Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

The Impact of Dynamics in Protein Assembly

Predicting the assembly of multiple proteins into specific complexes is critical to understanding their biological function in an organism, and thus the design of drugs to address their malfunction. Consequently, a significant body of research and development focuses on methods for elucidating protein quaternary structure. In silico techniques are used to propose models that decode experimental data, and independently as a structure prediction tool. These computational methods often consider proteins as rigid structures, yet proteins are inherently flexible molecules, with both local side-chain motion and larger conformational dynamics governing their behaviour. This treatment is particularly problematic for any protein docking engine, where even a simple rearrangement of the side-chain and backbone atoms at the interface of binding partners complicates the successful determination of the correct docked pose. Herein, we present a means of representing protein surface, electrostatics and local dynamics within a single volumetric descriptor, before applying it to a series of physical and biophysical problems to validate it as representative of a protein. We leverage this representation in a protein-protein docking context and demonstrate that its application bypasses the need to compensate for, and predict, specific side-chain packing at the interface of binding partners for both water-soluble and lipid-soluble protein complexes. We find little detriment in the quality of returned predictions with increased flexibility, placing our protein docking approach as highly competitive versus comparative methods. We then explore the role of larger, conformational dynamics in protein quaternary structure prediction, by exploiting large-scale Molecular Dynamics simulations of the SARS-CoV-2 spike glycoprotein to elucidate possible high-order spike-ACE2 oligomeric states. Our results indicate a possible novel path to therapeutics following the COVID-19 pandemic. Overall, we find that the structure of a protein alone is inadequate in understanding its function through its possible binding modes. Therefore, we must also consider the impact of dynamics in protein assembly

Visual Analysis of Variability and Features of Climate Simulation Ensembles

This PhD thesis is concerned with the visual analysis of time-dependent scalar field ensembles as occur in climate simulations. Modern climate projections consist of multiple simulation runs (ensemble members) that vary in parameter settings and/or initial values, which leads to variations in the resulting simulation data. The goal of ensemble simulations is to sample the space of possible futures under the given climate model and provide quantitative information about uncertainty in the results. The analysis of such data is challenging because apart from the spatiotemporal data, also variability has to be analyzed and communicated. This thesis presents novel techniques to analyze climate simulation ensembles visually. A central question is how the data can be aggregated under minimized information loss. To address this question, a key technique applied in several places in this work is clustering. The first part of the thesis addresses the challenge of finding clusters in the ensemble simulation data. Various distance metrics lend themselves for the comparison of scalar fields which are explored theoretically and practically. A visual analytics interface allows the user to interactively explore and compare multiple parameter settings for the clustering and investigate the resulting clusters, i.e. prototypical climate phenomena. A central contribution here is the development of design principles for analyzing variability in decadal climate simulations, which has lead to a visualization system centered around the new Clustering Timeline. This is a variant of a Sankey diagram that utilizes clustering results to communicate climatic states over time coupled with ensemble member agreement. It can reveal several interesting properties of the dataset, such as: into how many inherently similar groups the ensemble can be divided at any given time, whether the ensemble diverges in general, whether there are different phases in the time lapse, maybe periodicity, or outliers. The Clustering Timeline is also used to compare multiple climate simulation models and assess their performance. The Hierarchical Clustering Timeline is an advanced version of the above. It introduces the concept of a cluster hierarchy that may group the whole dataset down to the individual static scalar fields into clusters of various sizes and densities recording the nesting relationship between them. One more contribution of this work in terms of visualization research is, that ways are investigated how to practically utilize a hierarchical clustering of time-dependent scalar fields to analyze the data. To this end, a system of different views is proposed which are linked through various interaction possibilities. The main advantage of the system is that a dataset can now be inspected at an arbitrary level of detail without having to recompute a clustering with different parameters. Interesting branches of the simulation can be expanded to reveal smaller differences in critical clusters or folded to show only a coarse representation of the less interesting parts of the dataset. The last building block of the suit of visual analysis methods developed for this thesis aims at a robust, (largely) automatic detection and tracking of certain features in a scalar field ensemble. Techniques are presented that I found can identify and track super- and sub-levelsets. And I derive “centers of action” from these sets which mark the location of extremal climate phenomena that govern the weather (e.g. Icelandic Low and Azores High). The thesis also presents visual and quantitative techniques to evaluate the temporal change of the positions of these centers; such a displacement would be likely to manifest in changes in weather. In a preliminary analysis with my collaborators, we indeed observed changes in the loci of the centers of action in a simulation with increased greenhouse gas concentration as compared to pre-industrial concentration levels

Multimodal Biomedical Data Visualization: Enhancing Network, Clinical, and Image Data Depiction

In this dissertation, we present visual analytics tools for several biomedical applications. Our research spans three types of biomedical data: reaction networks, longitudinal multidimensional clinical data, and biomedical images. For each data type, we present intuitive visual representations and efficient data exploration methods to facilitate visual knowledge discovery. Rule-based simulation has been used for studying complex protein interactions. In a rule-based model, the relationships of interacting proteins can be represented as a network. Nevertheless, understanding and validating the intended behaviors in large network models are ineffective and error prone. We have developed a tool that first shows a network overview with concise visual representations and then shows relevant rule-specific details on demand. This strategy significantly improves visualization comprehensibility and disentangles the complex protein-protein relationships by showing them selectively alongside the global context of the network. Next, we present a tool for analyzing longitudinal multidimensional clinical datasets, that we developed for understanding Parkinson's disease progression. Detecting patterns involving multiple time-varying variables is especially challenging for clinical data. Conventional computational techniques, such as cluster analysis and dimension reduction, do not always generate interpretable, actionable results. Using our tool, users can select and compare patient subgroups by filtering patients with multiple symptoms simultaneously and interactively. Unlike conventional visualizations that use local features, many targets in biomedical images are characterized by high-level features. We present our research characterizing such high-level features through multiscale texture segmentation and deep-learning strategies. First, we present an efficient hierarchical texture segmentation approach that scales up well to gigapixel images to colorize electron microscopy (EM) images. This enhances visual comprehensibility of gigapixel EM images across a wide range of scales. Second, we use convolutional neural networks (CNNs) to automatically derive high-level features that distinguish cell states in live-cell imagery and voxel types in 3D EM volumes. In addition, we present a CNN-based 3D segmentation method for biomedical volume datasets with limited training samples. We use factorized convolutions and feature-level augmentations to improve model generalization and avoid overfitting

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science

Doctor of Philosophy

dissertationIn this dissertation, we advance the theory and practice of verifying visualization algorithms. We present techniques to assess visualization correctness through testing of important mathematical properties. Where applicable, these techniques allow us to distinguish whether anomalies in visualization features can be attributed to the underlying physical process or to artifacts from the implementation under verification. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. The contributions of this dissertation are manifold. We derive the mathematical framework for the expected behavior of several visualization algorithms, and compare them to experimentally observed results in the selected codes. In the Computational Science & Engineering community CS&E, this technique is know as the Method of Manufactured Solution (MMS). We apply MMS to the verification of geometrical and topological properties of isosurface extraction algorithms, and direct volume rendering. We derive the convergence of geometrical properties of isosurface extraction techniques, such as function value and normals. For the verification of topological properties, we use stratified Morse theory and digital topology to design algorithms that verify topological invariants. In the case of volume rendering algorithms, we provide the expected discretization errors for three different error sources. The results of applying the MMS is another important contribution of this dissertation. We report unexpected behavior for almost all implementations tested. In some cases, we were able to find and fix bugs that prevented the correctness of the visualization algorithm. In particular, we address an almost 2 0 -year-old bug with the core disambiguation procedure of Marching Cubes 33, one of the first algorithms intended to preserve the topology of the trilinear interpolant. Finally, an important by-product of this work is a range of responses practitioners can expect to encounter with the visualization technique under verification

Hypersweeps, Convective Clouds and Reeb Spaces

Isosurfaces are one of the most prominent tools in scientific data visualisation. An isosurface is a surface that defines the boundary of a feature of interest in space for a given threshold. This is integral in analysing data from the physical sciences which observe and simulate three or four dimensional phenomena. However it is time consuming and impractical to discover surfaces of interest by manually selecting different thresholds. The systematic way to discover significant isosurfaces in data is with a topological data structure called the contour tree. The contour tree encodes the connectivity and shape of each isosurface at all possible thresholds. The first part of this work has been devoted to developing algorithms that use the contour tree to discover significant features in data using high performance computing systems. Those algorithms provided a clear speedup over previous methods and were used to visualise physical plasma simulations. A major limitation of isosurfaces and contour trees is that they are only applicable when a single property is associated with data points. However scientific data sets often take multiple properties into account. A recent breakthrough generalised isosurfaces to fiber surfaces. Fiber surfaces define the boundary of a feature where the threshold is defined in terms of multiple parameters, instead of just one. In this work we used fiber surfaces together with isosurfaces and the contour tree to create a novel application that helps atmosphere scientists visualise convective cloud formation. Using this application, they were able to, for the first time, visualise the physical properties of certain structures that trigger cloud formation. Contour trees can also be generalised to handle multiple parameters. The natural extension of the contour tree is called the Reeb space and it comes from the pure mathematical field of fiber topology. The Reeb space is not yet fully understood mathematically and algorithms for computing it have significant practical limitations. A key difficulty is that while the contour tree is a traditional one dimensional data structure made up of points and lines between them, the Reeb space is far more complex. The Reeb space is made up of two dimensional sheets, attached to each other in intricate ways. The last part of this work focuses on understanding the structure of Reeb spaces and the rules that are followed when sheets are combined. This theory builds towards developing robust combinatorial algorithms to compute and use Reeb spaces for practical data analysis

Investigating capillary pressure and interfacial area for multiphase flow in porous media using pore-scale imaging and lattice-Boltzmann modeling

Recent advances in imaging technology and numerical modeling have greatly enhanced pore-scale investigations of multiphase flow and transport in porous media. It is now feasible to obtain high resolution 3-dimensional pore-scale data, and numerical methods such as the lattice- Boltzmann (LB) technique have been developed specifically for simulating such phenomena. Traditional macro-scale multiphase flow models rely heavily on empirical relationships. For example, the interaction between fluids at their interfaces is accounted for indirectly through the empirical relative permeability relationship. Nevertheless, it has recently been hypothesized that the single most important variable missing from current macro-scale models is the measure of interfacial dynamics between fluids within the pores. Furthermore, the empirical capillary pressure-saturation relationship used in macro-scale multiphase flow simulators has been shown to be a function of interfacial area per volume. This study focuses on (1) the measurement and modeling of the capillary pressure-saturation relationship; and (2) the characterization of the fluid-fluid interfacial area per volume as a function of saturation. The study synthesizes experimental results derived from pore-scale computerized micro-tomographic (CMT) images with LB simulations. An image analysis algorithm for quantifying fluid-fluid interfacial area per volume from experimental CMT and simulation images was developed and verified. The experimental results were shown to be in good agreement with values reported in the literature. Furthermore, the capillary ressure-saturation curves were used to validate a recently proposed macro-scale interfacial area model. New LB simulations of drainage and imbibition for an air-water system were developed, in which the full geometry from the experimental system was used to define the lattice. This allowed for the direct comparison of experimental and simulated phase distributions within the pores. LB simulations showed excellent agreement with experimental results, considering no optimization or calibration to the data was required. Collectively, results show that there is a complex functional relationship between capillary pressure, saturation and interfacial area that provides insights into multiphase flow and transport processes that can not be obtained from the capillary pressure-saturation relationship alone