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At least 829 records · Page 46

DESI mock challenge: constructing DESI galaxy catalogues based on FastPM simulations

Together with larger spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI), the precision of large-scale structure studies and thus the constraints on the cosmological parameters are rapidly improving. Therefore, one must build realistic simulations and robust covariance matrices. We build galaxy catalogues by applying a halo occupation distribution (HOD) model upon the FastPM simulations, such that the resulting galaxy clustering reproduces high-resolution N-body simulations. While the resolution and halo finder are different from the reference simulations, we reproduce the reference galaxy two-point clustering measurements – monopole and quadrupole – to a precision required by the DESI Year 1 emission line galaxy sample down to non-linear scales, i.e. $k\lt 0.5\, h\, \mathrm{Mpc}^{-1}$ or $s\gt 10\, \mathrm{Mpc}\, h^{-1}$. Furthermore, we compute covariance matrices based on the resulting FastPM galaxy clustering – monopole and quadrupole. We study for the first time the effect of fitting on Fourier conjugate (e.g. power spectrum) on the covariance matrix of the Fourier counterpart (e.g. correlation function). We estimate the uncertainties of the two parameters of a simple clustering model and observe a maximum variation of 20 per cent for the different covariance matrices. Nevertheless, for most studied scales the scatter is between 2 and 10 per cent. Consequently, using the current pipeline we can precisely reproduce the clustering of N-body simulations and the resulting covariance matrices provide robust uncertainty estimations against HOD fitting scenarios. We expect our methodology will be useful for the coming DESI data analyses and their extension for other studies.

79 ASTRONOMY AND ASTROPHYSICS↗

Encoding the structure of many-body localization with matrix product operators

Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. Here, we show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the G i matrices corresponding to the local ground state on site i and the E i matrices corresponding to the local excited state. All 2 n eigenstates can be generated from all possible combinations of these sets of matrices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

We discuss the relations between restricted Boltzmann machine (RBM) states and the matrix product states (MPS) for the ground states of 1D translational invariant stabilizer codes. A generic translational invariant and finitely connected RBM state can be expressed as an MPS, and the matrices of the resulting MPS are of rank 1. We dub such an MPS as an RBM-MPS. This provides a necessary condition for exactly realizing a quantum state as an RBM state, if the quantum state can be written as an MPS. For generic 1D stabilizer codes having a nondegenerate ground state with periodic boundary condition, we obtain an expression for the lower bound of their MPS bond dimension, and an upper bound for the rank of their MPS matrices. In terms of RBM, we provide an algorithm to derive the RBM for the cocycle Hamiltonians whose MPS matrices are proved to be of rank 1. Moreover, the RBM-MPS produced by our algorithm has the minimal bond dimension. A family of examples is provided to explain the algorithm. Furthermore, we finally conjecture that these features hold true for all the 1D stabilizer codes having a nondegenerate ground state with periodic boundary condition, as long as their MPS matrices are of rank 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗

Scaling Up Data-Parallel Analytics Platforms: Linear Algebraic Operation Cases

Linear algebraic operations such as matrix manipulations form the kernel of many machine learning and other crucial algorithms. Scaling up as well as scaling out such algorithms are key to supporting large scale data analysis that require efficient processing over millions of data samples. To this end, we present, ARION, a hardware acceleration based approach for scaling-up individual tasks of Spark, a popular data-parallel analytics platform. We support both linear algebraic operations of between two dense matrices, and between sparse and dense matrices in distributed environments. ARION provides a flexible control of acceleration according to matrix density, along with efficient scheduling based on runtime resource utilization. We demonstrate the benefit of our approach for general matrix multiplication operations over large matrices with up to four billion elements by using Gramian matrix computation that is commonly used in machine learning. Experiments show that our approach achieves more than 2× and 1.5× end-to-end performance speedups for dense and sparse matrices, respectively, and up to 57.04× faster computation compared to MLlib, a state of the art Spark-based implementation. This work is sponsored in part by the NSF under the grants: CNS-1565314, CNS-1405697, and CNS-1615411. The manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Xu, Luna↗

Reducing Communication in Graph Neural Network Training

Graph Neural Networks (GNNs) are powerful and flexible neural networks that use the naturally sparse connectivity information of the data. GNNs represent this connectivity as sparse matrices, which have lower arithmetic intensity and thus higher communication costs compared to dense matrices, making GNNs harder to scale to high concurrencies than convolutional or fully-connected neural networks. Here, we introduce a family of parallel algorithms for training GNNs and show that they can asymptotically reduce communication compared to previous parallel GNN training methods. We implement these algorithms, which are based on 1D, 1. 5D, 2D, and 3D sparse-dense matrix multiplication, using torch.distributed on GPU-equipped clusters. Our algorithms optimize communication across the full GNN training pipeline. We train GNNs on over a hundred GPUs on multiple datasets, including a protein network with over a billion edges.

97 MATHEMATICS AND COMPUTING↗

Organ doses for reference adult male and female undergoing computed tomography estimated by Monte Carlo simulations

Purpose: To develop a computed tomography (CT) organ dose estimation method designed to readily provide organ doses in a reference adult male and female for different scan ranges to investigate the degree to which existing commercial programs can reasonably match organ doses defined in these more anatomically realistic adult hybrid phantomsMethods: The x-ray fan beam in the SOMATOM Sensation 16 multidetector CT scanner was simulated within the Monte Carlo radiation transport code MCNPX2.6. The simulated CT scanner model was validated through comparison with experimentally measured lateral free-in-air dose profiles and computed tomography dose index (CTDI) values. The reference adult male and female hybrid phantoms were coupled with the established CT scanner model following arm removal to simulate clinical head and other body region scans. A set of organ dose matrices were calculated for a series of consecutive axial scans ranging from the top of the head to the bottom of the phantoms with a beam thickness of 10 mm and the tube potentials of 80, 100, and 120 kVp. The organ doses for head, chest, and abdomen/pelvis examinations were calculated based on the organ dose matrices and compared to those obtained from two commercial programs, CT-EXPO and CTDOSIMETRY. Organ dose calculations were repeated for an adult stylized phantom by using the same simulation method used for the adult hybrid phantom. Results: Comparisons of both lateral free-in-air dose profiles and CTDI values through experimental measurement with the Monte Carlo simulations showed good agreement to within 9%. Organ doses for head, chest, and abdomen/pelvis scans reported in the commercial programs exceeded those from the Monte Carlo calculations in both the hybrid and stylized phantoms in this study, sometimes by orders of magnitude. Conclusions: The organ dose estimation method and dose matrices established in this study readily provides organ doses for a reference adult male and female for different CT scan ranges and technical parameters. Organ doses from existing commercial programs do not reasonably match organ doses calculated for the hybrid phantoms due to differences in phantom anatomy, as well as differences in organ dose scaling parameters. The organ dose matrices developed in this study will be extended to cover different technical parameters, CT scanner models, and various age groups.

61 RADIATION PROTECTION AND DOSIMETRY↗

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually suitable for these purposes, but it can be much slower than the unpivoted QR algorithm. For large matrices, the difference in performance is due to increased communication between the processor and slow memory, which QRCP needs in order to choose pivots during decomposition. Our main algorithm, Randomized QR with Column Pivoting (RQRCP), uses randomized projection to make pivot decisions from a much smaller sample matrix, which we can construct to reside in a faster level of memory than the original matrix. This technique may be understood as trading vastly reduced communication for a controlled increase in uncertainty during the decision process. Furthermore, for rank-revealing purposes, the selection mechanism in RQRCP produces results that are the same quality as the standard algorithm, but with performance near that of unpivoted QR (often an order of magnitude faster for large matrices). Additionally, we also propose two formulas that facilitate further performance improvements. The first efficiently updates sample matrices to avoid computing new randomized projections. The second avoids large trailing updates during the decomposition in truncated low-rank approximations. Our truncated version of RQRCP also provides a key initial step in our truncated SVD approximation, TUXV. These advances open up a new performance domain for large matrix factorizations that will support efficient problem-solving techniques for challenging applications in science, engineering, and data analysis.

97 MATHEMATICS AND COMPUTING↗

Microporous structure in silicone polymers with polylactic acid and polyethylene glycol microspheres: Synthesis and characterization

Porosity in polymer parts could improve mechanical properties while reducing weight and density. Individual pores must be small enough that bulk mechanical properties are retained but significant enough to reduce the density of the material. Filler materials can be incorporated into polymer matrices and removed to create voids. Here, this paper focuses on creating spherical pores in silicone matrices by inserting and removing core materials or fillers during post-cure. A method was developed to incorporate pore formers into an uncured polymer resin and remove the pore former materials from the matrix. Polyethylene glycol (PEG) and polylactic acid (PLA) microspheres were created and incorporated into silicone matrices as pore formers. Microspheres with controllable size distributions were formed via an emulsion formation. Microspheres are removed from the matrix by solvent extraction and calcination. Thermogravimetric Analysis (TGA), Dynamic Mechanical Analysis (DMA), and optical imaging characterize and determine the successful creation of micropores in the polymer matrices.

36 MATERIALS SCIENCE↗

Optimizing Metalloporphyrin-Catalyzed Reduction Reactions for In Situ Remediation of DOE Contaminants

Past activities have resulted in a legacy of contaminated soil and groundwater at Department of Energy facilities nationwide. Uranium and chromium are among the most frequently encountered and highest-priority metal and radionuclide contaminants at DOE installations. Abiotic chemical reduction of uranium and chromium at contaminated DOE sites can be beneficial because the reduced metal species are less soluble in water, less mobile in the environment, and less toxic to humans and ecosystems. Although direct biological reduction has been reported for U(VI) and Cr(VI) in laboratory studies and at some field sites, the reactions can sometimes be slow or even inhibited due to unfavorable environmental conditions. One promising approach for the in-situ remediation of DOE contaminants is to develop electron shuttle catalysts that can be delivered precisely to the specific subsurface locations where contaminants reside. Previous research has shown that reduction of oxidized organic and inorganic contaminants often can be catalyzed by electron shuttle systems. Metalloporphyrins and their derivatives are well known electron shuttles for many biogeochemical systems, and thus were selected to study their catalytic capabilities for the reduction of chromium and uranium in the presence of reducing agents. Zero valent iron (ZVI) was chosen as the primary electron donor in most experimental systems. Research proceeded in three phases and the key findings of each phase are reported here. Phase I examined Cr(VI) reduction and utilized micro- and nano-sized ZVI as the electron donors. Electron shuttle catalysts tested were cobalt- and iron-containing metalloporphyrins and Vitamin B12. To aid in the recycle and reuse of the nano-sized ZVI and soluble catalysts, sol-gels and calcium-alginate gel beads were tested as immobilization/support matrices. Although the nano-sized ZVI could be incorporated within the alginate gel beads, preliminary attempts to trap it in sol-gels were not successful. Conversely, the water-soluble catalysts could be trapped within sol-gel matrices but they tended to leach out of the alginate gel beads during use. In general, immobilization of the nano-sized ZVI in gel beads and of the catalysts in sol-gels tended to result in slower rates of Cr(VI) reduction, but these effects could be overcome to some extent by using higher reactant/catalyst concentrations. In addition, the lowering of their effectiveness would likely be offset by the benefits obtained when recycling and reusing the materials because they were immobilized. Addition of the catalytic electron shuttles will be most useful when the micro-sized or nano-sized ZVI becomes less reactive with reaction time. Continued work in Phase II in the area of nano-sized ZVI immobilization led to procedures that were successful in incorporating the iron particles in sol-gel matrices. The water-soluble reductants sodium dithionite and L-ascorbic acid were also tested, but their use appeared to lead to formation of complexes with the uranyl cation which limited their effectiveness. Also, although the sol-gel supported nano-sized ZVI showed some promise at reducing uranium, the fluoride used in the sol-gel synthesis protocol appeared to lead to formation of uranyl-fluoride complexes that were less reactive. Because hexavalent chromium is an anion which does not form complexes with fluoride, it was used to demonstrate the intrinsic reactivity of the sol-gel immobilized nano-sized ZVI. Consistent with our observations in Phase I, the sol-gel matrix once again slowed down the reduction reaction but the expected benefits of recycle/reuse should outweigh this adverse effect. The major emphasis in Phase III of this study was to simultaneously incorporate nano-sized ZVI and water-soluble catalysts in the same sol-gel matrix. The catalysts utilized were cobalt complexes of uroporphyrin and protoporphyrin and Cr(VI) reduction was used to test the efficacy of the combined "catalyst + reductant" sol-gel matrix. When enough catalyst was added to the sol-gels, enhancement of the Cr(VI) reduction reaction was observed. At the lowest levels of catalyst addition, however, the rates of Cr(VI) reduction were similar to those systems which only used sol-gel immobilized nano-sized ZVI without any catalyst present. These findings suggest future areas of research that should be pursued to further optimize abiotic reduction reactions of metals with combined "catalyst + reductant" matrices.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Improved quantum algorithms for linear and nonlinear differential equations

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solar system applications of Mie theory and of radiative transfer of polarized light

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Whitehill, L. P.↗

Elimination on sparse symmetric systems of a special structure.

Consideration of the problem of finding a permutation of rows and columns and an algorithm for solving ordered systems of linear algebraic equations with sparse matrices having a certain regular structure. Two approaches to the solution of this problem, in which the sparsity is used to some extent, are outlined. One of them is a very general approach where optimal (or nearly optimal) ordering is sought and the algorithm for solving the ordered system treats the matrix element by element to perform only necessary operations. The other approach involves the use of band matrices. After comparing these two approaches, a third approach is then suggested which involves the use of pipe matrices, and a means of ordering the rows and columns to obtain this type of matrix is presented. Examples of matrices reordered by the proposed procedure are cited.

Segethova, J.↗

A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗

Compression Of Data In Imaging Radar Polarimetry

Algorithms developed to reduce number of radar polarimetric data processed to synthesize image of arbitrary combination of transmitting and receiving polarizations. Brings image-processing requirements within computing capabilities of typical users, without degrading images excessively. In scattering-matrix approach to reduction of image data, four adjacent picture elements combined into one by synthesizing new scattering matrix from scattering matrices of four elements. In phase-matrix approach, phase matrices generated from scattering matrices of four adjacent picture elements, and four phase matrices added to combine four picture elements into one.

Zebker, H. A.↗

Large-scale sparse singular value computations

Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

Berry, Michael W.↗

A visual detection model for DCT coefficient quantization

The discrete cosine transform (DCT) is widely used in image compression and is part of the JPEG and MPEG compression standards. The degree of compression and the amount of distortion in the decompressed image are controlled by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. One approach is to set the quantization level for each coefficient so that the quantization error is near the threshold of visibility. Results from previous work are combined to form the current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color. A model-based method of optimizing the quantization matrix for an individual image was developed. The model described above provides visual thresholds for each DCT frequency. These thresholds are adjusted within each block for visual light adaptation and contrast masking. For given quantization matrix, the DCT quantization errors are scaled by the adjusted thresholds to yield perceptual errors. These errors are pooled nonlinearly over the image to yield total perceptual error. With this model one may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.

Ahumada, Albert J., Jr.↗