Novel Randomized Algorithms for QR with Column Pivoting, and Their Implementations in RandLAPACK
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Melnichenko, Maksim↗
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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↗
Computing rank‐revealing factorizations of matrices stored out‐of‐core
This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.
97 MATHEMATICS AND COMPUTING↗
Bringing randomized algorithms to mainstream numerical linear algebra
Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.
97 MATHEMATICS AND COMPUTING↗
Selective electrified polyethylene upcycling by pore-modulated pyrolysis
Plastic waste is a increasing problem, accumulating in landfills and the environment. Pyrolysis is a promising and industrially relevant approach for transforming plastic waste into value-added chemicals. However, the selectivity and yield of traditional plastic pyrolysis are poor, with products featuring broad molar mass distributions. Here we report a highly selective, energy-efficient and catalyst-free pyrolysis method that can upcycle plastic into value-added chemicals via pore-modulated pyrolysis. Using a Joule-heated carbon column, we demonstrate the pivotal role of the reactor’s graded porous structure in decreasing the polydispersity of the reaction intermediates, enabling high product selectivity and yield. The decreasing pore size of the reactor modulates the mass transport in an apparent gating effect—preventing high-molar-mass species from exiting the reactor before sufficient pyrolysis has occurred. Using polyethylene as a model reactant, we demonstrate a high yield of 65.9 ± 5.2% and up to 80.8% selectivity toward value-added aviation fuel precursor (C8–C18 hydrocarbons) without the use of any catalysts.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Experimental parameters for plasma wakefield acceleration in a narrow plasma column
Recent theoretical advancements propose multiple positron acceleration schemes in plasma wakefield acceleration (PWFA). One of the most promising ideas involves the creation of an electron-driven blowout wake within a finite-radius pre-ionized plasma column. This leads to the formation of an elongated region of sheath electrons at the closing of the first wake period capable of accelerating positrons while simultaneously providing a transverse focusing force. Additionally, the proposed scheme has shown to be a potential means of suppressing instabilities. We present an experimental opportunity to explore the narrow column PWFA at the Facility for Advanced Accelerator Experimental Tests II (FACET-II): the E333 experiment. As a pivotal first step towards achieving positron acceleration in PWFA, we have planned a precursor experiment utilizing the currently available single-bunch electron beam to study the physics of the narrow plasma PWFA scheme. We outline the feasible experimental parameters, including beam and ionization laser parameters, along with the required laser optics for the experiment. The primary observable signatures for this stage of the experiment are the final energy spectrum and transverse position of the electron bunch, anticipating reduced energy loss and enhanced beam guidance in the narrow plasma column compared to the nominal PWFA. Comprehensive simulations are used to detail our experimental plan.
Lee, Valentina [University of Colorado, Boulder, C↗
Fox Trails
1. This software utilizes python pandas to pull data from P6 databases or XER files. The software transforms the datasets into multiple main tables by joining, filtering, iteratively flattening hierarchical structured data, and pivoting datasets to give simple flat output tables. The activity table includes all of the information related to an activity including activity codes, global, EPS, and project codes, UDFs, and WBS information as separate columns. This includes the code id, code value and sequence number for all levels in hierarchical codes. The resource table is similar to the activity table and includes all of the information related to resources on activities including UPFs and resource codes. The resource time phased table takes the resource information and time phases it for the budget, forecast, late, and actual dates/units/costs that closely matches P6's user interface's values as it implements the resource curve and calendars. The wbs table contains the WBS structure broken out by levels and includes UDFs, codes, and notebook topics. The final P6 data table is the relationships table which simply contains the relationships. 2. When a user updates the tool with data (via giving it P6 project names with database username/password information or XER files) the system creates the data in #1, then creates a networkx graph with the activity data imbedded in the node data and the relationships added as edges. Each edge also has it's float calculated (working time distance between the predecessor and successor) and attached to the edge. Activities are also tagged as a potential start of a path based on their constraints, constraint dates, remaining start date, and activity status. When a user enters an activity ID into the UI, it runs a shortest path calculation on the network graph between each node tagged as potential start to the entered activity id based on the float tagged on the edge. Each path returned by the algorithm contains all of the nodes on the path in order, as well as the total float of the edges that make the path. This data is then collected and returned to the user in the form of a gantt chart with groupings for each path that includes the total float for each group. 3. Similar to 2, if the user passes through a reference dataset each activity set in the path is checked to see if it had a path in the reference dataset, if that path was the primary path between the start and end activities, and what has changed regarding logic and durations. These changes are color coded and summarized before sent to the user to be displayed by the UI for simple discovery. 4. Utilizing the data from #1, the user can submit desired grouping code(s) and filters to the system. The system will then pull the activities, resources, and relationships and create a gantt chart based on the groupings sent and filtered based on the filters sent. 5. The system will produce a gantt chart in a similar method to #4, but allows interactivity with the data. As the user interacts with the gantt chart, the software captures the changes and stores it with the user making the change so that project controls and implement those changes in P6.
Fox, Ben↗
Dimensionality effects on multicomponent ionic transport and surface complexation in porous media
Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media. Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ~ 2.8, NaBr - 100 mM, HCl - pH ~ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H + (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup. Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na + , B – , and H + , and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.
58 GEOSCIENCES↗
Metapangenomics reveals depth-dependent shifts in metabolic potential for the ubiquitous marine bacterial SAR324 lineage
Abstract Background Oceanic microbiomes play a pivotal role in the global carbon cycle and are central to the transformation and recycling of carbon and energy in the ocean’s interior. SAR324 is a ubiquitous but poorly understood uncultivated clade of Deltaproteobacteria that inhabits the entire water column, from ocean surface waters to its deep interior. Although some progress has been made in elucidating potential metabolic traits of SAR324 in the dark ocean, very little is known about the ecology and the metabolic capabilities of this group in the euphotic and twilight zones. To investigate the comparative genomics, ecology, and physiological potential of the SAR324 clade, we examined the distribution and variability of key genomic features and metabolic pathways in this group from surface waters to the abyss in the North Pacific Subtropical Gyre, one of the largest biomes on Earth. Results We leveraged a pangenomic ecological approach, combining spatio-temporally resolved single-amplified genome, metagenomic, and metatranscriptomic datasets. The data revealed substantial genomic diversity throughout the SAR324 clade, with distinct depth and temporal distributions that clearly differentiated ecotypes. Phylogenomic subclade delineation, environmental distributions, genomic feature similarities, and metabolic capacities revealed strong congruence. The four SAR324 ecotypes delineated in this study revealed striking divergence from one another with respect to their habitat-specific metabolic potentials. The ecotypes living in the dark or twilight oceans shared genomic features and metabolic capabilities consistent with a sulfur-based chemolithoautotrophic lifestyle. In contrast, those inhabiting the sunlit ocean displayed higher plasticity energy-related metabolic pathways, supporting a presumptive photoheterotrophic lifestyle. In epipelagic SAR324 ecotypes, we observed the presence of two types of proton-pumping rhodopsins, as well as genomic, transcriptomic, and ecological evidence for active photoheterotrophy, based on xanthorhodopsin-like light-harvesting proteins. Conclusions Combining pangenomic and both metagenomic and metatranscriptomic profiling revealed a striking divergence in the vertical distribution, genomic composition, metabolic potential, and predicted lifestyle strategies of geographically co-located members of the SAR324 bacterial clade. The results highlight the utility of metapangenomic approaches employed across environmental gradients, to decipher the properties and variation in function and ecological traits of specific phylogenetic clades within complex microbiomes.
59 BASIC BIOLOGICAL SCIENCES↗
Comprehensive Review of DPF-based Flash Neutron Radiography Viability
MJOLNIR (MegaJOule Neutron Imaging Radiography) is a Dense Plasma Focus (DPF) being developed by LLNL as a prototype to assess the viability of a DPF as a flash neutron radiography source. To date, MJOLNIR has discharged up to 1.3 MJ of stored energy into a deuterium plasma load and achieved yields up to 1.2 × 10 12 neutrons per discharge. The MJOLNIR pulse length already meets the preliminary requirements for flash neutron radiography and we demonstrate in this report plausible paths forward to meet the yield requirement in a deuterium plasma. MJOLNIR’s neutron spot size has been characterized to be a factor of two greater than radiography requirements and presents the greatest challenge. A path forward to sufficiently shrinking spot size is outlined in this report, using a combination of gas dopants and a smaller anode implosion radius. A DPF is a plasma device with coaxial electrodes whose discharge ends with a stagnated hot and dense plasma column on-axis, at the tip of the central anode. Inside the MJOLNIR DPF plasma column, both thermal and beam target processes generate neutrons. To understand the underlying physics of neutron generation inside the DPF, we model the experiment using a combination of kinetic, fluid, and reduced-order models we have been developing for over ten years at LLNL. Our numerical tools are also pivotal to charting the path forward because they allow us to numerically test out which modifications would improve the DPF’s characteristic output.
42 ENGINEERING↗
Development and Optimization of a Purification Process to Recover 99 Mo from Low-enriched Uranium
Supported by the DOE-NNSA Office of Material Management & Minimization (M3), a number of domestic entities are pursuing non-highly enriched uranium (non-HEU) production of 99 Mo. As the production technologies of 99Mo pivot toward low-enriched uranium (LEU) or molybdenum targets, new reaction channels and accelerators are being evaluated. Superconducting electron linear accelerators (LINACs) with high-Z converter targets can generate bremsstrahlung photons and neutron fluxes that are capable of inducing photonuclear reactions and LEU fission. A particular advantage of a LINAC is that it does not rely on HEU-fueled reactor cores (which are currently slated for LEU conversion) and can operate on an almost continuous basis. Regarding the chemical purification of 99 Mo from irradiated uranium targets under acidic digestion, there exists a procedure known as Cintichem or modifications thereof with respect to LEU (LEU Modified Cintichem process, LMC). The process relies on a number of selective precipitation steps and column chromatography to purify Mo. It is important to note that LMC prescribes the addition of stable Mo to carry 99 Mo on alpha benzoin oxime, which reduces the specific activity of 99 Mo. This is especially important for processing 99 Mo batches with lower activities (~33 Ci of 99 Mo per batch).
07 ISOTOPE AND RADIATION SOURCES↗
A U.S. scientific community review of carbon cycle science gaps and opportunities to better support earth system science and carbon management
Greenhouse gas (GHG) emissions continue to grow, while natural carbon reservoirs are becoming increasingly vulnerable to anthropogenic pressures, climate extremes, and disturbance. These changes are impacting humans, ecosystems, and natural resources worldwide. Tracking and mitigating GHG emissions require a pivot to operational monitoring of regional carbon flux and stock changes. The current GHG observing system is addressing needs at two distinct scales: 1) Local scale (< 1 km), related to anthropogenic point source emissions, and 2) global scales (> 1000 km), related to land and ocean carbon sinks. More focus on intermediate (10–1000 km) scales is needed to more effectively monitor progress in reducing carbon emissions, enhancing removals, and maintaining sinks. Representatives from carbon cycle biomass and flux communities across United States government agencies and academic institutions met in September 2024 to discuss the rationale and scientific context for more effectively implementing an operational system for GHG monitoring in support of urban and national carbon management needs. To guide development of this system, we propose a multi-tiered global spaceborne observing framework for carbon flux and stock, prioritizing: 1) frequent GHG partial columns for carbon emissions and removals; 2) continuous time series and data fusion of biomass from Lidar and Synthetic Aperture Radar (SAR) for carbon stocks, and 3) expanded coverage of tropical, high latitude, and oceanic regions to monitor carbon cycle tipping points and feedbacks. This system should be complemented by expanded surface and airborne networks for oceanic and terrestrial/aquatic ecosystems for calibration, ground truthing, and study of under-sampled regions.
54 ENVIRONMENTAL SCIENCES↗
Digital Tools for the Preventive Conservation of Built Heritage: The Church of Santa Ana in Seville
Historic Building Information Modelling (HBIM) plays a pivotal role in heritage conservation endeavours, offering a robust framework for digitally documenting existing structures and supporting conservation practices. However, HBIM’s efficacy hinges upon the implementation of case-specific approaches to address the requirements and resources of each individual asset and context. This paper defines a flexible and generalisable workflow that encompasses various aspects (i.e., documentation, surveying, vulnerability assessment) to support risk-informed decision making in heritage management tailored to the peculiar conservation needs of the structure. This methodology includes an initial investigation covering historical data collection, metric and condition surveys and non-destructive testing. The second stage includes Finite Element Method (FEM) modelling and structural analysis. All data generated and processed are managed in a multi-purpose HBIM model. The methodology is tested on a relevant case study, namely, the church of Santa Ana in Seville, chosen for its historical significance, intricacy and susceptibility to seismic action. The defined level of detail of the HBIM model is sufficient to inform the structural analysis, being balanced by a more accurate representation of the alterations, through linked orthophotos and a comprehensive list of alphanumerical parameters. This ensures an adequate level of information, optimising the trade-off between model complexity, investigation time requirements, computational burden and reliability in the decision-making process. Field testing and FEM analysis provide valuable insight into the main sources of vulnerability in the building, including the connection between the tower and nave and the slenderness of the columns.
Chaves, Estefanía↗