamonds formed by the tetrahedra incident to each edge. Our method produces smoother, more accurate isosurfaces. Additionally, interpolating over diamonds, rather than linearly interpolating edge endpoints, enables us to identify up to two isosurface intersections per edge. This paper details how our new technique extracts isopoints, and presents a simple connection strategy for forming a triangle mesh isosurface.

CPA firms may need guidance on how jurors would perceive the appropriateness of their provision of cybersecurity attestation services. Would the auditor be expected to disclose areas of potential risk in emphasis of matter paragraphs? Likewise, would the use of a risk specialist enhance the juror's perception of a higher quality of service? We investigate these questions with a hypothetical case describing an auditor providing audit assurance services and cybersecurity attestation services for a client. Results show the use of an independent, external risk specialist and the use of emphasis of matter paragraphs had a significant impact on jurors' perceptions of the appropriateness of the CPA's decision that cybersecurity controls were operating effectively. The use of emphasis of matter paragraphs also had a significant impact in lessening the extent that jurors perceived that the CPA should be responsible for any potential shareholder losses from the cybersecurity controls not being effective. [ABSTRACT FROM AUTHOR]

A study highlighting the economic benefits resulting from integration of Statistical Process Control and maintenance management in the process management of an organization is presented.

ABSTRACT This study examines whether auditors will rate explanations for an unusual fluctuation provided by a decision aid as more sufficient than the same explanations provided by a client, when [...]

Author(s): Rong-guang Zhang [1]; Terina Pappas [2]; Jennifer L. Brace [1]; Paula C. Miller [3, 4]; Tim Oulmassov [3]; John M. Molyneaux [3, 4]; John C. Anderson [3]; James K. [...]

ABSTRACT An auditor generating potential explanations for an unusual variance in analytical review may utilize a decision aid, which provides many explanations. However, circumstances of budgetary constraints and limited cognitive [...]

The question of whether notary publics should serve as the model for a digital signature certification authority is discussed. Topics include parallels between notaries and a certification authority, the notary's role as a public officer, current drawbacks in the training and education of notaries, and the need for strict regulation.of certification authorities.