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Solving larger-sized problems is an important area of research in quantum computing. Designing hybrid quantum-classical algorithms is a promising approach to solving this. We discuss decomposition-based hybrid approaches for solving optimization problems and demonstrate them for applications related to community detection.
A Green’s function inverse heat transfer (IHT) approach is used to reconstruct the surface heating conditions on ablative thermal protection system (TPS) materials from embedded heat flux sensor and temperature probe measurements. The approach models the temperature time-history at the measurement location as a discrete linear system, allowing for the heat flux boundary condition to be recovered directly without the need for time-marching schemes. The effects of material decomposition and pyrolysis gas transport are modeled using an energy source/sink analogue. The performance of the reconstruction approach is analyzed on a 1D test case representative of an atmospheric entry heating scenario. The approach can recover the TPS surface heat flux to within 4% of the input heating condition with a computation time of 2-3 seconds (>3 orders of magnitude faster than current time-marching IHT methods). As a byproduct of the surface heating reconstruction, the algorithm also captures the surface pyrolysis gas mass flux and solid decomposition at multiple through-thickness locations within the TPS.
We have developed radionuclide identification algorithms for radiation portal monitor applications. One algorithm uses a spectral angle mapper to match the power spectral density of modified cumulative distribution functions of measured pulse height distributions to reference spectra, while the others rely on the decomposition of the observed spectrum as a linear mixture of known radionuclide spectra. Three algorithms were then tested for their ability to perform on-the-fly radionuclide identification on datasets acquired with a liquid organic scintillator-based pedestrian radiation portal monitor on moving special nuclear material and industrial radiological sources, as well as common medical isotopes. We quantified and compared the relative efficacies of the algorithms considered using F-score analysis. Measured radiation sources included 51 g of highly enriched uranium, 6.6 g of weapons grade plutonium, 241 Am, 133 Ba, 57 Co and 137 Cs sources with activities of several hundred kBq, as well as 260 kBq liquid solution samples of the medical isotopes 99m Tc, 111 In, 67 Ga, 123 I, 131 I, and 201 Tl. We achieved 100% positive identification, for three-second measurements of single sources moving at a source-transit speed of 1.2 m/s. For mixed sources with strongest and weakest sources having no more than a 5:1 ratio of detected counts, encouraging positive identification results were achieved with the un-mixing algorithms. Current radiation portal monitor designs suffer from a high incidence rate of nuisance radiation alarms caused in radiation portal monitor primary screenings by recent nuclear medicine patients and cargo containing large amounts of naturally occurring radioactive materials. Integrating reliable on-the-fly radionuclide identification into the radiation portal monitors could lower the number of nuisance alarms requiring time-consuming secondary inspections.
One major challenge in the field of shotgun metagenomics is the accurate identification of the organisms present within the community, based on classification of short sequence reads. Though microbial community profiling methods have emerged to attempt to rapidly classify the millions of reads output from contemporary sequencers, the combination of incomplete databases, similarity among otherwise divergent genomes, and the large volumes of sequencing data required for metagenome sequencing has led to unacceptably high false discovery rates (FDR). Here we present the application of a novel, gene-independent and signature-based metagenomic taxonomic profiling tool with significantly smaller FDR, which is also capable of classifying never-before seen genomes into the appropriate parent taxa.The algorithm is based upon three primary computational phases: (I) genomic decomposition into bit vectors, (II) bit vector intersections to identify shared regions, and (III) bit vector subtractions to remove shared regions and reveal unique, signature regions.In the Decomposition phase, genomic data is first masked to highlight only the valid (non-ambiguous) regions and then decomposed into overlapping 24-mers. The k-mers are sorted along with their start positions, de-replicated, and then prefixed, to minimize data duplication. The prefixes are indexed and an identical data structure is created for the start positions to mimic that of the k-mer data structure.During the Intersection phase -- which is the most computationally intensive phase -- as an all-vs-all comparison is made, the number of comparisons is first reduced by four methods: (a) Prefix restriction, (b) Overlap detection, (c) Overlap restriction, and (d) Result recording. In Prefix restriction, only k-mers of the same prefix are compared. Within that group, potential overlap of k-mer suffixes that would result in a non-empty set intersection are screened for. If such an overlap exists, the region which intersects is first reduced by performing a binary search of the boundary suffixes of the smaller set into the larger set, which defines the limits of the zipper-based intersection process. Rather than recording the actual k-mers of the intersection, another data structure of identical "shape" is created which consists of only bit vectors so that only a 1 or 0 will be stored in the location of the k-mer suffix that was found in the intersection. This reduces the amount of data generated and stored considerably.During the Subtraction phase, relevant intersection bitmasks are first unionized together to form a single bitmask which is then applied over the original genome to reveal only those regions of the genome that are unique. These regions are then exported to disk in FASTA format and used in the application of determining the constituents of an unknown metagenomic community.The DATABASE provided is the result of the algorithm described.
One major challenge in the field of shotgun metagenomics is the accurate identification of the organisms present within the community, based on classification of short sequence reads. Though microbial community profiling methods have emerged to attempt to rapidly classify the millions of reads output from contemporary sequencers, the combination of incomplete databases, similarity among otherwise divergent genomes, and the large volumes of sequencing data required for metagenome sequencing has led to unacceptably high false discovery rates (FDR). Here we present the application of a novel, gene-independent and signature-based metagenomic taxonomic profiling tool with significantly smaller FDR, which is also capable of classifying never-before seen genomes into the appropriate parent taxa.The algorithm is based upon three primary computational phases: (I) genomic decomposition into bit vectors, (II) bit vector intersections to identify shared regions, and (III) bit vector subtractions to remove shared regions and reveal unique, signature regions.In the Decomposition phase, genomic data is first masked to highlight only the valid (non-ambiguous) regions and then decomposed into overlapping 24-mers. The k-mers are sorted along with their start positions, de-replicated, and then prefixed, to minimize data duplication. The prefixes are indexed and an identical data structure is created for the start positions to mimic that of the k-mer data structure.During the Intersection phase -- which is the most computationally intensive phase -- as an all-vs-all comparison is made, the number of comparisons is first reduced by four methods: (a) Prefix restriction, (b) Overlap detection, (c) Overlap restriction, and (d) Result recording. In Prefix restriction, only k-mers of the same prefix are compared. Within that group, potential overlap of k-mer suffixes that would result in a non-empty set intersection are screened for. If such an overlap exists, the region which intersects is first reduced by performing a binary search of the boundary suffixes of the smaller set into the larger set, which defines the limits of the zipper-based intersection process. Rather than recording the actual k-mers of the intersection, another data structure of identical "shape" is created which consists of only bit vectors so that only a 1 or 0 will be stored in the location of the k-mer suffix that was found in the intersection. This reduces the amount of data generated and stored considerably.During the Subtraction phase, relevant intersection bitmasks are first unionized together to form a single bitmask which is then applied over the original genome to reveal only those regions of the genome that are unique. These regions are then exported to disk in FASTA format and used in the application of determining the constituents of an unknown metagenomic community.The DATABASE provided is the result of the algorithm described.
In this paper, the authors present a novel method of performing PARAFAC2 factorization of three-way data using a compact representation of that data. In the standard PARAFAC2 algorithm, two modes of the data are recovered directly during the decomposition while the third mode is returned as a transformation matrix, which is then used to rotate sets of orthogonal third-mode basis factors into interpretable factors. In our new method, the data are first decomposed into a core matrix and orthogonal factor loading matrices in the first two modes as well as sets of orthogonal factors in the third mode (as in standard PARAFAC2). The core matrix is then decomposed using a the standard PARAFAC2 strategy to produce transformation matrices in all three modes. The algorithm is particularly useful for very large data sets and essentially permits imposition of nonnegativity in all three modes.
We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.
The manycore paradigm shift, and the resulting change in modern computer architectures, has made the development of optimal numerical routines extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting with our algorithm design, performance analysis and programing model and moving to kernel optimization. Our goal, by targeting low-level and easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for use on manycore coprocessors, and to show significant performance improvements compared to existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications.
X-ray Photoelectron Spectroscopy of large bandgap or insulating material surfaces relies on an effective mechanism that compensates for the emission (loss) of electrons by maintaining the material surface at a steady-state uniform potential. While a steady-state may be attained by utilizing an active compensation, such as low power electron emitting filament, there is the possibility that the surface potential is not uniform over the area analyzed, leading to peak shifts and incorrect spectral interpretation. Here, in this work, a spectral data processing method based on mapping the ZrO 2 and Pd/ZrO 2 surfaces utilizing photoemission peak binding energy is proposed, which provides information about the response of specific material surfaces to charge compensation. Spectromicroscopy of ZrO 2 and Pd/ZrO 2 surfaces without spatial information is used to monitor the efficacy of charge compensation. Exploiting counts distributed over many bins require the use of procedures and algorithms essential to practical mapping peak positions. Iterative singular value decomposition is therefore introduced and utilized as a means of efficiently delivering spatially resolved spectra from which binding energy for peaks is computed. The concepts developed in this work result in robust and accurate peak models of ZrO 2 and Pd/ZrO 2 that can be applied in XPS analysis of not only ZrO 2 but other large bandgap or insulating material surfaces. Supporting arguments for a peak model representing signal from Zr 3p and Pd 3d are developed within this work are presented.
A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.
One major challenge in the field of shotgun metagenomics is the accurate identification of the organisms present within the community, based on classification of short sequence reads. Though microbial community profiling methods have emerged to attempt to rapidly classify the millions of reads output from contemporary sequencers, the combination of incomplete databases, similarity among otherwise divergent genomes, and the large volumes of sequencing data required for metagenome sequencing has led to unacceptably high false discovery rates (FDR). Here we present the application of a novel, gene-independent and signature-based metagenomic taxonomic profiling tool with significantly smaller FDR, which is also capable of classifying never-before seen genomes into the appropriate parent taxa.The algorithm is based upon three primary computational phases: (I) genomic decomposition into bit vectors, (II) bit vector intersections to identify shared regions, and (III) bit vector subtractions to remove shared regions and reveal unique, signature regions. In the Decomposition phase, genomic data is first masked to highlight only the valid (non-ambiguous) regions and then decomposed into overlapping 24-mers. The k-mers are sorted along with their start positions, de-replicated, and then prefixed, to minimize data duplication. The prefixes are indexed and an identical data structure is created for the start positions to mimic that of the k-mer data structure. During the Intersection phase -- which is the most computationally intensive phase -- as an all-vs-all comparison is made, the number of comparisons is first reduced by four methods: (a) Prefix restriction, (b) Overlap detection, (c) Overlap restriction, and (d) Result recording. In Prefix restriction, only k-mers of the same prefix are compared. Within that group, potential overlap of k-mer suffixes that would result in a non-empty set intersection are screened for. If such an overlap exists, the region which intersects is first reduced by performing a binary search of the boundary suffixes of the smaller set into the larger set, which defines the limits of the zipper-based intersection process. Rather than recording the actual k-mers of the intersection, another data structure of identical "shape" is created which consists of only bit vectors so that only a 1 or 0 will be stored in the location of the k-mer suffix that was found in the intersection. This reduces the amount of data generated and stored considerably. During the Subtraction phase, relevant intersection bitmasks are first unionized together to form a single bitmask which is then applied over the original genome to reveal only those regions of the genome that are unique. These regions are then exported to disk in FASTA format and used in the application of determining the constituents of an unknown metagenomic community.
SAND2021-3051 O CUBIT is a full-featured software toolkit for robust generation of two- and three-dimensional finite element meshes (grids) and geometry preparation. Its main goal is to reduce the time required to generate meshes - particularly large hex meshes of complicated, interlocking assemblies. It is a solid-modeler-based preprocessor that meshes volumes and surfaces for finite element analysis. CUBIT also includes state-of-the-art smoothing algorithms and provides an extensive suite of tools for geometry decomposition and mesh generation. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Tensor ELF is a user-friendly parallel tensor decomposition Python toolbox that includes a suite of machine learning algorithms for CPU and GPU architectures for the analysis of sparse and dense data including utility tools for pre-processing and post-processing.
This report analyzes the use of the modified Cholesky decomposition technique as applied to the feature selection and classification algorithms used in the analysis of remote sensing data (e.g., as in LARSYS). This technique is approximately 30% faster in classification and a factor of 2-3 faster in divergence, as compared with LARSYS. Also numerical stability and accuracy are slightly improved. Other methods necessary to deal with numerical stability problems are briefly discussed.
The accuracy of a two time scale approach to the output feedback regulator design problem is examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. A sequential numerical algorithm is defined which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. A procedure for optimally zeroing selected gain elements in an output feedback gain matrix is developed and demonstrated. A summary of conference and journal publications from this research is also provided.
Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.
One major challenge in the field of shotgun metagenomics is the accurate identification of the organisms present within the community, based on classification of short sequence reads. Though microbial community profiling methods have emerged to attempt to rapidly classify the millions of reads output from contemporary sequencers, the combination of incomplete databases, similarity among otherwise divergent genomes, and the large volumes of sequencing data required for metagenome sequencing has led to unacceptably high false discovery rates (FDR). Here we present the application of a novel, gene-independent and signature-based metagenomic taxonomic profiling tool with significantly smaller FDR, which is also capable of classifying never-before seen genomes into the appropriate parent taxa.The algorithm is based upon three primary computational phases: (I) genomic decomposition into bit vectors, (II) bit vector intersections to identify shared regions, and (III) bit vector subtractions to remove shared regions and reveal unique, signature regions. In the Decomposition phase, genomic data is first masked to highlight only the valid (non-ambiguous) regions and then decomposed into overlapping 24-mers. The k-mers are sorted along with their start positions, de-replicated, and then prefixed, to minimize data duplication. The prefixes are indexed and an identical data structure is created for the start positions to mimic that of the k-mer data structure. During the Intersection phase -- which is the most computationally intensive phase -- as an all-vs-all comparison is made, the number of comparisons is first reduced by four methods: (a) Prefix restriction, (b) Overlap detection, (c) Overlap restriction, and (d) Result recording. In Prefix restriction, only k-mers of the same prefix are compared. Within that group, potential overlap of k-mer suffixes that would result in a non-empty set intersection are screened for. If such an overlap exists, the region which intersects is first reduced by performing a binary search of the boundary suffixes of the smaller set into the larger set, which defines the limits of the zipper-based intersection process. Rather than recording the actual k-mers of the intersection, another data structure of identical "shape" is created which consists of only bit vectors so that only a 1 or 0 will be stored in the location of the k-mer suffix that was found in the intersection. This reduces the amount of data generated and stored considerably. During the Subtraction phase, relevant intersection bitmasks are first unionized together to form a single bitmask which is then applied over the original genome to reveal only those regions of the genome that are unique. These regions are then exported to disk in FASTA format and used in the application of determining the constituents of an unknown metagenomic community.
A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field integrals (the X2CAMF scheme) is reported. Furthermore, the present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. The CD-based implementation extends the applicability of X2CAMF-CC and EOMCC methods to medium-sized molecules with the correlation of around 1000 spinors. Benchmark calculations for uranium-containing small molecules have been performed to assess the dependence of CC results with respect to the Cholesky threshold. A Cholesky threshold of 10 –4 is shown to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond dissociation energy of the uranium hexafluoride molecule, UF 6 , with up to quadruple-zeta basis sets and the lowest excitation energy in solvated uranyl ion [UO 2 2+ (H 2 O) 12 ].