Algorithms and software for solving finite element equations on serial and parallel architectures

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained

Sparse matrix methods research using the CSM testbed software system

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV

Simultaneous Multislice Functional Magnetic Resonance Imaging.

Functional magnetic resonance imaging (fMRI) is a valuable tool for mapping brain activity in many fields. Since functional activity is determined by temporal signal changes, undesired fluctuations from physiological motion are problematic. Simultaneous multislice (SMS) imaging can alleviate these issues by accelerating image acquisition, increasing the temporal resolution. Furthermore, some applications require a temporal resolution higher than what conventional fMRI will allow. Current research in SMS has focused on Cartesian readouts due to their ease in analysis and reconstruction. However, non-Cartesian readouts such as spirals have shorter readout times and better signal recovery. This work explores the acquisition and reconstruction of both spiral and concentric ring readouts in parallel SMS. The concentric ring readout retains most of the benefits of spirals, but also increases the usability of alternative reconstruction techniques for non-Cartesian SMS such as generalized autocalibrating partially parallel acquisitions (GRAPPA). To date, non-Cartesian SMS imaging has only been reconstructed with sensitivity encoding (SENSE), but results in this work indicate GRAPPA-based reconstructions have reduced root-mean-square-error compared to SENSE and good subjective image quality as well. Furthermore, using point spread function analysis, the concentric ring trajectory is found to have superior slice separation properties compared to a spiral one. Since parallel imaging greatly magnifies the amount of data used for reconstruction, a novel coil compression method is developed, which outperforms conventional coil compression in fMRI, substantially decreasing the amount of reconstruction time needed for sufficient detection of functional activation. Results indicate that the proposed method can compress 3 simultaneous slice data using a 32-channel coil down to only 10 virtual coils without any adverse effects in functional activation, noise, or image artifacts. Competing methods require substantially more coils for preservation of the data, resulting in large reconstruction time savings for the proposed method. This work also explores the use of Hadamard-encoded fMRI for increased temporal resolution. Because Hadamard-encoded SMS uses data from multiple time frames to separate slices, physiological noise correction is critical. However, even with physiological noise correction, results indicate Hadamard-encoded fMRI is not as reliable as conventional fMRI due to undesired temporal fluctuations, most notably from uncorrected physiological noise.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120669/1/alanchu_1.pd

Selective rendering for efficient ray traced stereoscopic images

Depth-related visual effects are a key feature of many virtual environments. In stereo-based systems, the depth effect can be produced by delivering frames of disparate image pairs, while in monocular environments, the viewer has to extract this depth information from a single image by examining details such as perspective and shadows. This paper investigates via a number of psychophysical experiments, whether we can reduce computational effort and still achieve perceptually high-quality rendering for stereo imagery. We examined selectively rendering the image pairs by exploiting the fusing capability and depth perception underlying human stereo vision. In ray-tracing-based global illumination systems, a higher image resolution introduces more computation to the rendering process since many more rays need to be traced. We first investigated whether we could utilise the human binocular fusing ability and significantly reduce the resolution of one of the image pairs and yet retain a high perceptual quality under stereo viewing condition. Secondly, we evaluated subjects' performance on a specific visual task that required accurate depth perception. We found that subjects required far fewer rendered depth cues in the stereo viewing environment to perform the task well. Avoiding rendering these detailed cues saved significant computational time. In fact it was possible to achieve a better task performance in the stereo viewing condition at a combined rendering time for the image pairs less than that required for the single monocular image. The outcome of this study suggests that we can produce more efficient stereo images for depth-related visual tasks by selective rendering and exploiting inherent features of human stereo vision

Multi-Context Attention for Human Pose Estimation

In this paper, we propose to incorporate convolutional neural networks with a multi-context attention mechanism into an end-to-end framework for human pose estimation. We adopt stacked hourglass networks to generate attention maps from features at multiple resolutions with various semantics. The Conditional Random Field (CRF) is utilized to model the correlations among neighboring regions in the attention map. We further combine the holistic attention model, which focuses on the global consistency of the full human body, and the body part attention model, which focuses on the detailed description for different body parts. Hence our model has the ability to focus on different granularity from local salient regions to global semantic-consistent spaces. Additionally, we design novel Hourglass Residual Units (HRUs) to increase the receptive field of the network. These units are extensions of residual units with a side branch incorporating filters with larger receptive fields, hence features with various scales are learned and combined within the HRUs. The effectiveness of the proposed multi-context attention mechanism and the hourglass residual units is evaluated on two widely used human pose estimation benchmarks. Our approach outperforms all existing methods on both benchmarks over all the body parts.Comment: The first two authors contribute equally to this wor

Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in S4S^4

In this paper we prove that certain hyperbolic link complements of $2$-tori in $S^4$ do not contain closed embedded totally geodesic hyperbolic $3$-manifolds.Comment: 18 pages. arXiv admin note: text overlap with arXiv:2005.1125

Nearly Optimal Pricing for Multiproduct Firms

In principle, a multiproduct firm can set separate prices for all possible bundled combinations of its products (i.e., "mixed bundling"). However, this is impractical for firms with more than a few products, because the number of prices increases exponentially with the number of products. In this study we show that simple pricing strategies are often nearly optimal -- i.e., with surprisingly few prices a firm can obtain 99% of the profit that would be earned by mixed bundling. Specifically, we show that bundle-size pricing -- setting prices that depend only on the size of bundle purchased -- tends to be more profitable than offering the individual products priced separately, and tends to closely approximate the profits from mixed bundling. These findings are based on an array of numerical experiments covering a broad range of demand and cost scenarios, as well as an empirical analysis of the pricing problem for an 8-product firm (a theater company).