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At least 325 records · Page 18

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗

Deployment of ADTimePix3 areaDetector Driver at Neutron and X-ray User Facilities

TimePix3 is a 65k hybrid pixel readout chip with simultaneous Time-of-Arrival (ToA) and Time-over-Threshold (ToT) recording in each pixel*. The chip operates without a trigger signal with a sparse readout where only pixels containing events are read out. The flexible architecture allows 40 MHits/s/cm² readout throughput, using simultaneous readout and acquisition by sharing readout logic with transport logic of superpixel matrix formed using 2x4 structure. The chip ToA records 1.5625 ns time resolution. The X-ray and charged particle events are counted directly. However, indirect neutron counts use 6Li fission in a scintillator matrix, such as ZnS(Ag). The fission space-charge region is limited to 5-9 um. A photon from scintillator material excites a photocathode electron, which is further multiplied in dual-stack MCP. The neutron count event is a cluster of electron events at the chip. We report on the EPICS areaDetector** ADTimePix3 driver that controls Serval*** using json commands. The driver directs data to storage and to a real-time processing pipeline and configures the chip. The time-stamped data are stored in raw .tpx3 file format and passed through a socket where the clustering software identifies individual neutron events. The conventional 2D images are available as images for each exposure frame, and a preview is useful for sample alignment. The areaDetector driver allows integration of time-enhanced capabilities of this detector into SNS beamlines controls and unprecedented time resolution.

Gofron, Kaz↗

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-based architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.

97 MATHEMATICS AND COMPUTING↗

Vinculin is required for neuronal mechanosensing but not for axon outgrowth

Integrin receptors are transmembrane proteins that bind to the extracellular matrix (ECM). In most animal cell types integrins cluster together with adaptor proteins at focal adhesions that sense and respond to external mechanical signals. In the central nervous system (CNS), ECM proteins are sparsely distributed, the tissue is comparatively soft and neurons do not form focal adhesions. Thus, how neurons sense tissue stiffness is currently poorly understood. Here, we found that integrins and the integrin-associated proteins talin and focal adhesion kinase (FAK) are required for the outgrowth of neuronal processes. Vinculin, however, whilst not required for neurite outgrowth was a key regulator of integrin-mediated mechanosensing of neurons. During growth, growth cones of axons of CNS derived cells exerted dynamic stresses of around 10–12 Pa on their environment, and axons grew significantly longer on soft (0.4 kPa) compared to stiff (8 kPa) substrates. Depletion of vinculin blocked this ability of growth cones to distinguish between soft and stiff substrates. These data suggest that vinculin in neurons acts as a key mechanosensor, involved in the regulation of growth cone motility.

60 APPLIED LIFE SCIENCES↗

Detailed measurements of local thickness changes for U-7Mo dispersion fuel plates with Al-3.5Si matrix after irradiation at different powers in the RERTR-9B experiment

The Materials Management and Minimization program is developing fuel designs to replace highly enriched fuel with fuels of low enrichment. Swelling is an important irradiation behavior that needs to be well understood. Data from high resolution thickness measurements performed on U-7Mo dispersion fuel plates with Al-Si alloy matrices that were irradiated at high power is sparse. This paper reports the results of detailed thickness measurements performed on two dispersion fuel plates that were irradiated at relatively high power to high fission densities in the Advanced Test Reactor in the same RERTR-9B experiment. Both plates were irradiated to similar fission densities, but one was irradiated at a higher power than the other. The goal of this work is to identify any differences in the swelling behavior when fuel plates are irradiated at different powers to the same fission densities. Based on the results of detailed thickness measurments, more swelling occurs when a U-7Mo dispersion fuel with Al-3.5Si matrix is irradiated to a high fission density at high power compared to one irradiated at a lower power to high fission density.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Novel Sparse Compositional Technique Reveals Microbial Perturbations

ABSTRACT The central aims of many host or environmental microbiome studies are to elucidate factors associated with microbial community compositions and to relate microbial features to outcomes. However, these aims are often complicated by difficulties stemming from high-dimensionality, non-normality, sparsity, and the compositional nature of microbiome data sets. A key tool in microbiome analysis is beta diversity, defined by the distances between microbial samples. Many different distance metrics have been proposed, all with varying discriminatory power on data with differing characteristics. Here, we propose a compositional beta diversity metric rooted in a centered log-ratio transformation and matrix completion called robust Aitchison PCA. We demonstrate the benefits of compositional transformations upstream of beta diversity calculations through simulations. Additionally, we demonstrate improved effect size, classification accuracy, and robustness to sequencing depth over the current methods on several decreased sample subsets of real microbiome data sets. Finally, we highlight the ability of this new beta diversity metric to retain the feature loadings linked to sample ordinations revealing salient intercommunity niche feature importance. IMPORTANCE By accounting for the sparse compositional nature of microbiome data sets, robust Aitchison PCA can yield high discriminatory power and salient feature ranking between microbial niches. The software to perform this analysis is available under an open-source license and can be obtained at https://github.com/biocore/DEICODE ; additionally, a QIIME 2 plugin is provided to perform this analysis at https://library.qiime2.org/plugins/q2-deicode .

59 BASIC BIOLOGICAL SCIENCES↗

Bit-GraphBLAS: Bit-Level Optimizations of Matrix-Centric Graph Processing on GPU

In the graph data structure like adjacency matrix, the connectivity of two nodes can be sufficiently represented using only 1 bit, but they are generally treated as 32-bit full-precision in state-of-the-art graph frameworks to adopt common sparse format such as CSR. Meanwhile, bit-level parallelism has recently be explored to have high-performance potential and low storage requirement on GPUs with dense bit-tiles. To fill the gap, our solution is a hierarchical storage format that contains the bit-indexing base and dense bit-tile units. Inherently, the granularity of the bit-tile is an essential factor in achieving both storage compression and GPU parallelism. How to find a sweet spot that trades off between avoiding sparsity and exploiting is comprehensively researched in this work. In the experiment, we evaluate the proposed storage format and algorithms on modern generation GPUs, including Pascal and Volta, to figure out critical software co-designs in conjunction with existing hardware-specific optimization.

Chen, Jou-An↗

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A low-order block preconditioner for saddle point linear systems

A preconditioner is proposed for the large and sparse linear saddle point problems, which is based on a low-order three-by-three block saddle point form. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial for the preconditioned matrix are discussed. Numerical results show that the optimal convergence behavior can be achieved when the new preconditioner is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

97 MATHEMATICS AND COMPUTING↗

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.

36 MATERIALS SCIENCE↗

Novel Application of Machine Learning Techniques for Rapid Source Apportionment of Aerosol Mass Spectrometer Datasets

In this work, we apply machine learning approaches sparse multinomial logistic regression to classify aerosol mass spectrometer (AMS) unit mass resolution (UMR) data followed by an ensemble regression technique for source apportionment of organic aerosols (OA). The classifier was trained on 60 well characterized laboratory and positive matrix factorization (PMF) deconvolved reference spectra to identify eight OA types. These include four laboratory-derived secondary organic aerosol (SOA) spectra, which include isoprene photooxidation SOA, isoprene epoxydiols (IEPOX) SOA, a monoterpene SOA type that includes a-pinene and ß-pinene SOA, and aromatic SOA from oxidation of naphthalene and m-xylene precursors, as well as PMF deconvolved spectra for three primary organic aerosol (POA) types, namely, hydrocarbon-like organic aerosol (HOA), biomass burning organic aerosol (BBOA), and cooking OA (COA), and a more oxidized oxygenated OA type (MO-OOA). A 5-fold cross-validation strategy, repeated 10 times, was used to assess the classifier’s performance. The classifier had high classification accuracy for COA, aromatic SOA, and isoprene SOA spectra but incorrectly classified ~9% by number of MO-OOA spectra as BBOA, 12% of BBOA spectra as HOA (and vice versa), and 18% of IEPOX-SOA spectra as aromatic SOA. Next, an ensemble regression model was trained on an artificially generated dataset consisting of mixtures of different OA types to assess its ability to predict fractional mass abundances from classification probabilities of various OA species obtained from the multinomial logistic regression classifier trained on the reference spectra. Ultimately, the proposed approach was applied for source apportionment of aircraft-based AMS measurements of OA UMR spectra during the HI-SCALE field campaign. On two representative days (May 6th and 18th, 2016), the algorithm determined that ~50-60% of OA by mass was MO-OOA, which represented a highly aged organic aerosol mixture from different sources. On both days, BBOA was determined to contribute less than 10% to OA by mass. However, on May 18th, the aromatic SOA fraction was higher compared to that on May 6th. The proposed approach is capable of rapidly analyzing AMS data in real time, making it suitable for applications where rapid source apportionment of AMS OA spectra is desirable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sparsity of Radiating Characteristic Modes on Infinite Periodic Structures

Characteristic modes on infinite periodic structures are studied using spectral dyadic Green’s functions. This formulation demonstrates that, in contrast to the modal analysis of finite structures, the number of radiating characteristic modes is limited by unit cell size and incident wave vector (i.e., scan angle or phase shift per unit cell). Here, the reflection tensor is decomposed into modal contributions from radiating modes, indicating that characteristic modes are a predictably sparse basis in which to study reflection phenomena.

42 ENGINEERING↗

A method of surface marker location optimization for tumor motion estimation in lung stereotactic body radiation therapy

Purpose: Accurately localizing lung tumor localization is essential for high-precision radiation therapy techniques such as stereotactic body radiation therapy (SBRT). Since direct monitoring of tumor motion is not always achievable due to the limitation of imaging modalities for treatment guidance, placement of fiducial markers on the patient’s body surface to act as a surrogate for tumor position prediction is a practical alternative for tracking lung tumor motion during SBRT treatments. In this work, the authors propose an innovative and robust model to solve the multimarker position optimization problem. The model is able to overcome the major drawbacks of the sparse optimization approach (SOA) model. Methods: The principle-component-analysis (PCA) method was employed as the framework to build the authors’ statistical prediction model. The method can be divided into two stages. The first stage is to build the surrogate tumor matrix and calculate its eigenvalues and associated eigenvectors. The second stage is to determine the “best represented” columns of the eigenvector matrix obtained from stage one and subsequently acquire the optimal marker positions as well as numbers. Using 4-dimensional CT (4DCT) and breath hold CT imaging data, the PCA method was compared to the SOA method with respect to calculation time, average prediction accuracy, prediction stability, noise resistance, marker position consistency, and marker distribution. Results: The PCA and SOA methods which were both tested were on all 11 patients for a total of 130 cases including 4DCT and breath-hold CT scenarios. The maximum calculation time for the PCA method was less than 1 s with 64 752 surface points, whereas the average calculation time for the SOA method was over 12 min with 400 surface points. Overall, the tumor center position prediction errors were comparable between the two methods, and all were less than 1.5 mm. However, for the extreme scenarios (breath hold), the prediction errors for the PCA method were not only smaller, but were also more stable than for the SOA method. Results obtained by imposing a series of random noises to the surrogates indicated that the PCA method was much more noise resistant than the SOA method. The marker position consistency tests using various combinations of 4DCT phases to construct the surrogates suggested that the marker position predictions of the PCA method were more consistent than those of the SOA method, in spite of surrogate construction. Marker distribution tests indicated that greater than 80% of the calculated marker positions fell into the high cross correlation and high motion magnitude regions for both of the algorithms. Conclusions: The PCA model is an accurate, efficient, robust, and practical model for solving the multimarker position optimization problem to predict lung tumor motion during SBRT treatments. Due to its generality, PCA model can also be applied to other imaging guidance system whichever using surface motion as the surrogates.

60 APPLIED LIFE SCIENCES↗

Regulatory Technology Development Plan - Sodium Fast Reactor. Mechanistic Source Term - Metal Fuel Radionuclide Release

The development of an accurate and defensible mechanistic source term will be vital for the future licensing efforts of metal fuel, pool-type sodium fast reactors. To assist in the creation of a comprehensive mechanistic source term, the current effort sought to estimate the release fraction of radionuclides from metal fuel pins to the primary sodium coolant during fuel pin failures at a variety of temperature conditions. These release estimates were based on the findings of an extensive literature search, which reviewed past experimentation and reactor fuel damage accidents. Data sources for each radionuclide of interest were reviewed to establish release fractions, along with possible release dependencies, and the corresponding uncertainty levels. Although the current knowledge base is substantial, and radionuclide release fractions were established for the elements deemed important for the determination of offsite consequences following a reactor accident, gaps were found pertaining to several radionuclides. First, there is uncertainty regarding the transport behavior of several radionuclides (iodine, barium, strontium, tellurium, and europium) during metal fuel irradiation to high burnup levels. The migration of these radionuclides within the fuel matrix and bond sodium region can greatly affect their release during pin failure incidents. Post-irradiation examination of existing high burnup metal fuel can likely resolve this knowledge gap. Second, data regarding the radionuclide release from molten high burnup metal fuel in sodium is sparse, which makes the assessment of radionuclide release from fuel melting accidents at high fuel burnup levels difficult. This gap could be addressed through fuel melting experimentation with samples from the existing high burnup metal fuel inventory.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A Review of Advanced Test Reactor Fuel and Assessment of Its Compatibility with the ZIRCEX Chlorination Process

Advanced Test Reactor (ATR) fuel has been identified as a resource for high-assay low-enriched uranium (HALEU) production. A survey was performed on the published literature describing ATR fuel. The geometry of the fuel is complex; different parts of the fuel compact experience differing neutron flux and burnup. The literature is sparse, and access is controlled. Therefore, fundamental studies of fuel reprocessing must use a model fuel that represents the main chemical and structural features. Advanced chlorination, or chlorination with sulfur-chlorine bearing reagents is being investigated as way to separate the fuel from metal matrix alloys. A UAl x alloy will be fabricated with x = 3, 4, and 5. The potential chlorination of individual UAl x intermetallics will be assessed in the advanced chlorination process of Al-8001 and Al-6061 as well as a representative mixture. Initial studies will track the alloying elements of the Al, which are Si, Fe, Cu, Mn, Mg, Cr, Zn, and Ti, in addition to the U itself. Further studies will include fission product simulants. Because advanced chlorination solvents include sulfur, the chemistry of sulfur with major and minor constituents will also be investigated. The experimental work accompanied by neutronic calculations will allow the assessment of the feasibility of advanced chlorination to separate aluminum from uranium. If bench-scale testing appears promising, then small-scale tests in shielded facilities with irradiated cladding, lightly irradiated fuel, and spent nuclear fuel are recommended to track the complete inventory of fissile actinides, fission product impurities, and reagent solids and liquids.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems and then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.

Abdel-Rehim, A M↗