F. Wang, W. Li, S. Wang, C.R. Johnson.
Association Rules-Based Multivariate Analysis and Visualization of Spatiotemporal Climate Data, In ISPRS International Journal of Geo-Information, Vol. 7, No. 7, MDPI AG, pp. 266. July, 2018.
Understanding atmospheric phenomena involves analysis of large-scale spatiotemporal multivariate data. The complexity and heterogeneity of such data pose a significant challenge in discovering and understanding the association between multiple climate variables. To tackle this challenge, we present an interactive heuristic visualization system that supports climate scientists and the public in their exploration and analysis of atmospheric phenomena of interest. Three techniques are introduced: (1) web-based spatiotemporal climate data visualization; (2) multiview and multivariate scientific data analysis; and (3) data mining-enabled visual analytics. The Arctic System Reanalysis (ASR) data are used to demonstrate and validate the effectiveness and usefulness of our method through a case study of "The Great Arctic Cyclone of 2012". The results show that different variables have strong associations near the polar cyclone area. This work also provides techniques for identifying multivariate correlation and for better understanding the driving factors of climate phenomena.
Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. Current treatments for AF remain suboptimal due to a lack of understanding of the underlying atrial structures that directly sustain AF. Existing approaches for analyzing atrial structures in 3D, especially from late gadolinium-enhanced (LGE)-MRIs, rely heavily on manual segmentation methods which are extremely labor-intensive and prone to errors. As a result, a robust and automated method for analyzing atrial structures in 3D is of high interest. We have therefore developed AtriaNet, a 16-layer convolutional neural network (CNN), on 154 3D LGE-MRIs with a spatial resolution of 0.625 mm × 0.625 mm × 1.25 mm from patients with AF, to automatically segment the left atrial (LA) epicardium and endocardium. AtriaNet consists of a multi-scaled, dual pathway architecture that captures both the local atrial tissue geometry, and the global positional information of LA using 13 successive convolutions, and 3 further convolutions for merging. By utilizing computationally efficient batch prediction, AtriaNet was able to successfully process each 3D LGE-MRI within one minute. Furthermore, benchmarking experiments showed that AtriaNet outperformed state-of-the-art CNNs, with a DICE score of 0.940 and 0.942 for the LA epicardium and endocardium respectively, and an inter-patient variance of <0.001. The estimated LA diameter and volume computed from the automatic segmentations were accurate to within 1.59 mm and 4.01 cm³ of the ground truths. Our proposed CNN was tested on the largest known dataset for LA segmentation, and to the best of our knowledge, it is the most robust approach that has ever been developed for segmenting LGE-MRIs. The increased accuracy of atrial reconstruction and analysis could potentially improve the understanding and treatment of AF.
Z. Yang, D. Sahasrabudhe, A. Humphrey, M. Berzins. A Preliminary Port and Evaluation of the Uintah AMT Runtime on Sunway TaihuLight, In 9th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC 2018), IEEE, May, 2018.
The Sunway TaihuLight is the world's fastest supercomputer at the present time with a low power consumption per flop and a unique set of architectural features. Applications performance depends heavily on being able to adapt codes to make best use of these features. Porting large codes to novel architectures such as Sunway is both time-consuming and expensive, as modifications throughout the code may be needed. One alternative to conventional porting is to consider an approach based upon Asynchronous Many Task (AMT) Runtimes such as the Uintah framework considered here. Uintah structures the problem as a series of tasks that are executed by the runtime via a task scheduler. The central challenge in porting a large AMT runtime like Uintah is thus to consider how to devise an appropriate scheduler and how to write tasks to take advantage of a particular architecture. It will be shown how an asynchronous Sunway-specific scheduler, based upon MPI and athreads, may be written and how individual taskcode for a typical but model structured-grid fluid-flow problem needs to be refactored. Preliminary experiments show that it is possible to obtain a strong-scaling efficiency ranging from 31.7% to 96.1% for different problem sizes with full optimizations. The asynchronous scheduler developed here improves the overall performance over a synchronous alternative by at most 22.8%, and the fluid-flow simulation reaches 1.17% the theoretical peak of the running nodes. Conclusions are drawn for the porting of full-scale Uintah applications.
Spectral Element and hp Methods, In Encyclopedia of Computational Mechanics Second Edition, John Wiley & Sons, Ltd, pp. 1--43. 2018.Y. Yu, R.M. Kirby, G.E. Karniadakis.
Spectral/hp element methods provide high‐order discretization, which is essential in the longtime integration of advection–diffusion systems and for capturing dynamic instabilities in solids. In this chapter, we review the main formulations for simulations of incompressible and compressible viscous flows as well as for solid mechanics and present several examples with some emphasis on fluid–structure interactions and interfaces. The first generation of (nodal) spectral elements was limited to relatively simple geometries and smooth solutions. However, the new generation of spectral/hp elements, consisting of both nodal and modal forms, can handle very complex geometries using unstructured grids and can capture strong shocks by employing discontinuous Galerkin methods. New flexible formulations allow simulations of multiphysics problems including extremely complex geometries and multiphase flows. Several implementation strategies have also been developed on the basis of multilevel parallel algorithms that allow dynamic p ‐refinement at constant wall clock time. After three decades of intense developments, spectral element and hp methods are mature and efficient to be used effectively in applications of industrial complexity. They provide the capabilities that standard finite element and finite volume methods do, but, in addition, they exhibit high‐order accuracy and error control.
Y.Y. Yu, S.Y. Elhabian, R.T. Whitaker. Clustering With Pairwise Relationships: A Generative Approach, In CoRR, 2018.
Semi-supervised learning (SSL) has become important in current data analysis applications, where the amount of unlabeled data is growing exponentially and user input remains limited by logistics and expense. Constrained clustering, as a subclass of SSL, makes use of user input in the form of relationships between data points (e.g., pairs of data points belonging to the same class or different classes) and can remarkably improve the performance of unsupervised clustering in order to reflect user-defined knowledge of the relationships between particular data points. Existing algorithms incorporate such user input, heuristically, as either hard constraints or soft penalties, which are separate from any generative or statistical aspect of the clustering model; this results in formulations that are suboptimal and not sufficiently general. In this paper, we propose a principled, generative approach to probabilistically model, without ad hoc penalties, the joint distribution given by user-defined pairwise relations. The proposed model accounts for general underlying distributions without assuming a specific form and relies on expectation-maximization for model fitting. For distributions in a standard form, the proposed approach results in a closed-form solution for updated parameters.
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scattered nodes on the boundary of the input mesh as data sites in an interpolation problem. Our technique produces high-quality meshes in the deformed domain even when the deformation maps are singular due to a new iterative algorithm based on modification of the RBF shape parameter. Due to the use of RBF interpolation, our technique is applicable to both 2D and 3D curvilinear mesh generation without significant modification.
We developed a new method to manufacture dense, aligned, and porous collagen scaffolds using biaxial plastic compression of type I collagen gels. Using a novel compression apparatus that constricts like an iris diaphragm, low density collagen gels were compressed to yield a permanently densified, highly aligned collagen material. Micro-porosity scaffolds were created using hydrophilic elastomer porogens that can be selectively removed following biaxial compression, with porosity modulated by using different porogen concentrations. The resulting scaffolds exhibit collagen densities that are similar to native connective tissues (∼10% collagen by weight), pronounced collagen alignment across multiple length scales, and an interconnected network of pores, making them highly relevant for use in tissue culture, the study of physiologically relevant cell-matrix interactions, and tissue engineering applications. The scaffolds exhibited highly anisotropic material behavior, with the modulus of the scaffolds in the fiber direction over 100 times greater than the modulus in the transverse direction. Adipose-derived mesenchymal stem cells were seeded onto the biaxially compressed scaffolds with minimal cell death over seven days of culture, along with cell proliferation and migration into the pore spaces. This fabrication method provides new capabilities to manufacture structurally and mechanically relevant cytocompatible scaffolds that will enable more physiologically relevant cell culture studies. Further improvement of manufacturing techniques has the potential to produce engineered scaffolds for direct replacement of dense connective tissues such as meniscus and annulus fibrosus.
M. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, L. Ziegelmeier. Vietoris-Rips and Cech Complexes of Metric Gluings, In CoRR, 2017.
We study Vietoris-Rips and Cech complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips (resp. Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp. Cech) complexes. We also provide generalizations for certain metric gluings, i.e. when two metric spaces are glued together along a common isometric subset. As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path. As a result, we can describe the persistent homology, in all homological dimensions, of the Vietoris-Rips complexes of a wide class of metric graphs.
M. Berzins, D. A. Bonnell, Jr. Cizewski, K. M. Heeger, A.J.G. Hey, C. J. Keane, B. A. Ramsey, K. A. Remington, J.L. Rempe. Department of Energy, Advanced Scientific Computing Advisory Committee (ASCAC), Subcommittee on LDRD Review Final Report, May, 2017.
V International Conference on Particle-based Methods – Fundamentals and Applications. PARTICLES 2017, Edited by P. Wriggers, M. Bischoff, E. O˜nate, D.R.J. Owen, & T. Zohdi, pp. 671--682. 2017.M. Berzins. Nonlinear Stability of the MPM Method, In
The Material Point Method (MPM) has been very successful in providing solutions to many challenging problems involving large deformations. The nonlinear nature of MPM makes it necessary to use a full nonlinear stability analysis to determine a stable timestep. The stability analysis of Spigler and Vianello is adapted to MPM and used to derive a stable timestep bound for a model problem. This bound is contrasted against a traditional CFL bound.
A. Bhaduri, Y. He, M.D. Shields, L. Graham-Brady, R.M. Kirby. Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis, In CoRR, 2017.
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic collocation method with adaptive mesh refinement (SCAMR) to deal with high dimensional stochastic systems with discontinuities. Specifically, the proposed approach uses generalized polynomial chaos (gPC) expansion with Legendre polynomial basis and solves for the gPC coefficients using the least squares method. It also implements an adaptive mesh (element) refinement strategy which checks for abrupt variations in the output based on the second order gPC approximation error to track discontinuities or non-smoothness. In addition, the proposed method involves a criterion for checking possible dimensionality reduction and consequently, the decomposition of the full-dimensional problem to a number of lower-dimensional subproblems. Specifically, this criterion checks all the existing interactions between input dimensions of a specific problem based on the high-dimensional model representation (HDMR) method, and therefore automatically provides the subproblems which only involve interacting dimensions. The efficiency of the approach is demonstrated using both smooth and non-smooth function examples with input dimensions up to 300, and the approach is compared against other existing algorithms.
Controlling the spread of infectious diseases in large populations is an important societal challenge. Mathematically, the problem is best captured as a certain class of reaction-diffusion processes (referred to as contagion processes) over appropriate synthesized interaction networks. Agent-based models have been successfully used in the recent past to study such contagion processes. We describe EpiSimdemics, a highly scalable, parallel code written in Charm++ that uses agent-based modeling to simulate disease spreads over large, realistic, co-evolving interaction networks. We present a new parallel implementation of EpiSimdemics that achieves unprecedented strong and weak scaling on different architectures — Blue Waters, Cori and Mira. EpiSimdemics achieves five times greater speedup than the second fastest parallel code in this field. This unprecedented scaling is an important step to support the long term vision of real-time epidemic science. Finally, we demonstrate the capabilities of EpiSimdemics by simulating the spread of influenza over a realistic synthetic social contact network spanning the continental United States (∼280 million nodes and 5.8 billion social contacts).
L. Bos, A. Narayan, N. Levenberg, F. Piazzon.
An Orthogonality Property of the Legendre Polynomials, In Constructive Approximation, Vol. 45, No. 1, pp. 65--81. Feb, 2017.
ISSN: 0176-4276, 1432-0940
We give a remarkable additional othogonality property of the classical Legendre polynomials on the real interval [−1,1]: polynomials up to degree n from this family are mutually orthogonal under the arcsine measure weighted by the degree-n normalized Christoffel function
A. Brown, B. Wang. Sheaf-Theoretic Stratification Learning, In CoRR, 2017.
In this paper, we investigate a sheaf-theoretic interpretation of stratification learning. Motivated by the work of Alexandroff (1937) and McCord (1978), we aim to redirect efforts in the computational topology of triangulated compact polyhedra to the much more computable realm of sheaves on partially ordered sets. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (2012), and the cohomology stratification algorithm given in Nanda (2017). We envision that our sheaf-theoretic algorithm could give rise to a larger class of stratification beyond homology-based stratification. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.
We compared the cranial base of newborn Pax7-deficient and wildtype mice using a computational shape modeling technology called particle-based modeling (PBM). We found systematic differences in the morphology of the basiooccipital bone, including a broadening of the basioccipital bone and an antero-inferior inflection of its posterior edge in the Pax7-deficient mice. We show that the Pax7 cell lineage contributes to the basioccipital bone and that the location of the Pax7 lineage correlates with the morphology most effected by Pax7 deficiency. Our results suggest that the Pax7-deficient mouse may be a suitable model for investigating the genetic control of the location and orientation of the foramen magnum, and changes in the breadth of the basioccipital.
M. Chen, G. Grinstein, C. R. Johnson, J. Kennedy, M. Tory. Pathways for Theoretical Advances in Visualization, In IEEE Computer Graphics and Applications, IEEE, pp. 103--112. July, 2017.
More than a decade ago, Chris Johnson proposed the "Theory of Visualization" as one of the top research problems in visualization. Since then, there have been several theory-focused events, including three workshops and three panels at IEEE Visualization (VIS) Conferences. Together, these events have produced a set of convincing arguments.
J. Docampo-Sánchez, J.K. Ryan, M. Mirzargar, R.M. Kirby.
Multi-Dimensional Filtering: Reducing the Dimension Through Rotation Read More: https://epubs.siam.org/doi/abs/10.1137/16M1097845, In SIAM Journal on Scientific Computing, Vol. 39, No. 5, SIAM, pp. A2179--A2200. Jan, 2017.
Over the past few decades there has been a strong effort toward the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this postprocessor. These advantages can be exploited during flow visualization, for example, by applying the SIAC filter to DG data before streamline computations [M. Steffen, S. Curtis, R. M. Kirby, and J. K. Ryan, IEEE Trans. Vis. Comput. Graphics, 14 (2008), pp. 680--692]. However, introducing these filters in engineering applications can be challenging since a tensor product filter grows in support size as the field dimension increases, becoming computationally expensive. As an alternative, [D. Walfisch, J. K. Ryan, R. M. Kirby, and R. Haimes, J. Sci. Comput., 38 (2009), pp. 164--184] proposed a univariate filter implemented along the streamline curves. Until now, this technique remained a numerical experiment. In this paper we introduce the line SIAC filter and explore how the orientation, structure, and filter size affect the order of accuracy and global errors. We present theoretical error estimates showing how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs, becoming an attractive tool for the scientific visualization community.
In many image segmentation problems involving limited and low-quality data, employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result. However, defining probability densities in the space of shapes is an open and challenging problem, especially if the object to be segmented comes from a shape density involving multiple modes (classes). Existing techniques in the literature estimate the underlying shape distribution by extending Parzen density estimator to the space of shapes. In these methods, the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries. In such scenarios, employing both shape- and class-dependent discriminative feature priors can aid the segmentation process. Such features may involve, e.g., intensity-based, textural, or geometric information about the objects to be segmented. In this paper, we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by Parzen density estimation. We incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation. The resulting optimization problem is solved using active contours. We present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities. Experimental results demonstrate the potential of the proposed method.
M. Feiszli, A. Narayan.
Numerical Computation of Weil-Peterson Geodesics in the Universal Teichmueller Space, In SIAM Journal on Imaging Sciences, Vol. 10, No. 3, SIAM, pp. 1322--1345. Jan, 2017.
We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson (WP) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus our algorithm addresses a fundamental problem in computer vision: compute the distance between two given shapes. The identification of smooth shapes with elements on T(1) allows us to represent a shape as a diffeomorphism on S1. Then given two diffeomorphisms on S1 (i.e., two shapes we want connect with a flow), we formulate a discretized WP energy and the resulting problem is a boundary-value minimization problem. We numerically solve this problem, providing several examples of geodesic flow on the space of shapes, and verifying mathematical properties of T(1). Our algorithm is more general than the application here in the sense that it can be used to compute geodesics on any other Riemannian manifold.
Rank Constrained Diffeomorphic Density Motion Estimation for Respiratory Correlated Computed Tomography, In Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics, Springer International Publishing, pp. 177--185. 2017.
Motion estimation of organs in a sequence of images is important in numerous medical imaging applications. The focus of this paper is the analysis of 4D Respiratory Correlated Computed Tomography (RCCT) Imaging. It is hypothesized that the quasi-periodic breathing induced motion of organs in the thorax can be represented by deformations spanning a very low dimension subspace of the full infinite dimensional space of diffeomorphic transformations. This paper presents a novel motion estimation algorithm that includes the constraint for low-rank motion between the different phases of the RCCT images. Low-rank deformation solutions are necessary for the efficient statistical analysis and improved treatment planning and delivery. Although the application focus of this paper is RCCT the algorithm is quite general and applicable to various motion estimation problems in medical imaging.