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At least 1,063 records · Page 59

Improved estimates of coordinate error for molecular replacement

A function for estimating the effective root-mean-square deviation in coordinates between two proteins has been developed that depends on both the sequence identity and the size of the protein and is optimized for use with molecular replacement in Phaser. A top peak translation-function Z-score of over 8 is found to be a reliable metric of when molecular replacement has succeeded. The estimate of the root-mean-square deviation (r.m.s.d.) in coordinates between the model and the target is an essential parameter for calibrating likelihood functions for molecular replacement (MR). Good estimates of the r.m.s.d. lead to good estimates of the variance term in the likelihood functions, which increases signal to noise and hence success rates in the MR search. Phaser has hitherto used an estimate of the r.m.s.d. that only depends on the sequence identity between the model and target and which was not optimized for the MR likelihood functions. Variance-refinement functionality was added to Phaser to enable determination of the effective r.m.s.d. that optimized the log-likelihood gain (LLG) for a correct MR solution. Variance refinement was subsequently performed on a database of over 21 000 MR problems that sampled a range of sequence identities, protein sizes and protein fold classes. Success was monitored using the translation-function Z-score (TFZ), where a TFZ of 8 or over for the top peak was found to be a reliable indicator that MR had succeeded for these cases with one molecule in the asymmetric unit. Good estimates of the r.m.s.d. are correlated with the sequence identity and the protein size. A new estimate of the r.m.s.d. that uses these two parameters in a function optimized to fit the mean of the refined variance is implemented in Phaser and improves MR outcomes. Perturbing the initial estimate of the r.m.s.d. from the mean of the distribution in steps of standard deviations of the distribution further increases MR success rates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Compartment modeling of dynamic brain PET—The impact of scatter corrections on parameter errors

Purpose: The aim of this study was to investigate the effect of scatter and its correction on kinetic parameters in dynamic brain positron emission tomography (PET) tumor imaging. The 2-tissue compartment model was used, and two different reconstruction methods and two scatter correction (SC) schemes were investigated. Methods: The GATE Monte Carlo (MC) software was used to perform 2 × 15 full PET scan simulations of a voxelized head phantom with inserted tumor regions. The two sets of kinetic parameters of all tissues were chosen to represent the 2-tissue compartment model for the tracer 3′-deoxy-3′-({sup 18}F)fluorothymidine (FLT), and were denoted FLT{sub 1} and FLT{sub 2}. PET data were reconstructed with both 3D filtered back-projection with reprojection (3DRP) and 3D ordered-subset expectation maximization (OSEM). Images including true coincidences with attenuation correction (AC) and true+scattered coincidences with AC and with and without one of two applied SC schemes were reconstructed. Kinetic parameters were estimated by weighted nonlinear least squares fitting of image derived time–activity curves. Calculated parameters were compared to the true input to the MC simulations. Results: The relative parameter biases for scatter-eliminated data were 15%, 16%, 4%, 30%, 9%, and 7% (FLT{sub 1}) and 13%, 6%, 1%, 46%, 12%, and 8% (FLT{sub 2}) for K{sub 1}, k{sub 2}, k{sub 3}, k{sub 4}, V{sub a}, and K{sub i}, respectively. As expected, SC was essential for most parameters since omitting it increased biases by 10 percentage points on average. SC was not found necessary for the estimation of K{sub i} and k{sub 3}, however. There was no significant difference in parameter biases between the two investigated SC schemes or from parameter biases from scatter-eliminated PET data. Furthermore, neither 3DRP nor OSEM yielded the smallest parameter biases consistently although there was a slight favor for 3DRP which produced less biased k{sub 3} and K{sub i} estimates while OSEM resulted in a less biased V{sub a}. The uncertainty in OSEM parameters was about 26% (FLT{sub 1}) and 12% (FLT{sub 2}) larger than for 3DRP although identical postfilters were applied. Conclusions: SC was important for good parameter estimations. Both investigated SC schemes performed equally well on average and properly corrected for the scattered radiation, without introducing further bias. Furthermore, 3DRP was slightly favorable over OSEM in terms of kinetic parameter biases and SDs.

60 APPLIED LIFE SCIENCES↗

Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data

This paper studies here the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the k-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris–Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

97 MATHEMATICS AND COMPUTING↗

The Suppression of Energy Discretization Errors in Multigroup Transport Calculations

The Objective of this project is to develop, implement, and test new deterministric methods to solve, as efficiently as possible, multigroup neutron transport problems having an extremely large number of groups. Our approach was to (i) use the standard CMFD method to "coarsen" the space-angle grid, yielding a multigroup diffusion equation, and (ii) use a new multigrid-in-space-and-energy technique to efficiently solve the multigroup diffusion problem. The overall strategy of (i) how to coarsen the spatial an energy grids, and (ii) how to navigate through the various grids, has the goal of minimizing the overall computational effort. This approach yields not only the fine-grid solution, but also coarse-group flux-weighted cross sections that can be used for other related problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cyclops I: Modeling Error Study for Inertially Confined Detonation of Insensitive High Explosive (IHE) PBX-9502

A validation study is performed using the hydrodynamics code PAGOSA to assess the accuracy of reflected shock, burn front propagation, and Photon Doppler Velocimetry (PDV) predictions using several burn models and strength models. Experimental data collected from proton radiography (pRad) is compared to burn front propagation times and reflected shock patterns. Burn front isochrones are computed and the lag time for the burn front is quantified for a given burn model. The effect of strength models and damage are assessed by comparison of simulations to experimental PDV data.

97 MATHEMATICS AND COMPUTING↗

Errors in shaping by a planetary mechanism

The proposed planetary reaming method permits discontinuous turning in which the cutting edge moves relative to the cutting surfaces. As a result, individual sections of the cutting zone move successfully in and out of the machining zone. Discontinuous turning is free of the deficiencies of continuous turning.

42 ENGINEERING↗

Assessment of Gamma-Ray-Spectra Analysis Method Utilizing the Fireworks Algorithm for Various Error Measures

The analysis of measured data plays a significant role in enhancing nuclear nonproliferation mainly by inferring the presence of patterns associated with special nuclear materials. Among various types of measurements, gamma-ray spectra is the widest utilized type of data in nonproliferation applications. In this paper, a method that employs the fireworks algorithm (FWA) for analyzing gamma-ray spectra aiming at detecting gamma signatures is presented. In particular, FWA is utilized to fit a set of known signatures to a measured spectrum by optimizing an objective function, where non-zero coefficients express the detected signatures. FWA is tested on a set of experimentally obtained measurements optimizing various objective functions—MSE, RMSE, Theil-2, MAE, MAPE, MAP—with results exhibiting its potential in providing highly accurate and precise signature detection. Finally and furthermore, FWA is benchmarked against genetic algorithms and multiple linear regression, showing its superiority over those algorithms regarding precision with respect to MAE, MAPE, and MAP measures.

97 MATHEMATICS AND COMPUTING↗

A method for reducing the largest relative errors in Monte Carlo iterated-fission-source calculations

In Monte Carlo iterated-fission-source calculations relative uncertainties on local tallies tend to be larger in lower-power regions and smaller in higher-power regions. Reducing the largest uncertainties to an acceptable level simply by running a larger number of neutron histories is often prohibitively expensive. The uniform fission site method has been developed to yield a more spatially-uniform distribution of relative uncertainties. This is accomplished by biasing the density of fission neutron source sites while not biasing the solution. The method is integrated into the source iteration process, and does not require any auxiliary forward or adjoint calculations. For a given amount of computational effort, the use of the method results in a reduction of the largest uncertainties relative to the standard algorithm. Two variants of the method have been implemented and tested. Both have been shown to be effective. (authors)

97 MATHEMATICS AND COMPUTING↗

Complexity and error potential of digital I and C - 135

Utilization of digital I and C for application in nuclear power plants led to a growing discussion on how to create methods for a probabilistic evaluation on such systems. Issues arise on the one hand due to a lack of commonly accepted models for quantitative evaluation of availability and reliability and on the other hand due to the integration of such models into the evaluation of reliability of an overall system. Nevertheless programmable and even more complex systems are implemented to satisfy growing functionality requirements. Therefore the question for a method to evaluate the reliability of systems based on software or on programmable logic became even more urgent. The approach described is based on the commonly accepted assumption that more complex designs are less reliable. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Tomographic Volumetric Additive Manufacturing of Silica Glass with In Situ Error Calculation and Projection Tiling

The optical, thermal, and chemical properties of glass make it an ideal material for use in a wide range of applications, from optics and chemistry reactionware to consumer products. Tomographic volumetric additive manufacturing (tVAM) creates 3D objects by selectively gelling material within a rotating vial of photo-sensitive material by exposure to a series of tomographically-determined images. Here, in this study, tVAM is investigated for fabrication of complex, centimeter-scale, 3D silica glass parts. By optimizing the post-processing procedure, fully-dense glass parts with up to 2 cm 2 cross sectional area are achieved. The changes in optical properties during printing are leveraged for in situ metrology during printing, and the non-Newtonian nature of the glass-filled photoresin system to facilitate larger fabrication volumes via tiled projections. Printed structures are finally demonstrated for applications as MEMS components, optics, fluidics, and consumer products.

Materials science↗

CheKiPEUQ Intro 1: Bayesian Parameter Estimation Considering Uncertainty or Error from both Experiments and Theory**

A common goal is extraction of physico-chemical parameter values such as pre-exponentials and activation energies from experiment. Ever increasing knowledge from experiments and computations is enabling semi-quantitative prior predictions of such values. When prior knowledge of physically realistic ranges is available, a method named Bayesian parameter estimation (BPE) enables more physically realistic parameter estimation relative to unsophisticated fitting by seeking the most probable value when considering together the uncertainties from prior knowledge, experimental data, and approximations in the model. An impediment to widespread use of BPE is a lack of understanding, training, and user-friendly software. Along with this invited publication, a general software package for BPE is being released that is user-friendly and that does not require understanding of the math behind the methodology. Overall, two previously unpublished catalysis science examples are provided along with considerations and guidelines for successful application of BPE. Following this work, BPE can become more widespread to enable extraction of physically meaningful parameter values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗