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NASA NTRS2010

Modeling Common-Sense Decisions in Artificial Intelligence

A methodology has been conceived for efficient synthesis of dynamical models that simulate common-sense decision- making processes. This methodology is intended to contribute to the design of artificial-intelligence systems that could imitate human common-sense decision making or assist humans in making correct decisions in unanticipated circumstances. This methodology is a product of continuing research on mathematical models of the behaviors of single- and multi-agent systems known in biology, economics, and sociology, ranging from a single-cell organism at one extreme to the whole of human society at the other extreme. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the three most recent and relevant being Characteristics of Dynamics of Intelligent Systems (NPO -21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; Self-Supervised Dynamical Systems (NPO-30634), NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72; and Complexity for Survival of Living Systems (NPO- 43302), NASA Tech Briefs, Vol. 33, No. 7 (July 2009), page 62. The methodology involves the concepts reported previously, albeit viewed from a different perspective. One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Models of motor dynamics are used to simulate the observable behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. Autonomy is imparted to the decisionmaking process by feedback from mental to motor dynamics. This feedback replaces unavailable external information by information stored in the internal knowledge base. Representation of the dynamical models in a parameterized form reduces the task of common-sense-based decision making to a solution of the following hetero-associated-memory problem: store a set of m predetermined stochastic processes given by their probability distributions in such a way that when presented with an unexpected change in the form of an input out of the set of M inputs, the coupled motormental dynamics converges to the corresponding one of the m pre-assigned stochastic process, and a sample of this process represents the decision.

Zak, Michail↗

NASA NTRS2018

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗

NASA NTRSDate not supplied

TPSAS-NF1676L-27509-DND

The information about composition of aerosols has a great importance for monitoring and understanding of climate and environment dynamics. Such information can be obtained using situ measurements or chemical transport models. However, in situ sampling has limited spatial and temporal coverage, while estimations have large uncertainties. The present work enables the monitoring of aerosol chemical species from space-borne observations, providing observationally-based results with spatial and temporal coverage. Following the ideas of Schuster et al.(2005, 2009, 2016), we retrieve chemical composition directly from satellite observations without intermediate retrieval of the refractive index (in contrast with Schuster's approach). This approach is expected to reduce the influence of modeling uncertainties, and to provide additional constraints in situations where remote sensing observations do not have enough spectral sensitivity to refractive index. One of principal difficulties is the identification of an adequate model for linking refractive index to chemical composition. Therefore, the initial effort of this work has focused on identifying an optimal physico-chemistry to refractive index conversion model. With that purpose, we first tested the retrieval approach using a simplified volume-weighting model and updated by the Maxwell Garnett mixing model. This concept was incorporated into the GRASP algorithm designed to retrieve an extended set of atmospheric parameters from remote sensing observations. Then a series of sensitivity tests using synthetic data of POLDER/PARASOL were conducted, and followed by inversion of real PARASOL observations over Africa. The sensitivity tests showed that these two models allow the retrieval to distinguish amongst the assumed chemical species. Results obtained from real PARASOL data demonstrated good agreement with the optical characteristics provided by AERONET. In addition, the obtained patterns of chemical component distribution agreed with known physical expectations. We also compared the chemical composition retrievals to GOCART model simulations and obtained good consistencies.

Lei Li↗

DOE OSTI2015

Nano-Composite Material Development for 3-D Printers

Graphene possesses excellent mechanical properties with a tensile strength that may exceed 130 GPa, excellent electrical conductivity, and good thermal properties. Future nano-composites can leverage many of these material properties in an attempt to build designer materials for a broad range of applications. 3-D printing has also seen vast improvements in recent years that have allowed many companies and individuals to realize rapid prototyping for relatively low capital investment. This research sought to create a graphene reinforced, polymer matrix nano-composite that is viable in commercial 3D printer technology, study the effects of ultra-high loading percentages of graphene in polymer matrices and determine the functional upper limit for loading. Loadings varied from 5 wt. % to 50 wt. % graphene nanopowder loaded in Acrylonitrile Butadiene Styrene (ABS) matrices. Loaded sample were characterized for their mechanical properties using three point bending, tensile tests, as well as dynamic mechanical analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Radioactive Material Inventory Optimization Using the Plutonium-239 Equivalent Curie Methodology

ABSTRACT The purpose of this paper is to provide the technical basis for application of the Plutonium 239 equivalent curies (PEC) concept used to optimize and limit the material-at-risk (MAR) in the Irradiated Materials Characterization Laboratory (IMCL) located at the Materials and Fuels Complex (MFC). The PEC concept offers a method to normalize all radionuclides to a common radiotoxic hazard index that can be summed to a single value. This paper describes the technical approach to applying the PEC concept, documents the weighting factors and specific activities to be utilized in the calculation, and provides an example of the application of the concept to a radionuclide distribution that is representative of materials encountered in the IMCL. The IMCL is operated to provide a dynamic, re-configurable capability to analyze and characterize irradiated or non-irradiated radioactive material samples. The operations unique to the IMCL include sample storage, preparation, and analysis using experiment-specific instrumentation such as, Electron probe micro-analyzer (EPMA), Focused ion beam (FIB), Transmission electron microscope (TEM), and Scanning electron microscope (SEM). The methodology used to characterize the radioactive material inventory enables the IMCL to operate in such a way that complements their capability and program goals without compromising the safety of the worker, co-located worker, or the general public. The PEC concept offers a method in which all radionuclide inventory is normalized to a common radiotoxic hazard index that can be summed to a single value. The PEC concept is useful in the comparison of various material types for hazard categorization and for identifying worst-case and bounding inventory.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2020

Understanding the Structure and Dynamics of Complex Biomembrane Interactions by Neutron Scattering Techniques

The membrane is one of the key structural materials of biology at the cellular level. Composed predominantly of a bilayer of lipids with embedded and bound proteins, it defines the boundaries of the cell and many organelles essential to life and therefore is involved in almost all biological processes. Membrane-specific interactions, such as drug binding to a membrane receptor or the interactions of an antimicrobial compound with the lipid matrix of a pathogen membrane, are of interest across the scientific disciplines. Herein we present a review, aimed at nonexperts, of the major neutron scattering techniques used in membrane studies: small-angle neutron scattering, neutron membrane diffraction, neutron reflectometry, quasielastic neutron scattering, and neutron spin echo. Neutron scattering techniques are well suited to studying biological membranes. The nondestructive nature of cold neutrons means that samples can be measured for long periods without fear of beam damage from ultraviolet, electron, or X-ray radiation, and neutron beams are highly penetrating, thus offering flexibility in samples and sample environments. Most important is the strong difference in neutron scattering lengths between the two most abundant forms of hydrogen, protium and deuterium. Changing the relative amounts of protium/deuterium in a sample allows the production of a series of neutron scattering data sets, enabling the observation of differing components within complex membrane architectures. This approach can be as simple as using the naturally occurring neutron contrast between different biomolecules to study components in a complex by changing the solution H 2 O/D 2 O ratio or as complex as selectively labeling individual components with hydrogen isotopes. This review presents an overview of each experimental technique with the neutron instrument configuration, related sample preparation and sample environment, and data analysis, highlighted by a special emphasis on using prominent neutron contrast to understand structure and dynamics. This review gives researchers a practical introduction to the often enigmatic suite of neutron beamlines, thereby lowering the barrier to taking advantage of these large-facility techniques to achieve new understandings of membranes and their interactions with other molecules.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2015

Avalanching strain dynamics during the hydriding phase transformation in individual palladium nanoparticles

Phase transitions in reactive environments are crucially important in energy and information storage, catalysis and sensors. Nanostructuring active particles can yield faster charging/ discharging kinetics, increased lifespan and record catalytic activities. However, establishing the causal link between structure and function is challenging for nanoparticles, as ensemble measurements convolve intrinsic single-particle properties with sample diversity. Here we study the hydriding phase transformation in individual palladium nanocubes in situ using coherent X-ray diffractive imaging. The phase transformation dynamics, which involve the nucleation and propagation of a hydrogen-rich region, are dependent on absolute time (aging) and involve intermittent dynamics (avalanching). A hydrogen-rich surface layer dominates the crystal strain in the hydrogen-poor phase, while strain inversion occurs at the cube corners in the hydrogen-rich phase. A three-dimensional phase-field model is used to interpret the experimental results. In conclusion, our experimental and theoretical approach provides a general framework for designing and optimizing phase transformations for single nanocrystals in reactive environments.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗

DOE OSTI2023

Nanoparticle Diffusion in Miscible Polymer Nanocomposite Melts

X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2R g , where R g is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2015

Coherent pulse interrogation system for fiber Bragg grating sensing of strain and pressure in dynamic extremes of materials

A 100 MHz fiber Bragg grating (FBG) interrogation system is described and applied to strain and pressure sensing. The approach relies on coherent pulse illumination of the FBG sensor with a broadband short pulse from a femtosecond modelocked erbium fiber laser. After interrogation of the FBG sensor, a long multi-kilometer run of single mode fiber is used for chromatic dispersion to temporally stretch the spectral components of the reflected pulse from the FBG sensor. Dynamic strain or pressure induced spectral shifts in the FBG sensor are detected as a pulsed time domain waveform shift after encoding by the chromatic dispersive line. Signals are recorded using a single 35 GHz photodetector and a 50 G Samples per second, 25 GHz bandwidth, digitizing oscilloscope. Application of this approach to high-speed strain sensing in magnetic materials in pulsed magnetic fields to ~150 T is demonstrated. The FBG wavelength shifts are used to study magnetic field driven magnetostriction effects in LaCoO₃. A sub-microsecond temporal shift in the FBG sensor wavelength attached to the sample under first order phase change appears as a fractional length change (strain: ΔL/L<10⁻⁴) in the material. A second application used FBG sensing of pressure dynamics to nearly 2 GPa in the thermal ignition of the high explosive PBX-9501 is also demonstrated. Both applications demonstrate the use of this FBG interrogation system in dynamical extreme conditions that would otherwise not be possible using traditional FBG interrogation approaches that are deemed too slow to resolve such events.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Towards the Accurate Thermodynamic Characterization of Enzyme Reaction Mechanisms

We employed QM/MM molecular dynamics (MD) simulations to characterize the rate-limiting step of the glycosylation reaction of pancreatic α-amylase with combined DFT/molecular dynamics methods (PBE/def2-SVP : AMBER). Upon careful choice of four starting active site conformations based on thorough reactivity criteria, Gibbs energy profiles were calculated with umbrella sampling simulations within a statistical convergence of 1 -2 kcal · mol -1 . Nevertheless, Gibbs activation barriers and reaction energies still varied from 11.0 to 16.8 kcal · mol -1 and -6.3 to +3.8 kcal · mol -1 depending on the starting conformations, showing that despite significant state-of-the-art QM/MM MD sampling (0.5 ns/profile) the result still depends on the starting structure. In conclusion, the results supported the one step dissociative mechanism of Asp197 glycosylation preceded by an acid-base reaction by the Glu233, which are qualitatively similar to those from multi-PES QM/MM studies, and thus support the use of the latter to determine enzyme reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

SU-G-JeP1-15: Sliding Window Prior Data Assisted Compressed Sensing for MRI Lung Tumor Tracking

Purpose: Prior Data Assisted Compressed Sensing (PDACS) is a partial k-space acquisition and reconstruction method for mobile tumour (i.e. lung) tracking using on-line MRI in radiotherapy. PDACS partially relies on prior data acquired at the beginning of dynamic scans, and is therefore susceptible to artifacts in longer duration scan due to slow drifts in MR signal. A novel sliding window strategy is presented to mitigate this effect. Methods: MRI acceleration is simulated by retrospective removal of data from the fully sampled sets. Six lung cancer patients were scanned (clinical 3T MRI) using a balanced steady state free precession (bSSFP) sequence for 3 minutes at approximately 4 frames per second, for a total of 650 dynamics. PDACS acceleration is achieved by undersampling of k-space in a single pseudo-random pattern. Reconstruction iteratively minimizes the total variations while constraining the images to satisfy both the currently acquired data and the prior data in missing k-space. Our novel sliding window technique (SW-PDACS), uses a series of distinct pseudo-random under-sampling patterns of partial k-space – with the prior data drawn from a sliding window of the most recent data available. Under-sampled data, simulating 2 – 5x acceleration are reconstructed using PDACS and SW-PDACS. Three quantitative metrics: artifact power, centroid error and Dice’s coefficient are computed for comparison. Results: Quantitively metric values from all 6 patients are averaged in 3 bins, each containing approximately one minute of dynamic data. For the first minute bin, PDACS and SW-PDACS give comparable results. Progressive decline in image quality metrics in bins 2 and 3 are observed for PDACS. No decline in image quality is observed for SW-PDACS. Conclusion: The novel approach presented (SW-PDACS) is a more robust for accelerating longer duration (>1 minute) dynamic MRI scans for tracking lung tumour motion using on-line MRI in radiotherapy. B.G. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Dynamic Succession of Groundwater Sulfate-Reducing Communities during Prolonged Reduction of Uranium in a Contaminated Aquifer

To further understand the diversity and dynamics of SRB in response to substrate amendment, we sequenced genes coding for the dissimilatory sulfite reductase (dsrA) in groundwater samples collected after an emulsified vegetable oil (EVO) amendment, which sustained U(VI)-reducing conditions for one year in a fast-flowing aquifer. EVO amendment significantly altered the composition of groundwater SRB communities. Sequences having no closely related-described species dominated (80%) the indigenous SRB communities in nonamended wells. After EVO amendment, Desulfococcus , Desulfobacterium , and Desulfovibrio , known for long-chain-fatty-acid, short-chain-fatty-acid and H 2 oxidation and U(VI) reduction, became dominant accounting for 7 ± 2%, 21 ± 8%, and 55 ± 8% of the SRB communities, respectively. Succession of these SRB at different bioactivity stages based on redox substrates/products (acetate, SO 4 –2 , U(VI), NO 3 – , Fe(II), and Mn(II)) was observed. Desulfovibrio and Desulfococcus dominated SRB communities at 4–31 days, whereas Desulfobacterium became dominant at 80–140 days. By the end of the experiment (day 269), the abundance of these SRB decreased but the overall diversity of groundwater SRB was still higher than non-EVO controls. Up to 62% of the SRB community changes could be explained by groundwater geochemical variables, including those redox substrates/products. A significant ( P < 0.001) correlation was observed between groundwater U(VI) concentrations and Desulfovibrio abundance. Lastly, our results showed that the members of SRB and their dynamics were correlated significantly with slow EVO biodegradation, electron donor production and maintenance of U(VI)-reducing conditions in the aquifer.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Horizontal 1 K refrigerator with novel loading mechanism for polarized solid targets

We describe a helium evaporation refrigerator used to cool dynamically polarized proton and deuteron targets for electron-scattering experiments using the CEBAF Large Acceptance Spectrometer CLAS12 at Jefferson Lab. The geometry of the CLAS12 detector systems places severe design and construction constraints on the refrigerator and its ancillary equipment, resulting in a horizontal cryostat with a length of 4 m. The 16 cm 3 target samples, consisting of frozen ammonia (NH 3 or ND 3 ), are loaded at the upstream end of the cryostat and moved to the beam-interaction region using a novel transport mechanism. At this location they are cooled with superfluid helium and polarized via dynamic nuclear polarization at 1 K and 5 T. In this manner samples can be replaced and cooled to 1 K in about 30 minutes without disturbing any elements of the electron beam line or particle detection system. In conclusion, we estimate that this method saved 18 days of valuable beam time over the course of a recent, 88-day long experiment.

Evaporation refrigerator↗

NASA NTRS2018

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

numerical analysi↗

DOE OSTI2022

Multitask Machine Learning of Collective Variables for Enhanced Sampling of Rare Events

Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space and separate downstream parts map the latent space to predictions of basin class labels and potential energies. Here, the resulting latent space is shown to be an effective low-dimensional representation, capturing the reaction progress and guiding effective umbrella sampling to obtain accurate free energy landscapes. This approach is successfully applied to model systems including a 5D Müller Brown model, a 5D three-well model, the alanine dipeptide in vacuum, and an Au(110) surface reconstruction unit reaction. It enables automated dimensionality reduction for energy controlled reactions in complex systems, offers a unified and data-efficient framework that can be trained with limited data, and outperforms single-task learning approaches, including autoencoders.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Establishing temperature from radiance of dynamically compressed metals

Precise temperature determination is a significant challenge in extreme environments of dynamic compression studies. How can radiance measurements taken in high-pressure shock experiments constrain temperature in a meaningful and physically consistent way? Experiments maintaining sample compression against a transparent window can be tailored to present a uniform measurement area with uncertain spectral emissivity. We compare several methods to analyze radiance collected at multiple wavelengths, applying statistical methods and physical principles to improve temperature inference. With proper radiance collection and analysis, dynamic temperature uncertainties become comparable to thermomechanical ambiguities of the emitting surface.

36 MATERIALS SCIENCE↗

NASA NTRS2016

The Atacama Cosmology Telescope: Dynamical Masses for 44 SZ-Selected Galaxy Clusters over 755 Square Degrees

We present galaxy velocity dispersions and dynamical mass estimates for 44 galaxy clusters selected via the Sunyaev-Zeldovich (SZ) effect by the Atacama Cosmology Telescope. Dynamical masses for 18 clusters are reported here for the first time. Using N-body simulations, we model the different observing strategies used to measure the velocity dispersions and account for systematic effects resulting from these strategies. We find that the galaxy velocity distributions may be treated as isotropic, and that an aperture correction of up to 7 per cent in the velocity dispersion is required if the spectroscopic galaxy sample is sufficiently concentrated towards the cluster centre. Accounting for the radial profile of the velocity dispersion in simulations enables consistent dynamical mass estimates regardless of the observing strategy. Cluster masses M200 are in the range (1 - 15) times 10 (sup 14) Solar Masses. Comparing with masses estimated from the SZ distortion assuming a gas pressure profile derived from X-ray observations gives a mean SZ-to-dynamical mass ratio of 1:10 plus or minus 0:13, but there is an additional 0.14 systematic uncertainty due to the unknown velocity bias; the statistical uncertainty is dominated by the scatter in the mass-velocity dispersion scaling relation. This ratio is consistent with previous determinations at these mass scales.

Sunyaev-Zeldovich (SZ)↗