Global Topology of 3D Symmetric Tensor Fields.

There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do not live in isolation. Instead, they intriguingly interact with each other. In this paper, we introduce the notion of topological graph for 3D symmetric tensor fields to facilitate global topological analysis of such fields. The nodes of the graph include degenerate curves and regions bounded by neutral surfaces in the domain. The edges in the graph denote the adjacency information between the regions and degenerate curves. In addition, we observe that a degenerate curve can be a loop and even a knot and that two degenerate curves (whether in the same region or not) can form a link. We provide a definition and theoretical analysis of individual degenerate curves in order to help understand why knots and links may occur. Moreover, we differentiate between wedges and trisectors, thus making the analysis more detailed about degenerate curves. We incorporate this information into the topological graph. Such a graph can not only reveal the global structure in a 3D symmetric tensor field but also allow two symmetric tensor fields to be compared. We demonstrate our approach by applying it to solid mechanics and material science data sets.

Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic Orbifolds.

Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds. Given any arbitrary two-dimensional kaleidoscopic orbifold, we provide an algorithm to construct a Euclidean, spherical, or hyperbolic polygon to match the orbifold. This polygon is then used to create a room for which the polygon serves as the floor and the ceiling. With our system that implements Möbius transformations, the user can interactively edit the scene and see the reflections of the edited objects. To correctly visualize non-Euclidean orbifolds, we adapt the rendering algorithms to account for the geodesics in these spaces, which light rays follow. Our interactive orbifold design system allows the user to create arbitrary two-dimensional kaleidoscopic orbifolds. In addition, our mirror-based orbifold visualization approach has the potential of helping our users gain insight on the orbifold, including its orbifold notation as well as its universal cover, which can also be the spherical space and the hyperbolic space.

Scalable Hypergraph Visualization.

Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive self-intersections when the input dataset is relatively large. In this paper, we propose a framework in which the hypergraph is iteratively simplified through a set of atomic operations. Then, the layout of the simplest hypergraph is optimized and used as the foundation for a reverse process that brings the simplest hypergraph back to the original one, but with an improved layout. At the core of our approach is the set of atomic simplification operations and an operation priority measure to guide the simplification process. In addition, we introduce necessary definitions and conditions for hypergraph planarity within the polygon representation. We extend our approach to handle simultaneous simplification and layout optimization for both the hypergraph and its dual. We demonstrate the utility of our approach with datasets from a number of real-world applications.

Effects of individual differences, society, and culture on youth-rated problems and strengths in 38 societies.

BACKGROUND: Clinicians increasingly serve youths from societal/cultural backgrounds different from their own. This raises questions about how to interpret what such youths report. Rescorla et al. (2019, European Child & Adolescent Psychiatry, 28, 1107) found that much more variance in 72,493 parents' ratings of their offspring's mental health problems was accounted for by individual differences than by societal or cultural differences. Although parents' reports are essential for clinical assessment of their offspring, they reflect parents' perceptions of the offspring. Consequently, clinical assessment also requires self-reports from the offspring themselves. To test effects of individual differences, society, and culture on youths' self-ratings of their problems and strengths, we analyzed Youth Self-Report (YSR) scores for 39,849 11-17 year olds in 38 societies. METHODS: Indigenous researchers obtained YSR self-ratings from population samples of youths in 38 societies representing 10 culture cluster identified in the Global Leadership and Organizational Behavioral Effectiveness study. Hierarchical linear modeling of scores on 17 problem scales and one strengths scale estimated the percent of variance accounted for by individual differences (including measurement error), society, and culture cluster. ANOVAs tested age and gender effects. RESULTS: Averaged across the 17 problem scales, individual differences accounted for 92.5% of variance, societal differences 6.0%, and cultural differences 1.5%. For strengths, individual differences accounted for 83.4% of variance, societal differences 10.1%, and cultural differences 6.5%. Age and gender had very small effects. CONCLUSIONS: Like parents' ratings, youths' self-ratings of problems were affected much more by individual differences than societal/cultural differences. Most variance in self-rated strengths also reflected individual differences, but societal/cultural effects were larger than for problems, suggesting greater influence of social desirability. The clinical significance of individual differences in youths' self-reports should thus not be minimized by societal/cultural differences, which-while important-can be taken into account with appropriate norms, as can gender and age differences.

WYSIWYG Design of Hypnotic Line Art.

Hypnotic line art is a modern form in which white narrow curved ribbons, with the width and direction varying along each path over a black background, provide a keen sense of 3D objects regarding surface shapes and topological contours. However, the procedure of manually creating such line art work can be quite tedious and time-consuming. In this article, we present an interactive system that offers a What-You-See-Is-What-You-Get (WYSIWYG) scheme for producing hypnotic line art images by integrating and placing evenly-spaced streamlines in tensor fields. With an input picture segmented, the user just needs to sketch a few illustrative strokes to guide the construction of a tensor field for each part of the objects therein. Specifically, we propose a new method which controls, with great precision, the aesthetic layout and artistic drawing of an array of streamlines in each tensor field to emulate the style of hypnotic line art. Given several parameters for streamlines such as density, thickness, and sharpness, our system is capable of generating professional-level hypnotic line art work. With great ease of use, it allows art designers to explore a wide variety of possibilities to obtain hypnotic line art results of their own preferences.

Automatic Polygon Layout for Primal-Dual Visualization of Hypergraphs.

N-ary relationships, which relate $N$ entities where $N$ is not necessarily two, can be visually represented as polygons whose vertices are the entities of the relationships. Manually generating a high-quality layout using this representation is labor-intensive. In this paper, we provide an automatic polygon layout generation algorithm for the visualization of N-ary relationships. At the core of our algorithm is a set of objective functions motivated by a number of design principles that we have identified. These objective functions are then used in an optimization framework that we develop to achieve high-quality layouts. Recognizing the duality between entities and relationships in the data, we provide a second visualization in which the roles of entities and relationships in the original data are reversed. This can lead to additional insight about the data. Furthermore, we enhance our framework for a joint optimization on the primal layout (original data) and the dual layout (where the roles of entities and relationships are reversed). This allows users to inspect their data using two complementary views. We apply our visualization approach to a number of datasets that include co-authorship data and social contact pattern data.

Feature Curves and Surfaces of 3D Asymmetric Tensor Fields.

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more challenging than 3D symmetric tensors. Existing research in tensor field visualization focuses on 2D asymmetric tensor fields and 3D symmetric tensor fields. In this paper, we address the analysis and visualization of 3D asymmetric tensor fields. We introduce six topological surfaces and one topological curve, which lead to an eigenvalue space based on the tensor mode that we define. In addition, we identify several non-topological feature surfaces that are nonetheless physically important. Included in our analysis are the realizations that triple degenerate tensors are structurally stable and form curves, unlike the case for 3D symmetric tensors fields. Furthermore, there are two different ways of measuring the relative strengths of rotation and angular deformation in the tensor fields, unlike the case for 2D asymmetric tensor fields. We extract these feature surfaces using the A-patches algorithm. However, since three of our feature surfaces are quadratic, we develop a method to extract quadratic surfaces at any given accuracy. To facilitate the analysis of eigenvector fields, we visualize a hyperstreamline as a tree stem with the other two eigenvectors represented as thorns in the real domain or the dual-eigenvectors as leaves in the complex domain. To demonstrate the effectiveness of our analysis and visualization, we apply our approach to datasets from solid mechanics and fluid dynamics.

Mode Surfaces of Symmetric Tensor Fields: Topological Analysis and Seamless Extraction.

Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only degenerate curves and neutral surfaces, but also how these features transition into each other. Moreover, the geometry and topology of mode surfaces can help domain scientists better understand the tensor fields in their applications. Existing mode surface extraction methods can miss features in the surfaces. Moreover, the mode surfaces extracted from neighboring cells have gaps, which make their subsequent analysis difficult. In this paper, we provide novel analysis on the topological structures of mode surfaces, including a common parameterization of all mode surfaces of a tensor field using 2D asymmetric tensors. This allows us to not only better understand the structures in mode surfaces and their interactions with degenerate curves and neutral surfaces, but also develop an efficient algorithm to seamlessly extract mode surfaces, including neutral surfaces. The seamless mode surfaces enable efficient analysis of their geometric structures, such as the principal curvature directions. We apply our analysis and visualization to a number of solid mechanics data sets.

Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces.

Asymmetric tensor fields have found applications in many science and engineering domains, such as fluid dynamics. Recent advances in the visualization and analysis of 2D asymmetric tensor fields focus on pointwise analysis of the tensor field and effective visualization metaphors such as colors, glyphs, and hyperstreamlines. In this paper, we provide a novel multi-scale topological analysis framework for asymmetric tensor fields on surfaces. Our multi-scale framework is based on the notions of eigenvalue and eigenvector graphs. At the core of our framework are the identification of atomic operations that modify the graphs and the scale definition that guides the order in which the graphs are simplified to enable clarity and focus for the visualization of topological analysis on data of different sizes. We also provide efficient algorithms to realize these operations. Furthermore, we provide physical interpretation of these graphs. To demonstrate the utility of our system, we apply our multi-scale analysis to data in computational fluid dynamics.

Testing Syndromes of Psychopathology in Parent and Youth Ratings Across Societies.

As societies become increasingly diverse, mental health professionals need instruments for assessing emotional, behavioral, and social problems in terms of constructs that are supported within and across societies. Building on decades of research findings, multisample alignment confirmatory factor analyses tested an empirically based 8-syndrome model on parent ratings across 30 societies and youth self-ratings across 19 societies. The Child Behavior Checklist for Ages 6-18 and Youth Self-Report for Ages 11-18 were used to measure syndromes descriptively designated as Anxious/Depressed, Withdrawn/Depressed, Somatic Complaints, Social Problems, Thought Problems, Attention Problems, Rule-Breaking Behavior, and Aggressive Behavior. For both parent ratings (N = 61,703) and self-ratings (N = 29,486), results supported aggregation of problem items into 8 first-order syndromes for all societies (configural invariance), plus the invariance of item loadings (metric invariance) across the majority of societies. Supported across many societies in both parent and self-ratings, the 8 syndromes offer a parsimonious phenotypic taxonomy with clearly operationalized assessment criteria. Mental health professionals in many societies can use the 8 syndromes to assess children and youths for clinical, training, and scientific purposes.

Robust and Fast Extraction of 3D Symmetric Tensor Field Topology.

3D symmetric tensor fields appear in many science and engineering fields, and topology-driven analysis is important in many of these application domains, such as solid mechanics and fluid dynamics. Degenerate curves and neutral surfaces are important topological features in 3D symmetric tensor fields. Existing methods to extract degenerate curves and neutral surfaces often miss parts of the curves and surfaces, respectively. Moreover, these methods are computationally expensive due to the lack of knowledge of structures of degenerate curves and neutral surfaces. In this paper, we provide theoretical analysis on the geometric and topological structures of degenerate curves and neutral surfaces of 3D linear tensor fields. These structures lead to parameterizations for degenerate curves and neutral surfaces that can not only provide more robust extraction of these features but also incur less computational cost. We demonstrate the benefits of our approach by applying our degenerate curve and neutral surface detection techniques to solid mechanics simulation data sets.

Interactive Design and Visualization of Branched Covering Spaces.

Branched covering spaces are a mathematical concept which originates from complex analysis and topology and has applications in tensor field topology and geometry remeshing. Given a manifold surface and an -way rotational symmetry field, a branched covering space is a manifold surface that has an -to-1 map to the original surface except at the ramification points, which correspond to the singularities in the rotational symmetry field. Understanding the notion and mathematical properties of branched covering spaces is important to researchers in tensor field visualization and geometry processing, and their application areas. In this paper, we provide a framework to interactively design and visualize the branched covering space (BCS) of an input mesh surface and a rotational symmetry field defined on it. In our framework, the user can visualize not only the BCSs but also their construction process. In addition, our system allows the user to design the geometric realization of the BCS using mesh deformation techniques as well as connecting tubes. This enables the user to verify important facts about BCSs such as that they are manifold surfaces around singularities, as well as the Riemann-Hurwitz formula which relates the Euler characteristic of the BCS to that of the original mesh. Our system is evaluated by student researchers in scientific visualization and geometry processing as well as faculty members in mathematics at our university who teach topology. We include their evaluations and feedback in the paper.

The Planteome database: an integrated resource for reference ontologies, plant genomics and phenomics.

The Planteome project (http://www.planteome.org) provides a suite of reference and species-specific ontologies for plants and annotations to genes and phenotypes. Ontologies serve as common standards for semantic integration of a large and growing corpus of plant genomics, phenomics and genetics data. The reference ontologies include the Plant Ontology, Plant Trait Ontology and the Plant Experimental Conditions Ontology developed by the Planteome project, along with the Gene Ontology, Chemical Entities of Biological Interest, Phenotype and Attribute Ontology, and others. The project also provides access to species-specific Crop Ontologies developed by various plant breeding and research communities from around the world. We provide integrated data on plant traits, phenotypes, and gene function and expression from 95 plant taxa, annotated with reference ontology terms. The Planteome project is developing a plant gene annotation platform; Planteome Noctua, to facilitate community engagement. All the Planteome ontologies are publicly available and are maintained at the Planteome GitHub site (https://github.com/Planteome) for sharing, tracking revisions and new requests. The annotated data are freely accessible from the ontology browser (http://browser.planteome.org/amigo) and our data repository.

Data-Driven NPR Illustrations of Natural Flows in Chinese Painting.

Introducing motion into existing static paintings is becoming a field that is gaining momentum. This effort facilitates keeping artworks current and translating them to different forms for diverse audiences. Chinese ink paintings and Japanese Sumies are well recognized in Western cultures, yet not easily practiced due to the years of training required. We are motivated to develop an interactive system for artists, non-artists, Asians, and non-Asians to enjoy the unique style of Chinese paintings. In this paper, our focus is on replacing static water flow scenes with animations. We include flow patterns, surface ripples, and water wakes which are challenging not only artistically but also algorithmically. We develop a data-driven system that procedurally computes a flow field based on stroke properties extracted from the painting, and animate water flows artistically and stylishly. Technically, our system first extracts water-flow-portraying strokes using their locations, oscillation frequencies, brush patterns, and ink densities. We construct an initial flow pattern by analyzing stroke structures, ink dispersion densities, and placement densities. We cluster extracted strokes as stroke pattern groups to further convey the spirit of the original painting. Then, the system automatically computes a flow field according to the initial flow patterns, water boundaries, and flow obstacles. Finally, our system dynamically generates and animates extracted stroke pattern groups with the constructed field for controllable smoothness and temporal coherence. The users can interactively place the extracted stroke patterns through our adapted Poisson-based composition onto other paintings for water flow animation. In conclusion, our system can visually transform a static Chinese painting to an interactive walk-through with seamless and vivid stroke-based flow animations in its original dynamic spirits without flickering artifacts.

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Automated nutrient screening system enables high-throughput optimisation of microalgae production conditions.

BACKGROUND: Microalgae provide an excellent platform for the production of high-value-products and are increasingly being recognised as a promising production system for biomass, animal feeds and renewable fuels. RESULTS: Here, we describe an automated screen, to enable high-throughput optimisation of 12 nutrients for microalgae production. Its miniaturised 1,728 multiwell format allows multiple microalgae strains to be simultaneously screened using a two-step process. Step 1 optimises the primary elements nitrogen and phosphorous. Step 2 uses Box-Behnken analysis to define the highest growth rates within the large multidimensional space tested (Ca, Mg, Fe, Mn, Zn, Cu, B, Se, V, Si) at three levels (-1, 0, 1). The highest specific growth rates and maximum OD750 values provide a measure for continuous and batch culture. CONCLUSION: The screen identified the main nutrient effects on growth, pairwise nutrient interactions (for example, Ca-Mg) and the best production conditions of the sampled statistical space providing the basis for a targeted full factorial screen to assist with optimisation of algae production.

Pairwise harmonics for shape analysis.

This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization.

Cross-informant agreement between parent-reported and adolescent self-reported problems in 25 societies.

We used population sample data from 25 societies to answer the following questions: (a) How consistently across societies do adolescents report more problems than their parents report about them? (b) Do levels of parent-adolescent agreement vary among societies for different kinds of problems? (c) How well do parents and adolescents in different societies agree on problem item ratings? (d) How much do parent-adolescent dyads within each society vary in agreement on item ratings? (e) How well do parent-adolescent dyads within each society agree on the adolescent's deviance status? We used five methods to test cross-informant agreement for ratings obtained from 27,861 adolescents ages 11 to 18 and their parents. Youth Self-Report (YSR) mean scores were significantly higher than Child Behavior Checklist (CBCL) mean scores for all problem scales in almost all societies, but the magnitude of the YSR-CBCL discrepancy varied across societies. Cross-informant correlations for problem scale scores varied more across societies than across types of problems. Across societies, parents and adolescents tended to rate the same items as low, medium, or high, but within-dyad parent-adolescent item agreement varied widely in every society. In all societies, both parental noncorroboration of self-reported deviance and adolescent noncorroboration of parent-reported deviance were common. Results indicated many multicultural consistencies but also some important differences in parent-adolescent cross-informant agreement. Our findings provide valuable normative baselines against which to compare multicultural findings for clinical samples.

International epidemiology of child and adolescent psychopathology ii: integration and applications of dimensional findings from 44 societies.

OBJECTIVE: To build on Achenbach, Rescorla, and Ivanova (2012) by (a) reporting new international findings for parent, teacher, and self-ratings on the Child Behavior Checklist, Youth Self-Report, and Teacher's Report Form; (b) testing the fit of syndrome models to new data from 17 societies, including previously underrepresented regions; (c) testing effects of society, gender, and age in 44 societies by integrating new and previous data; (d) testing cross-society correlations between mean item ratings; (e) describing the construction of multisociety norms; (f) illustrating clinical applications. METHOD: Confirmatory factor analyses (CFAs) of parent, teacher, and self-ratings, performed separately for each society; tests of societal, gender, and age effects on dimensional syndrome scales, DSM-oriented scales, Internalizing, Externalizing, and Total Problems scales; tests of agreement between low, medium, and high ratings of problem items across societies. RESULTS: CFAs supported the tested syndrome models in all societies according to the primary fit index (Root Mean Square Error of Approximation [RMSEA]), but less consistently according to other indices; effect sizes were small-to-medium for societal differences in scale scores, but very small for gender, age, and interactions with society; items received similarly low, medium, or high ratings in different societies; problem scores from 44 societies fit three sets of multisociety norms. CONCLUSIONS: Statistically derived syndrome models fit parent, teacher, and self-ratings when tested individually in all 44 societies according to RMSEAs (but less consistently according to other indices). Small to medium differences in scale scores among societies supported the use of low-, medium-, and high-scoring norms in clinical assessment of individual children.

Isolation and evaluation of oil-producing microalgae from subtropical coastal and brackish waters.

Microalgae have been widely reported as a promising source of biofuels, mainly based on their high areal productivity of biomass and lipids as triacylglycerides and the possibility for cultivation on non-arable land. The isolation and selection of suitable strains that are robust and display high growth and lipid accumulation rates is an important prerequisite for their successful cultivation as a bioenergy source, a process that can be compared to the initial selection and domestication of agricultural crops. We developed standard protocols for the isolation and cultivation for a range of marine and brackish microalgae. By comparing growth rates and lipid productivity, we assessed the potential of subtropical coastal and brackish microalgae for the production of biodiesel and other oil-based bioproducts. This study identified Nannochloropsis sp., Dunaniella salina and new isolates of Chlorella sp. and Tetraselmis sp. as suitable candidates for a multiple-product algae crop. We conclude that subtropical coastal microalgae display a variety of fatty acid profiles that offer a wide scope for several oil-based bioproducts, including biodiesel and omega-3 fatty acids. A biorefinery approach for microalgae would make economical production more feasible but challenges remain for efficient harvesting and extraction processes for some species.