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The Mineralogical and Chemical Case for Habitability at Yellowknife Bay, Gale Crater, Mars

Sediments of the Yellowknife Bay formation (Gale crater) include the Sheepbed member, a mudstone cut by light-toned veins. Two drill samples, John Klein and Cumberland, were collected and analyzed by the CheMin XRD/XRF instrument and the Sample Analysis at Mars (SAM) evolved gas and isotopic analysis suite of instruments. Drill cuttings were also analyzed by the Alpha Particle X-ray Spectrometer (APXS) for bulk composition. The CheMin XRD analysis shows that the mudstone contains basaltic minerals (Fe-forsterite, augite, pigeonite, plagioclase), as well as Fe-oxide/hydroxides, Fe-sulfides, amorphous materials, and trioctahedral phyllosilicates. SAM evolved gas analysis of higher-temperature OH matches the CheMin XRD estimate of ~20% clay minerals in the mudstone. The light-toned veins contain Ca-sulfates; anhydrite and bassanite are detected by XRD but gypsum is also indicated from Mastcam spectral mapping. These sulfates appear to be almost entirely restricted to late-diagenetic veins. The sulfate content of the mudstone matrix itself is lower than other sediments analyzed on Mars. The presence of phyllosilicates indicates that the activity of water was high during their formation and/or transport and deposition (should they have been detrital). Lack of chlorite places limits on the maximum temperature of alteration (likely <100 C). The presence of Ca-sulfates rather than Mg- or Fe-sulfates suggests that the pore water pH was near-neutral and of relatively low ionic strength (although x-ray amorphous Mg-and Fe- sulfates could be present and undetectable by CheMin). The presence of Fe and S in both reduced and oxidized states represents chemical disequilibria that could have been utilized by chemolithoautotrophic biota, if present. When compared to the nearby Rocknest sand shadow mineralogy or the normative mineralogy of Martian soil, both John Klein and Cumberland exhibit a near-absence of olivine and a surplus of magnetite (7-9% of the crystalline component). The magnetite is interpreted as an authigenic product formed when olivine was altered to phyllosilicate. Saponitization of olivine (a process analogous to serpentinization) could have produced H2 in situ. Indeed, early diagenetic hollow nodules ("minibowls") present in the Cumberland mudstone are interpreted by some as forming when gas bubbles accumulated in the unconsolidated mudstone. Lastly, all of these early diagenetic features appear to have been preserved with minimal alteration since their formation, as indicated by the ease of drilling (weak lithification, lack of cementing phases), the presence of 20-30% amorphous material, and the late-stage fracturing with emplacement of calcium sulfate veins and minibowl infills, where they were intersected by veins. A rough estimate of the minimum duration of the lacustrine environment is provided by the minimum thickness of the Sheepbed member. Given 1.5 meters, and applying a mean sediment accumulation rate for lacustrine strata of 1 m/1000 yrs yields a duration of 1,500 years. If the aqueous environments represented by overlying strata are considered, such as Gillespie Lake and Shaler, then this duration increases. The Sheepbed mudstone meets all the requirements of a habitable environment: Aqueous deposition at clement conditions of P, T, pH, Eh and ionic strength, plus the availability of sources of chemical energy.

Blake, David Frederick↗

The Stability of Bioactive Compounds in Spaceflight Foods

The status and stability of bioactive compounds in the processed and shelf-stable spaceflight food system have not previously been investigated though the presence of such compounds in aged space foods could have health significance for crews on long duration exploration missions. Over forty foods - either existing International Space Station (ISS) food provisioning items, newly developed foods for spaceflight, or commercially-available ready-to-eat foods - that were predicted to have a relatively high concentrations of one or more bioactive compounds (lycopene, lutein, omega-3 fatty acids, phenolics, sterols, and/or flavonoids) were selected for the study. Food samples were sent overnight to the Food Composition Laboratory of the Linus Pauling Institute at Oregon State University (Corvallis, OR) for bioactive compound analysis. Three packages of each product were blended together for the analysis to reduce package-to-package variability. All ISS food items and commercial foods were analyzed initially and after 12 and 24 months of 21degC storage. Food development occurred in a staggered fashion, so data collection for the newly developed foods continues. Lastly, sensory evaluation and additional temperature storage data (4degC, 35degC) for select foods were collected to establish additional stability parameters. Efficacious concentrations of lycopene, lutein, and omega-3 fatty acids were measured in limited spaceflight foods; two grams of sterols a day may be difficult to achieve with the current space diet. Total polyphenol delivery appears stable and adequate, but individual phenolic compounds vary in stability and were not specifically evaluated in this study. The data suggests that some bioactive compounds, like lycopene and lutein, degrade and then plateau at some equilibrium concentration. The anthocyanin stability appears to be related to storage temperature and food matrix, and lutein stability in leafy vegetables may be impacted by storage temperature. Because of the limited number of foods with high concentrations of the bioactive compounds, additional menu variety, formulation optimization, and reduced temperature storage will be required to ensure delivery of several bioactive compounds in the space food system. Validation of stability to five years will enable provisioning of these functional foods within the space food system for a mission to Mars.

Cooper, M. R.↗

First measurement of the cross section for top quark pair production with additional charm jets using dileptonic final states in pp collisions at $\sqrt{s}$= 13 TeV

The first measurement of the inclusive cross section for top quark pairs ($t\bar{t}$) produced in association with two additional charm jets is presented. The analysis uses the dileptonic final states of $t\bar{t}$ events produced in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 41.5 fb -1 recorded by the CMS experiment at the LHC. A new charm jet identification algorithm provides input to a neural network that is trained to distinguish among $t\bar{t}$ events with two additional charm ($t\bar{t}c\bar{c}$), bottom ($t\bar{t}b\bar{b}$), and light-flavour or gluon ($t\bar{t}LL$) jets. By means of a template fitting procedure, the inclusive $t\bar{t}c\bar{c}$, $t\bar{t}b\bar{b}$, and $t\bar{t}LL$ cross sections are simultaneously measured, together with their ratios to the inclusive $t\bar{t}$ + two jets cross section. This provides measurements of the $t\bar{t}c\bar{c}$ and $t\bar{t}b\bar{b}$ cross sections of 10.1 ± 1.2 (stat) ± 1.4 (syst) pb and 4.54 ± 0.35 (stat) ± 0.56 (syst) pb, respectively, in the full phase space. The results are compared and found to be consistent with predictions from two different matrix element generators with next-to-leading order accuracy in quantum chromodynamics, interfaced with a parton shower simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A 28 nm multiply-accumulate ASIC architecture for on-chip data compression in MHz frame rate X-ray and electron pixel detectors

Modern X-ray detector systems urgently require compact, efficient, and fast data compression schemes to handle the transmission of big data from pixel arrays, enabling frame rates in the MHz regime. Here, in this work, a data compression ASIC that implements a streaming fixed-length lossy compression scheme is introduced and analyzed, proving the feasibility and benefits of on-chip compression. The compression scheme utilizes a vector matrix product logic, which performs a number of floating-point multiplications, additions, and accumulations. The logic is verified, synthesized, and shown to fit in the area resource available for the X-ray detector under study, which comprises 192 × 168 pixels each of 12-bit width, and having a total area of 20 mm× 20 mm, about 2 mm× 20 mm of which are available for the digital logic. Several system architectures, precisions, and compression ratios ranging from 100 to 250 were analyzed to pave the way for on-chip fixed-length compression (e.g., principal component analysis, singular value decomposition) and data reduction (e.g., azimuthal integration) for X-ray and electron detectors.

Data compression↗

Plutonium migration and phase evolution in irradiated U-Pu-Zr metallic fuels: An integrated EPMA-SEM-TEM study

Constituent redistribution is a defining feature of irradiated U-Pu-Zr metallic fuels, yet its mechanisms and effects on fuel performance are not sufficiently resolved to guide model development. Although decades of irradiation testing have established broad trends, a true mechanistic understanding of constituent redistribution has not been achieved. Here, in this study, we use electron probe microanalysis (EPMA), scanning electron microscopy (SEM), and transmission electron microscopy-based (TEM) selective area electron diffraction (SAED) on a EBR-II irradiated U-19 wt.% Pu-6 wt.% Zr fuel pin cross-section to correlate the composition, porosity, and crystallographic phases formed after irradiation. Constituent redistribution is thought to consist of three distinct zones, in which uranium and zirconium migrate while plutonium remains relatively unchanged. Our EPMA results resolve eight distinct compositional regions, and more importantly, show that plutonium redistributes alongside zirconium, contrary to historical assumptions. The distribution of fission products was highly asymmetric with a few large lanthanide precipitates observed at isolated sites on the pin periphery instead of a uniform distribution of smaller precipitates around the periphery. Using thermodynamic data from TAF-ID and the measured EPMA compositions, matrix phase fractions were predicted across the fuel radius. Phase predictions based on composition did not match TEM/SAED results, which revealed a much higher fraction of α−U phase than would be expected if phases were retained from reactor temperatures. These findings highlight the need for expanded SAED phase identification to capture post-irradiation and storage effects, as well as rigorous uncertainty quantification in fuel performance and phase diagram modeling to better constrain predictions from compositional data.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Probing quantum entanglement with generalized parton distributions at the Electron-Ion Collider

Within the collinear factorization framework based on generalized parton distributions, we calculate the spin density matrix of exclusively produced quark and antiquark pairs $𝑢\bar{𝑢}$, $𝑑⁢\bar{d}$, $𝑠⁢\bar{𝑠}$, $𝑐\bar{⁢𝑐}$, $𝑏\bar{𝑏}$ in electron-proton scattering. The presence of both real and imaginary parts in the scattering amplitudes leads to a rich pattern of entanglement between the quark and the antiquark. We map out kinematical regions where the pairs exhibit entanglement, Bell nonlocality, and nonstabilizerness. We also predict that massive quarks and antiquarks are transversely polarized, similar to the well-known transverse hyperon polarization in unpolarized collisions. In strangeness, charm, and bottom productions, the polarization can reach 50%–80% in certain kinematic regions in the low-energy runs of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A System-Level Cost Modeling Framework for Design for Remanufacturing: A Case Study of an Agricultural Machine Transmission

Remanufacturing offers significant environmental and economic benefits by restoring end-of-life products to as-new conditions. Although extensive research has been conducted on the topic, the adoption of remanufacturing practices remains limited across various industries. A primary barrier to broader implementation is the substantial upfront investment required, which necessitates reliable cost modeling to justify potential future savings. Most existing models treat components independently and ignore inter-component dependencies. We develop a probabilistic, system-level cost modeling framework that integrates reliability, reusability, and a dependency matrix to capture cascading effects across components over multiple life cycles. Our model identifies those critical components that maximize remanufacturing benefits across a product's many lives. A toy example and an industry case study (John Deere PowrQuad transmission subassembly) illustrate how design alternatives affect cumulative cost. Using a Monte Carlo simulation (MCS) to perform life cycle cost analysis on the system with different design changes, we show the normalized average cost savings after three remanufacturing cycles. Accounting for dependencies meaningfully alters cost projections and ignoring them underestimates accumulated cost by up to 20% in our examples. Furthermore, the results of our study confirm that accounting for component interdependencies is necessary to produce cost estimates that meet industry standards.

Life Cycle Analysis and Design↗

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Microstructural and Rheological Transitions in Bacterial Biofilms

Biofilms are aggregated bacterial communities structured within an extracellular matrix (ECM). ECM controls biofilm architecture and confers mechanical resistance against shear forces. From a physical perspective, biofilms can be described as colloidal gels, where bacterial cells are analogous to colloidal particles distributed in the polymeric ECM. However, the influence of the ECM in altering the cellular packing fraction (Φ) and the resulting viscoelastic behavior of biofilm remains unexplored. Using biofilms of Pantoea sp. (WT) and its mutant (ΔUDP), the correlation between biofilm structure and its viscoelastic response is investigated. Experiments show that the reduction of exopolysaccharide production in ΔUDP biofilms corresponds with a seven-fold increase in Φ, resulting in a colloidal glass-like structure. Consequently, the rheological signatures become altered, with the WT behaving like a weak gel, whilst the ΔUDP displayed a glass-like rheological signature. By co-culturing the two strains, biofilm Φ is modulated which allows us to explore the structural changes and capture a change in viscoelastic response from a weak to a strong gel, and to a colloidal glass-like state. The results reveal the role of exopolysaccharide in mediating a structural transition in biofilms and demonstrate a correlation between biofilm structure and viscoelastic response.

viscoelasticity↗

Single-Transducer, Ultrasonic Imaging Method for High-Temperature Structural Materials Eliminates the Effect of Thickness Variation in the Image

NASA Lewis Research Center's Life Prediction Branch, in partnership with Sonix, Inc., and Cleveland State University, recently advanced the development of, refined, and commercialized an advanced nondestructive evaluation (NDE) inspection method entitled the Single Transducer Thickness-Independent Ultrasonic Imaging Method. Selected by R&D Magazine as one of the 100 most technologically significant new products of 1996, the method uses a single transducer to eliminate the superimposing effects of thickness variation in the ultrasonic images of materials. As a result, any variation seen in the image is due solely to microstructural variation. This nondestructive method precisely and accurately characterizes material gradients (pore fraction, density, or chemical) that affect the uniformity of a material's physical performance (mechanical, thermal, or electrical). Advantages of the method over conventional ultrasonic imaging include (1) elimination of machining costs (for precision thickness control) during the quality control stages of material processing and development and (2) elimination of labor costs and subjectivity involved in further image processing and image interpretation. At NASA Lewis, the method has been used primarily for accurate inspections of high temperature structural materials including monolithic ceramics, metal matrix composites, and polymer matrix composites. Data were published this year for platelike samples, and current research is focusing on applying the method to tubular components. The initial publicity regarding the development of the method generated 150 requests for further information from a wide variety of institutions and individuals including the Federal Bureau of Investigation (FBI), Lockheed Martin Corporation, Rockwell International, Hewlett Packard Company, and Procter & Gamble Company. In addition, NASA has been solicited by the 3M Company and Allison Abrasives to use this method to inspect composite materials that are manufactured by these companies.

Roth, Don J.↗

Unravelling the origins of shale nanoporosity using small-angle neutron scattering (SANS)

Hydrocarbon production from tight rocks is constrained by slow diffusion within the shale matrix, limited by small pore sizes and low permeability. The nanopore proportion and size distribution significantly influence matrix permeability, a key property for optimizing hydrocarbon recovery and supporting hydrogen production while minimizing environmental impacts. Small-angle neutron scattering (SANS) has been an important tool for exploring the characteristics and structure of shale nanopores. This study used SANS to analyze nanoporosity and pore size distribution (<100 nm) in tight rocks with varying compositions to determine the influence of rock heterogeneity on SANS measurements. Results showed that nanoporosity correlates with clay content, with the highest clay-rich shale (52.48 wt% clay) exhibiting 8.8 % nanoporosity. SANS also revealed more nanopores than traditional nitrogen adsorption measurements, affirming its ability to reflect bulk mineralogy and upholding the relevance of experimental findings using this technique to optimize field operational approaches.

03 NATURAL GAS↗

Nuclear Fuel and Pu Redox Studies from The Glenn T. Seaborg Institute at Idaho National Laboratory

The Glenn T. Seaborg Institute at Idaho National Laboratory (INL-GTSI) focuses on advancing fundamental research in the actinide sciences by providing unique opportunities to early career scientists and engineers to gain experience studying the actinide elements and their associated systems. The INL-GTSI is built from three focus areas that are based on the expertise and supporting infrastructure at INL and include solid state chemistry and physics, solution phase chemistry and physics, and forensic and isotope science. INL is the lead Laboratory for nuclear energy research and development in the U. S. and the research on nuclear fuels performed under the INL-GTSI gives good examples of solid state studies. Uranium-Molybdenum (U-Mo) alloys are leading fuel candidates for conversion of high performance research and test reactors to low-enriched fuels. During irradiation, generated fission gas accumulates into bubbles and self-organizes into a gas bubble superlattice (GBS) that effectively stores fission gases and inhibits fuel swelling. A study on the early self- organizing behavior of the GBS shows that not only grain boundaries but the interfaces between the U-Mo matrix and uranium carbide (UC) impurities are important to GBS formation.[1] In solution, understanding the complex redox behavior of plutonium in aqueous environments is critical for establishing optimized nuclear waste reprocessing solvent systems and storage tank environments. INL-GTSI researchers have produced an experimentally validated multi-scale model of the gamma radiation induced behavior of plutonium ions in concentrated aqueous HNO3 solutions.[2] Here, gamma radiation effected only minimal steady state changes in the redox distribution of the plutonium oxidation states. The redox cycling between Pu(IV) and Pu(III) is demonstrated to be mediated by the •OH/NO3• radical oxidation of Pu(III) and the H2O2/HNO3 driven reduction of Pu(IV). The INL-GTSI offers young researchers the unique chance to work directly with actinide bearing materials in a U. S. National Laboratory environment. Further topical areas of interest to the INL-GTSI include, but are not limited to, fundamental actinide properties, structure/property (electronic, magnetic, thermal) relations, actinide quantum criticality, f- electron interactions, electron correlations, computational studies, new phases, defect effects, interface interactions, isotope production and separation, forensic analytical chemistry, structure and dynamic properties of actinides in non-aqueous media, separations chemistry and kinetics for advanced nuclear fuel cycles, radiation effects, and innovative and advanced ligand design for complexation of the actinides.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dissociative Recombination (DR) and Associative Ionization (AI) Cross Section Calculations for the NO+ + e yields N + O (2D+3P, 2P+3P, and 2D+1D) Reaction for Atmospheric Entry Modeling

During entry of a space craft into Earth atmosphere, the flow surrounding the vehicle becomes partially ionized leading to significant cation and free-electron production. Subsequently, electron impact excitation and dissociation form radiating excited state species that contribute to the heat load on the vehicle. While experimental data on selected total cross sections are available, few experiments address the need for accurate AI cross sections for metastable atomic states at the high temperatures realized in atmospheric re-entry. In order to maintain desired safety margins during atmospheric entry of a space vehicle, chemical reaction models need to accurately account for this process. For the present study, we have computed vibrationally resolved cross sections for the DR of NO+ for electron energies between 0.01 to 10 eV and apply microscopic reversibility to obtain the AI cross sections and rate coefficients. For the DR cross section calculations, we use state-of-the-art MRCI potential energy curves. The resulting adiabatic potential curves are transformed to a diabatic representation, which is used in time-dependent wave packet calculations to describe the nuclear motion of the dissociating cation upon collision with an electron. Based on the wave function evolution in time, these calculations provide T-matrix and cross sections for the DR including recombination into the low energy metastable atomic states. The DR and AI rate coefficients are compared with the available experimental data.

Ewa Papajak↗

Chemical durability assessment of enhanced low-activity waste glasses through EPA method 1313

In this work, we report the progress of the Glass Leaching Assessment for Durability (GLAD) program on the implementation of the United States Environmental Protection Agency (EPA) Leaching Environmental Assessment Framework pH-dependent leach test (EPA Method 1313) to low-activity nuclear waste (LAW) glasses. The GLAD program seeks to develop new strategies to understand the chemical durability of nuclear waste glasses for the disposal in near-surface conditions. A series of 16 high-waste loading LAW glasses, currently under development, were selected using machine learning methods to study the corrosion behavior using EPA Method 1313. Reacted glass powders were examined using scanning electron microscopy and the eluate compositions were examined using inductively coupled plasma-optical emission spectroscopy. Compositional modeling was used to fit the measured elemental releases from EPA Method 1313. The compositional models demonstrated that elements such as Si reduce elemental release while B can increase elemental release (consistent with elemental modeling of the Product Consistency Test and Vapor Hydration Test) while other elements, such as Fe, exhibit pH-dependent behavior. The amount of acid added during the EPA testing was found to significantly impact the observed result, which was only apparent after preforming the present matrix study. The overall titration curves were able to be compositionally modeled for future process optimization.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

High-Temperature SiC Cladding Bowing Irradiation Design and HFIR Readiness

Silicon carbide fiber–reinforced silicon carbide (SiC/SiC) matrix composites are candidate materials for long-term accident-tolerant fuel cladding for use in light water reactors (LWRs). This report documents the design of a dry SiC/SiC composite cladding bowing experiment intended for irradiation in the High Flux Isotope Reactor. The dry experiment allows for testing at representative LWR temperatures for comparison to previous experimental results. This report describes detailed neutronics, thermal, and bowing analyses supporting the irradiation. The design leverages calculations from previous irradiation experiments and production targets for reduced design complexity. The thermal analysis provides a map of SiC thermometer temperatures for comparison during post-irradiation examination to determine the experiment’s irradiation temperatures. Finally, two concepts for introducing localized constraints representative of pressurized water reactor grid spacers are presented.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Cyclotron production of a 204 Bi/ 204m Pb generator by 24 MeV proton irradiation of natural Pb foil targets

This work focuses on the formation of a generator of 204 Bi/ 204m Pb for future applications in perturbed angular correlation spectroscopy and biological radiotracing with lead and bismuth isotopes. Generators were formed from the irradiation of natural Pb targets with 24 MeV protons producing 203,204,205,206,207 Bi that were rapidly dissolved in 3 M HNO 3 and 30 % H 2 O 2 and exchanged into a 0.1 M HCl matrix. Use of 100 mg anion exchange resin (AG 1-x8) allowed 203,204m Pb to be eluted in 600 μL of 0.1 M HCl. Furthermore, the longer-lived 205,206 Bi were eluted in 5 mL or 3 mL of either 0.25 M sodium acetate buffer pH 4.4 or 1.0 M H 2 SO 4 . Initial radiolabeling was conducted with eluted 206 Bi using DTPA and DOTA and 203 Pb using TCMC-Azide.

07 ISOTOPE AND RADIATION SOURCES↗

Reservoir-scale model of geologic hydrogen production from serpentinization: Cyclic injection in a dual-permeability fracture-matrix system

Geologic hydrogen (GeoH 2 ) from serpentinization is a promising low-carbon resource, but its reservoir-scale behavior remains poorly understood. We develop a dual-permeability reactive transport model for an injector–producer well pair in ultramafic rock that couples multiphase flow, heat transfer, geochemistry, and porosity–permeability evolution. Here, the model is calibrated to olivine flow-through experiments and upscaled to two-year long simulations with continuous injection and cyclic injection with shut-in-to-injection ratios (SIR = 1, 0.5, 0.1). Olivine reacts along high-flux pathways to form lizardite and magnetite, increasing pH; H 2 (aq) and H 2 (g) peak early and then decline as exsolution and advective export outpace local generation. Continuous injection yields the highest cumulative H 2 but the lowest water-use efficiency (1.138 x 10 –6 mol/kgw). Cyclic injection increases this ratio to 1.35 x 10 –6 , 1.377 x 10 –6 , and 1.182 x 10 –6 mol/kgw for SIR = 1, 0.5, and 0.1, respectively; SIR = 0.5 provides a ~20% improvement over continuous injection and the best compromise for pilot design.

08 HYDROGEN↗

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗