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DOE OSTI2017

Computing the binding affinity of a ligand buried deep inside a protein with the hybrid steered molecular dynamics

Computing the ligand-protein binding affinity (or the Gibbs free energy) with chemical accuracy has long been a challenge for which many methods/approaches have been developed and refined with various successful applications. False positives and, even more harmful, false negatives have been and still are a common occurrence in practical applications. Inevitable in all approaches are the errors in the force field parameters we obtain from quantum mechanical computation and/or empirical fittings for the intra- and inter-molecular interactions. These errors propagate to the final results of the computed binding affinities even if we were able to perfectly implement the statistical mechanics of all the processes relevant to a given problem. And they are actually amplified to various degrees even in the mature, sophisticated computational approaches. In particular, the free energy perturbation (alchemical) approaches amplify the errors in the force field parameters because they rely on extracting the small differences between similarly large numbers. In this paper, we develop a hybrid steered molecular dynamics (hSMD) approach to the difficult binding problems of a ligand buried deep inside a protein. Sampling the transition along a physical (not alchemical) dissociation path of opening up the binding cavity- -pulling out the ligand- -closing back the cavity, we can avoid the problem of error amplifications by not relying on small differences between similar numbers. We tested this new form of hSMD on retinol inside cellular retinol-binding protein 1 and three cases of a ligand (a benzylacetate, a 2-nitrothiophene, and a benzene) inside a T4 lysozyme L99A/M102Q(H) double mutant. In all cases, we obtained binding free energies in close agreement with the experimentally measured values. This indicates that the force field parameters we employed are accurate and that hSMD (a brute force, unsophisticated approach) is free from the problem of error amplification suffered by many sophisticated approaches in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

DOE OSTI2023

Incorporating the Effect of Large‐Scale Vertical Motion on Convection Through Convective Mass Flux Adjustment in E3SMv2

Abstract Recent observational studies suggest that the large‐scale dynamical forcing (vertical motion) plays important roles in deep convection development. In this study we propose a convective mass flux adjustment (MAdj) approach to represent the dynamical effects of large‐scale vertical motion on convection in the Department of Energy's Energy Exascale Earth System Model version 2 (E3SMv2). With MAdj, convection is enhanced (suppressed) when there is large‐scale ascending (descending) motion at the planetary boundary layer top. The coupling of convection with large‐scale circulation significantly improves the simulation of climate variability in E3SMv2 across multiple scales from the diurnal cycle, convectively coupled equatorial waves, to the Madden‐Julian Oscillation (MJO). The standard E3SMv2 tends to simulate overly weak diurnal amplitude of precipitation and overly weak variance of convectively coupled equatorial Kelvin and westward inertio‐gravity (WIG) waves. It also fails to simulate the essential characteristics of the MJO: continuous eastward propagation. With MAdj, the amplitude of diurnal cycle of precipitation is systematically increased and its probability density distribution is much closer to observations. The MAdj can also simulate more realistic eastward propagation of the MJO and much stronger convectively coupled Kelvin and WIG waves. Moreover, the MAdj approach slightly improves the climatology simulations in precipitation, cloud, radiation, circulation, temperature, and moisture fields, with overall root‐mean‐square error (RMSE) of major climatological fields reduced by about 2%. The MAdj approach suppresses excessive grid‐scale precipitation, reducing precipitation wet biases over South China Sea, Philippine Sea, Himalayas, and South Pacific Convergence Zone in western Pacific in summer.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

The JLAB UV Undulator

Recently the JLAB FEL has demonstrated 150 W at 400 nm and 200 W at 700 nm using a 33mm period undulator designed and built by STI Optronics. This paper describes the undulator design and performance. Two key requirements were low phase error, zero steering and offset end fields and small rms trajectory errors. We will describe a new genetic algorithm that allowed phase error minimization to 1.8 degrees while exceeding specifications. The mechanical design, control system and EPICS interface will also be summarized.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Moonshine, superconformal symmetry, and quantum error correction

Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a c = 24 twodimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway symmetry group of a c = 12 CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu group M24 has led to the study of K3 sigma models with large symmetry groups. A particular K3 CFT with a maximal symmetry group preserving (4, 4) superconformal symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland [41]. The present paper shows that in both the GTVW and c = 12 theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism groups of these codes lift to symmetry groups in the CFT preserving the superconformal generators. In the case of the N = 1 supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the symmetry group is the maximal subgroup of M24 known as the sextet group. (The sextet group is also known as the holomorph of the hexacode.) Building on [41] the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a group of symmetries of RR states. Moreover, (4, 1) superconformal symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the N = 4 superconformal algebra. The symmetry group preserving (4, 1) is larger than that preserving (4, 4).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Validating Molecular Dynamics Simulations against Experimental Observables in Light of Underlying Conformational Ensembles

Far from the static, idealized conformations deposited into structural databases, proteins are highly dynamic molecules that undergo conformational changes on temporal and spatial scales that may span several orders of magnitude. These conformational changes, often intimately connected to the functional roles that proteins play, may be obscured by traditional biophysical techniques. Over the past 40 years, molecular dynamics (MD) simulations have complemented these techniques by providing the “hidden” atomistic details that underlie protein dynamics. However, there are limitations of the degree to which molecular simulations accurately and quantitatively describe protein motions. Here we show that although four molecular dynamics simulation packages (AMBER, GROMACS, NAMD, and il mm) reproduced a variety of experimental observables for two different proteins (engrailed homeodomain and RNase H) equally well overall at room temperature, there were subtle differences in the underlying conformational distributions and the extent of conformational sampling obtained. This leads to ambiguity about which results are correct, as experiment cannot always provide the necessary detailed information to distinguish between the underlying conformational ensembles. Furthermore, the results with different packages diverged more when considering larger amplitude motion, for example, the thermal unfolding process and conformational states sampled, with some packages failing to allow the protein to unfold at high temperature or providing results at odds with experiment. While most differences between MD simulations performed with different packages are attributed to the force fields themselves, there are many other factors that influence the outcome, including the water model, algorithms that constrain motion, how atomic interactions are handled, and the simulation ensemble employed. Here four different MD packages were tested each using best practices as established by the developers, utilizing three different protein force fields and three different water models. Differences between the simulated protein behavior using two different packages but the same force field, as well as two different packages with different force fields but the same water models and approaches to restraining motion, show how other factors can influence the behavior, and it is incorrect to place all the blame for deviations and errors on force fields or to expect improvements in force fields alone to solve such problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Muon capture on the deuteron in chiral effective field theory

Here, we consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of $Γ^{1/2}_{μd}$ = 399.1 ± 7.6 ± 4.4 s –1 for capture from the atomic doublet state, and $Γ^{3/2}_{μd}$= 12.31 ± 0.47 ± 0.04 s –1 for capture from the quartet state and the first and second uncertainties given here are due to the effective field theory truncation error and the uncertainty in the axial radius, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

TU-F-CAMPUS-T-02: Vernier Picket Fence Test: A Non-Imaging Method to Localize the Radiation Isocenter with Submillimeter Accuracy

Purpose: The purpose of this study is to propose a new non-imaging method to localize the radiation isocenter with submillimeter accuracy. Methods: The Vernier picket fence (VPF) is a multileaf collimator (MLC) picket fence sequence in which the fence spacing is 1/N smaller than the detector spacing of the QA phantom, where N is the magnification factor, typically set to 10 or 20. Similar to reading a Vernier caliper, the user can easily achieve the resolution of 1/N of the detector spacing by visually inspecting the maximum signal. To achieve higher accuracy, a Gaussian model was used to interpolate the peak position, which can fall between adjacent detectors. In two separate tests, precise MLC offsets and imprecise couch offsets were applied to a 2D detector array (MapCheck, Sun Nuclear Corp., Melbourne, Florida) to introduce setup errors. Two vertical VPF fields were delivered with collimator angles at 0° and 90° to detect the lateral and longitudinal setup errors, respectively. For a rotational QA phantom, an additional lateral VPF field is needed to detect the vertical setup error for three-dimensional capabilities. Results: With N set to 20 and a detector spacing of 5 mm for MapCheck, the resolution of the VPF’s visual analysis is 0.25 mm. With the Gaussian interpretation, the VPF can achieve an accuracy of 0.02 mm, as shown by the MLC offset test. The couch offset test measured the couch hysteresis and demonstrated that the setup error detected by the VPF differed from the ExacTrac™ (Brainlab AG, Feldkirchen, Germany) optical tracking by 0.055 mm in the lateral direction and 0.041 mm in the longitudinal direction on average. The VPF was also shown to be feasible in the vertical direction as well. Conclusion: This study verified the VPF as a non-imaging method to localize the radiation isocenter with submillimeter accuracy. Funding is in part by the Portland Chapter of the Achievement Rewards for College Scientists. The content is solely the responsibility of the authors, and does not necessarily represent the official views of the sponsors. The authors declare no conflict of interest.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Portal dosimetry for VMAT using integrated images obtained during treatment

Purpose: Portal dosimetry provides an accurate and convenient means of verifying dose delivered to the patient. A simple method for carrying out portal dosimetry for volumetric modulated arc therapy (VMAT) is described, together with phantom measurements demonstrating the validity of the approach. Methods: Portal images were predicted by projecting dose in the isocentric plane through to the portal image plane, with exponential attenuation and convolution with a double-Gaussian scatter function. Appropriate parameters for the projection were selected by fitting the calculation model to portal images measured on an iViewGT portal imager (Elekta AB, Stockholm, Sweden) for a variety of phantom thicknesses and field sizes. This model was then used to predict the portal image resulting from each control point of a VMAT arc. Finally, all these control point images were summed to predict the overall integrated portal image for the whole arc. The calculated and measured integrated portal images were compared for three lung and three esophagus plans delivered to a thorax phantom, and three prostate plans delivered to a homogeneous phantom, using a gamma index for 3% and 3 mm. A 0.6 cm{sup 3} ionization chamber was used to verify the planned isocentric dose. The sensitivity of this method to errors in monitor units, field shaping, gantry angle, and phantom position was also evaluated by means of computer simulations. Results: The calculation model for portal dose prediction was able to accurately compute the portal images due to simple square fields delivered to solid water phantoms. The integrated images of VMAT treatments delivered to phantoms were also correctly predicted by the method. The proportion of the images with a gamma index of less than unity was 93.7% ± 3.0% (1SD) and the difference between isocenter dose calculated by the planning system and measured by the ionization chamber was 0.8% ± 1.0%. The method was highly sensitive to errors in monitor units and field shape, but less sensitive to errors in gantry angle or phantom position. Conclusions: This method of predicting integrated portal images provides a convenient means of verifying dose delivered using VMAT, with minimal image acquisition and data processing requirements.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2015

AN IMAGE-PLANE ALGORITHM FOR JWST'S NON-REDUNDANT APERTURE MASK DATA

The high angular resolution technique of non-redundant masking (NRM) or aperture masking interferometry (AMI) has yielded images of faint protoplanetary companions of nearby stars from the ground. AMI on James Webb Space Telescope (JWST)'s Near Infrared Imager and Slitless Spectrograph (NIRISS) has a lower thermal background than ground-based facilities and does not suffer from atmospheric instability. NIRISS AMI images are likely to have 90%-95% Strehl ratio between 2.77 and 4.8 μm. In this paper we quantify factors that limit the raw point source contrast of JWST NRM. We develop an analytic model of the NRM point spread function which includes different optical path delays (pistons) between mask holes and fit the model parameters with image plane data. It enables a straightforward way to exclude bad pixels, is suited to limited fields of view, and can incorporate effects such as intra-pixel sensitivity variations. We simulate various sources of noise to estimate their effect on the standard deviation of closure phase, σ{sub CP} (a proxy for binary point source contrast). If σ{sub CP} < 10{sup –4} radians—a contrast ratio of 10 mag—young accreting gas giant planets (e.g., in the nearby Taurus star-forming region) could be imaged with JWST NIRISS. We show the feasibility of using NIRISS' NRM with the sub-Nyquist sampled F277W, which would enable some exoplanet chemistry characterization. In the presence of small piston errors, the dominant sources of closure phase error (depending on pixel sampling, and filter bandwidth) are flat field errors and unmodeled variations in intra-pixel sensitivity. The in-flight stability of NIRISS will determine how well these errors can be calibrated by observing a point source. Our results help develop efficient observing strategies for space-based NRM.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗

DOE OSTI2024

Quantum error thresholds for gauge-redundant digitizations of lattice field theories

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to mitigate and correct quantum errors by checking and restoring Gauss’s law. In this work, we consider the correctable errors for generic finite gauge groups and design the quantum circuits to detect and correct them. We calculate the error thresholds below which the gauge-redundant digitization with Gauss’s law error correction has better fidelity than the gauge-fixed digitization involving only gauge-invariant states. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Memory Errors in Modern Systems: The Good, The Bad, and The Ugly

Several recent publications have shown that hardware faults in the memory subsystem are commonplace. These faults are predicted to become more frequent in future systems that contain orders of magnitude more DRAM and SRAM than found in current memory subsystems. These memory subsystems will need to provide resilience techniques to tolerate these faults when deployed in high-performance computing systems and data centers containing tens of thousands of nodes. Therefore, it is critical to understand the efficacy of current hardware resilience techniques to determine whether they will be suitable for future systems. In this paper, we present a study of DRAM and SRAM faults and errors from the field. We use data from two leadership-class high-performance computer systems to analyze the reliability impact of hardware resilience schemes that are deployed in current systems. Our study has several key findings about the efficacy of many currently deployed reliability techniques such as DRAM ECC, DDR address/command parity, and SRAM ECC and parity. We also perform a methodological study, and find that counting errors instead of faults, a common practice among researchers and data center operators, can lead to incorrect conclusions about system reliability. Lastly, we use our data to project the needs of future large-scale systems. We find that SRAM faults are unlikely to pose a significantly larger reliability threat in the future, while DRAM faults will be a major concern and stronger DRAM resilience schemes will be needed to maintain acceptable failure rates similar to those found on today's systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

DOE OSTI2020

Investigation of the effect of noise parameters of a 3D lidar on the error in estimating relief signatures of distant objects from 2D field intensity distributions of reflected radiation

We consider the influence of noise parameters of a 3D lidar and external background radiation on the error in estimating the relief signatures of distant objects from 2D field intensity distributions of the reflected radiation. A physical and mathematical model is developed to analyse the effect of noise. The dependence of the error in estimating the relief signatures at various signal-to-noise ratios is investigated taking into account the parameters of real multi-element photodetectors (MEPDs). The obtained results indicate the possibility of evaluating relief signatures of distant objects with high accuracy based on standard MEPDs simultaneously for a large number of points on the object’s surface with a signal-to-noise ratio of more than 4. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

A divergence-free constrained magnetic field interpolation method for scattered data

An interpolation method to evaluate magnetic fields, given its unstructured and scattered magnetic data, is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constraint in the cost function, allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Finally, applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

SU-F-T-229: A Novel Method for EPID-Based In-Vivo Exit Dose Verification for Intensity Modulated Radiotherapy

Purpose: Electronic portal imaging device (EPID) can be used to acquire a two-dimensional exit dose distribution during treatment delivery, thus allowing the in-vivo verification of the dose delivery through a comparison of measured portal images to predicted portal dose images (PDI). The aim of this study was to present a novel method to easily and accurately predict PDI, and to establish an EPID-based in-vivo dose verification method during IMRT treatments. Methods: We developed a model to determine the predicted portal dose at the same plane of the EPID detector location. The Varian EPID (aS1000) positions at 150cm source-to-detector-distance (SDD), and can be used to acquire in-vivo exit dose using Portal Dosimetry (PD) function. Our model was generated to make an equivalent water thickness represent the buildup plate of EPID. The exit dose at extend SDD plane with patient CT data in the beam can be calculated as the predicted PDI in the treatment planning system (TPS). After that, the PDI was converted to the fluence at SDD of 150cm using the inverse square law coded in MATLAB. Five head-and-neck and prostate IMRT patient plans contain 32 fields were investigated to evaluate the feasibility of this new method. The measured EPID image was compared with PDI using the gamma analysis. Results: The average results for cumulative dose comparison were 81.9% and 91.6% for 3%, 3mm and 4%, 4mm gamma criteria, respectively. Results indicate that the patient transit dosimetry predicted algorithm compares well with EPID measured PD doses for test situations. Conclusion: Our new method can be used as an easy and feasible tool for online EPID-based in-vivo dose delivery verification for IMRT treatments. It can be implemented for fast detecting those obvious treatment delivery errors for individual field and patient quality assurance.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with NuStar

We present NuSTAR observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, F{sub Edd}, of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K{sub α} line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be R{sub in}=1.03±0.03 ISCO (innermost stable circular orbit), assuming a dimensionless spin parameter a{sub ∗}=cJ/GM{sup 2}=0.0, and R{sub in}=1.08±0.06 ISCO for a{sub ∗}=0.3 (errors quoted at 1σ). This value proves to be model independent. For a{sub ∗}=0.3 and M=1.4 M{sub ⊙}, for example, 1.08 ± 0.06 ISCO translates to a physical radius of R=10.8±0.6 km, and the NS would have to be smaller than this radius (other outcomes are possible for allowed spin parameters and masses). For GX 17+2, R{sub in}=1.00--1.04 ISCO for a{sub ∗}=0.0 and R{sub in}=1.03--1.30 ISCO for a{sub ∗}=0.3. For a{sub ∗}=0.3 and M=1.4 M{sub ⊙}, R{sub in}=1.03--1.30 ISCO translates to R=10.3--13.0 km. The inner accretion disk in 4U 1705-44 may be truncated just above the stellar surface, perhaps by a boundary layer or magnetosphere; reflection models give a radius of 1.46–1.64 ISCO for a{sub ∗}=0.0 and 1.69–1.93 ISCO for a{sub ∗}=0.3. We discuss the implications our results may have on the equation of state of ultradense, cold matter and our understanding of the innermost accretion flow onto NSs with low surface magnetic fields, and systematic errors related to the reflection models and spacetime metric around less idealized NSs.

79 ASTRONOMY AND ASTROPHYSICS↗