Resistive Memory Device Requirements for a Neural Algorithm Accelerator.
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The emergence of leadership class systems with GPU-equipped nodes has the potential to vastly increase the performance of existing distributed applications. However, the inclusion of GPU computation into existing extreme scale distributed applications can reveal scalability issues that were absent in the CPU version. The issues exposed in scaling by a GPU can become limiting factors to overall application performance. We developed an extreme scale GPU-based application to perform data clustering on multi-billion point datasets. In this application, called Mr. Scan, we ran into several of these performance limiting issues. Through the use of complete end-to-end benchmarking of Mr. Scan (measuring time from reading and distribution to final output), we were able to identify three major sources of real world performance issues: data distribution, GPU load balancing, and system specific issues such as start-up time. These issues comprised a vast majority of the run time of Mr. Scan. Data distribution alone accounted for 68% of the total run time of Mr. Scan when processing 6.5 billion points on Cray Titan at 8192 nodes. With improvements in these areas, we have been able able to cut total run time of Mr. Scan from 17.5 minutes to 8.3 minutes when clustering 6.5 billion points.
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In a stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media (BSM) is to use the atomic mix approximation in which the transport problem is solved using homogenized (volume-averaged) material properties. A common deterministic model developed for solving BSM particle transport problems is the Levermore-Pomraning (LP) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the LP equations and another Monte Carlo algorithm (Algorithm B) that locally preserves the sampled material realization; we refer to these Monte Carlo algorithms as the LP and LPLRP (LP local realization preserving) algorithms, respectively. One-dimensional (1D) planar geometry benchmark studies have shown that the LPLRP algorithm is often significantly more accurate than the LP algorithm for problems with an incident angular flux as well as for problems with an interior source. The LPLRP algorithm implementation in these benchmark comparisons made explicit use of the one-dimensional nature of the problem. The LP model is derived by assuming an 'upwind' closure in the coupling term relating the two materials in a binary stochastic medium. Su and Pomraning developed a modified form of this closure by considering the small correlation length limit and requiring the modified closure to produce the correct exponential decay for a source-free half-line albedo problem in rod geometry. They concluded that the modified closure is generally not inferior to the LP closure and in some cases is significantly better. Brantley investigated the use of the Su-Pomraning (SP) closure in the Monte Carlo LP algorithm (LP-SP) for the suite of benchmark problems and concluded that 1) the LP-SP algorithm was somewhat more accurate overall than the LP algorithm and somewhat less accurate overall than the LPLRP algorithm for an incident angular flux benchmark suite, and 2) the LP-SP algorithm was generally the least accurate of the algorithms for an interior source benchmark suite. Larsen et al. performed an asymptotic analysis of the transport equation in 1D planar geometry for the situation in which the physical system is 1) a random binary stochastic medium with material macroscopic total cross sections and mean slab width values of O(1) or smaller and 2) optically thick with weak absorption and sources at each spatial point and therefore globally diffusive. The asymptotic analysis demonstrates that, under these assumptions, the transport equation limits to the conventional diffusion equation with atomically-mixed (volume-averaged) material properties. Larsen et al. also demonstrate that, under these same assumptions, the LP equations asymptotically limit to an atomically-mixed diffusion equation with a diffusion coefficient that is too large, leading to an unphysical flattening of the ensemble-averaged scalar flux distribution. Vasques and Yadav recently performed an asymptotic analysis of an adjusted Levermore-Pomraning closure in which the Markovian transition functions are rescaled such that the equations asymptotically limit to the correct atomically-mixed diffusion equation; we refer to this model as LP-VY. In this paper, we demonstrate that the adjusted LP closure proposed by Vasques and Yadav is a special case of the SP closure obtained by assuming that the absorption cross sections in the two materials are equal. We further demonstrate that the Su-Pomraning closure has the correct asymptotic limit for the diffusive physical system and is therefore an appropriate closure for these problems. We also describe how to incorporate these various closures into the Monte Carlo LP and LPLRP particle transport algorithms, and we present numerical results comparing the accuracy of the Monte Carlo LP, LP-VY, LP-SP, LPLRP, and LPLRP-SP algorithms for the set of diffusive benchmark problems. We demonstrated that the SP closure has the correct asymptotic limit for the diffusive physical system under investigation in this paper and that the VY closure is a special case of the SP closure obtained by assuming equal absorption in the two materials. Both of these closures are readily implemented in the Monte Carlo LP and LPLRP algorithms for particle transport in BSM. Through numerical comparisons to a diffusive benchmark suite, we confirmed that 1) the LP and LPLRP algorithms do not limit to the appropriate diffusion solution and 2) the LP-VY, LP-SP, and LPLRP-SP algorithms limit to the appropriate diffusion solution and are of comparable accuracy. The LPLRP algorithm has been shown to be generally more accurate than the LP algorithm for non-diffusive problems. However, the numerical results in this paper indicate that the LPLRP algorithm does not limit to the correct diffusion equation for the asymptotic limit under consideration. The work in this paper demonstrates that the SP algorithm does limit to the correct diffusion equation for the asymptotic limit considered. Future work will investigate the possibility of whether the LPLRP-SP algorithm is accurate for both diffusive and non-diffusive problems.
Purpose: The spatial accuracy of deformable image registration (DIR) is important in the implementation of image guided adaptive radiotherapy techniques for cancer in the pelvic region. Validation of algorithms is best performed on phantoms with fiducial markers undergoing controlled large deformations. Excised porcine bladders, exhibiting similar filling and voiding behavior as human bladders, provide such an environment. The aim of this study was to determine the spatial accuracy of different DIR algorithms on CT images ofex vivo porcine bladders with radiopaque fiducial markers applied to the outer surface, for a range of bladder volumes, using various accuracy metrics. Methods: Five excised porcine bladders with a grid of 30–40 radiopaque fiducial markers attached to the outer wall were suspended inside a water-filled phantom. The bladder was filled with a controlled amount of water with added contrast medium for a range of filling volumes (100–400 ml in steps of 50 ml) using a luer lock syringe, and CT scans were acquired at each filling volume. DIR was performed for each data set, with the 100 ml bladder as the reference image. Six intensity-based algorithms (optical flow or demons-based) implemented in theMATLAB platform DIRART, a b-spline algorithm implemented in the commercial software package VelocityAI, and a structure-based algorithm (Symmetric Thin Plate Spline Robust Point Matching) were validated, using adequate parameter settings according to values previously published. The resulting deformation vector field from each registration was applied to the contoured bladder structures and to the marker coordinates for spatial error calculation. The quality of the algorithms was assessed by comparing the different error metrics across the different algorithms, and by comparing the effect of deformation magnitude (bladder volume difference) per algorithm, using the Independent Samples Kruskal-Wallis test. Results: The authors found good structure accuracy without dependency on bladder volume difference for all but one algorithm, and with the best result for the structure-based algorithm. Spatial accuracy as assessed from marker errors was disappointing for all algorithms, especially for large volume differences, implying that the deformations described by the registration did not represent anatomically correct deformations. The structure-based algorithm performed the best in terms of marker error for the large volume difference (100–400 ml). In general, for the small volume difference (100–150 ml) the algorithms performed relatively similarly. The structure-based algorithm exhibited the best balance in performance between small and large volume differences, and among the intensity-based algorithms, the algorithm implemented in VelocityAI exhibited the best balance. Conclusions: Validation of multiple DIR algorithms on a novel physiological bladder phantom revealed that the structure accuracy was good for most algorithms, but that the spatial accuracy as assessed from markers was low for all algorithms, especially for large deformations. Hence, many of the available algorithms exhibit sufficient accuracy for contour propagation purposes, but possibly not for accurate dose accumulation.