Search NASA⌕ Search

SEARCH · Search NASA

Results for “error fields”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55

Estimating PV power from aggregate power measurements within the distribution grid

The increased integration of photovoltaic (PV) systems in distribution grids reduces visibility and situational awareness for utilities because the PV systems' power production is usually not monitored by them. To address this problem, a method called Contextually Supervised Source Separation (CSSS) has been recently adapted for real-time estimation of aggregate PV active power generation from aggregate net active and reactive power measurements at a point in a radially configured distribution grid (e.g., substation). In its original version, PV disaggregation is formulated as an optimization problem that fits linear regression models for the aggregate PV active power generation and true substation active power load. This paper extends the previous work by adding regularization terms in the objective function to capture additional contextual information such as smoothness, by adding new constraints, by introducing new regressors such as ambient temperature, and by investigating the use of time-varying regressors. Furthermore, we perform extensive parametric analysis to study tuning of the objective function weighting factors in a way that maximizes performance and robustness. The proposed PV disaggregation method can be applied to networks with either a single PV system (e.g., megawatt scale) or many distributed ones (e.g., residential scale) connected downstream of the substation. Simulation studies with real field recorded data show that the enhancements of the proposed method reduce disaggregation error by 58% in winter and 35% in summer compared to previous CSSS-based work. When compared against a commonly used transposition model based approach, the reduction in disaggregation error is more pronounced (78% reduction in winter and 45% in summer). Additional simulations indicate that the proposed algorithm is also applicable for PV systems with time-varying power factors. In conclusion, overall, our results show that—with appropriate modeling and tuning—it is possible to accurately estimate the aggregated PV active power generation of a distribution feeder with minimal or no additional sensor deployment.

14 SOLAR ENERGY↗

MEASURING LENSING MAGNIFICATION OF QUASARS BY LARGE SCALE STRUCTURE USING THE VARIABILITY-LUMINOSITY RELATION

We introduce a technique to measure gravitational lensing magnification using the variability of type I quasars. Quasars' variability amplitudes and luminosities are tightly correlated, on average. Magnification due to gravitational lensing increases the quasars' apparent luminosity, while leaving the variability amplitude unchanged. Therefore, the mean magnification of an ensemble of quasars can be measured through the mean shift in the variability-luminosity relation. As a proof of principle, we use this technique to measure the magnification of quasars spectroscopically identified in the Sloan Digital Sky Survey (SDSS), due to gravitational lensing by galaxy clusters in the SDSS MaxBCG catalog. The Palomar-QUEST Variability Survey, reduced using the DeepSky pipeline, provides variability data for the sources. We measure the average quasar magnification as a function of scaled distance (r/R{sub 200}) from the nearest cluster; our measurements are consistent with expectations assuming Navarro-Frenk-White cluster profiles, particularly after accounting for the known uncertainty in the clusters' centers. Variability-based lensing measurements are a valuable complement to shape-based techniques because their systematic errors are very different, and also because the variability measurements are amenable to photometric errors of a few percent and to depths seen in current wide-field surveys. Given the volume data of the expected from current and upcoming surveys, this new technique has the potential to be competitive with weak lensing shear measurements of large-scale structure.

79 ASTRONOMY AND ASTROPHYSICS↗

A GMBCG GALAXY CLUSTER CATALOG OF 55,424 RICH CLUSTERS FROM SDSS DR7

We present a large catalog of optically selected galaxy clusters from the application of a new Gaussian Mixture Brightest Cluster Galaxy (GMBCG) algorithm to SDSS Data Release 7 data. The algorithm detects clusters by identifying the red-sequence plus brightest cluster galaxy (BCG) feature, which is unique for galaxy clusters and does not exist among field galaxies. Red-sequence clustering in color space is detected using an Error Corrected Gaussian Mixture Model. We run GMBCG on 8240 deg{sup 2} of photometric data from SDSS DR7 to assemble the largest ever optical galaxy cluster catalog, consisting of over 55,000 rich clusters across the redshift range from 0.1 < z < 0.55. We present Monte Carlo tests of completeness and purity and perform cross-matching with X-ray clusters and with the maxBCG sample at low redshift. These tests indicate high completeness and purity across the full redshift range for clusters with 15 or more members.

79 ASTRONOMY AND ASTROPHYSICS↗

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

A Review of Human Reliability Needs in the U.S. Nuclear Industry

In this survey, 34 subject matter experts from the U.S. nuclear industry were interviewed to determine specific needs for human reliability analysis (HRA). Conclusions from the interviews are detailed in this article. A summary of the findings includes: (1) The need for improved guidance on the use of HRA methods generally and for specific applications. (2) The need for additional training in HRA to provide more hands-on experience in the application of HRA methods. (3) Thedevelopment of HRA approaches suitable for advanced reactors, severe accident situations, and low-power and shutdown applications. (4) The refinement of HRA methods to account forfactors such as crew variability, latent errors, more sophisticated dependency modeling, and errors of commission. (5) The continued need for simplified HRA methods appropriate for field applications. (6) The need for tighter coupling of HRA and human factors. (7) The need for improvements in the quantitative basis of HRA methods. These findings suggest the field of HRA is mature but still benefits from refinements.

human reliability analysis↗

WE-D-9A-02: Automated Landmark-Guided CT to Cone-Beam CT Deformable Image Registration

Purpose: The anatomical changes that occur between the simulation CT and daily cone-beam CT (CBCT) are investigated using an automated landmark-guided deformable image registration (LDIR) algorithm with simultaneous intensity correction. LDIR was designed to be accurate in the presence of tissue intensity mismatch and heavy noise contamination. Method: An auto-landmark generation algorithm was used in conjunction with a local small volume (LSV) gradient matching search engine to map corresponding landmarks between the CBCT and planning CT. The LSVs offsets were used to perform an initial deformation, generate landmarks, and correct local intensity mismatch. The landmarks act as stabilizing controlpoints in the Demons objective function. The accuracy of the LDIR algorithm was evaluated on one synthetic case with ground truth and data of ten head and neck cancer patients. The deformation vector field (DVF) accuracy was accessed using a synthetic case. The Root mean square error of the 3D canny edge (RMSECE), mutual information (MI), and feature similarity index metric (FSIM) were used to access the accuracy of LDIR on the patient data. The quality of the corresponding deformed contours was verified by an attending physician. Results: The resulting 90 percentile DVF error for the synthetic case was within 5.63mm for the original demons algorithm, 2.84mm for intensity correction alone, 2.45mm using controlpoints without intensity correction, and 1.48 mm for the LDIR algorithm. For the five patients the mean RMSECE of the original CT, Demons deformed CT, intensity corrected Demons CT, control-point stabilized deformed CT, and LDIR CT was 0.24, 0.26, 0.20, 0.20, and 0.16 respectively. Conclusion: LDIR is accurate in the presence of multimodal intensity mismatch and CBCT noise contamination. Since LDIR is GPU based it can be implemented with minimal additional strain on clinical resources. This project has been supported by a CPRIT individual investigator award RP11032.

60 APPLIED LIFE SCIENCES↗

Daily QA of linear accelerators using only EPID and OBI

Purpose: As treatment delivery becomes more complex, there is a pressing need for robust quality assurance (QA) tools to improve efficiency and comprehensiveness while simultaneously maintaining high accuracy and sensitivity. This work aims to present the hardware and software tools developed for comprehensive QA of linear accelerator (LINAC) using only electronic portal imaging devices (EPIDs) and kV flat panel detectors. Methods: A daily QA phantom, which includes two orthogonally positioned phantoms for QA of MV-beams and kV onboard imaging (OBI) is suspended from the gantry accessory holder to test both geometric and dosimetric components of a LINAC and an OBI. The MV component consists of a 0.5 cm water-equivalent plastic sheet incorporating 11 circular steel plugs for transmission measurements through multiple thicknesses and one resolution plug for MV-image quality testing. The kV-phantom consists of a Leeds phantom (TOR-18 FG phantom supplied by Varian) for testing low and high contrast resolutions. In the developed process, the existing LINAC tools were used to automate daily acquisition of MV and kV images and software tools were developed for simultaneous analysis of these images. A method was developed to derive and evaluate traditional QA parameters from these images [output, flatness, symmetry, uniformity, TPR{sub 20/10}, and positional accuracy of the jaws and multileaf collimators (MLCs)]. The EPID-based daily QA tools were validated by performing measurements on a detuned 6 MV beam to test its effectiveness in detecting errors in output, symmetry, energy, and MLC positions. The developed QA process was clinically commissioned, implemented, and evaluated on a Varian TrueBeam LINAC (Varian Medical System, Palo Alto, CA) over a period of three months. Results: Machine output constancy measured with an EPID (as compared against a calibrated ion-chamber) is shown to be within ±0.5%. Beam symmetry and flatness deviations measured using an EPID and a 2D ion-chamber array agree within ±0.5% and ±1.2% for crossline and inline profiles, respectively. MLC position errors of 0.5 mm can be detected using a picket fence test. The field size and phantom positioning accuracy can be determined within 0.5 mm. The entire daily QA process takes ∼15 min to perform tests for 5 photon beams, MLC tests, and imaging checks. Conclusions: The exclusive use of EPID-based QA tools, including a QA phantom and simultaneous analysis software tools, has been demonstrated as a viable, efficient, and comprehensive process for daily evaluation of LINAC performance.

60 APPLIED LIFE SCIENCES↗

Characterizing spatiotemporal information loss in sparse-sampling-based dynamic MRI for monitoring respiration-induced tumor motion in radiotherapy

Purpose: Sparse-sampling and reconstruction techniques represent an attractive strategy to achieve faster image acquisition speeds, while maintaining adequate spatial resolution and signal-to-noise ratio in rapid magnetic resonance imaging (MRI). The authors investigate the use of one such sequence, broad-use linear acquisition speed-up technique (k-t BLAST) in monitoring tumor motion for thoracic and abdominal radiotherapy and examine the potential trade-off between increased sparsification (to increase imaging speed) and the potential loss of “true” information due to greater reliance on a priori information. Methods: Lung tumor motion trajectories in the superior–inferior direction, previously recorded from ten lung cancer patients, were replayed using a motion phantom module driven by an MRI-compatible motion platform. Eppendorf test tubes filled with water which serve as fiducial markers were placed in the phantom. The modeled rigid and deformable motions were collected in a coronal image slice using balanced fast field echo in conjunction with k-t BLAST. Root mean square (RMS) error was used as a metric of spatial accuracy as measured trajectories were compared to input data. The loss of spatial information was characterized for progressively increasing acceleration factor from 1 to 16; the resultant sampling frequency was increased approximately from 2.5 to 19 Hz when the principal direction of the motion was set along frequency encoding direction. In addition to the phantom study, respiration-induced tumor motions were captured from two patients (kidney tumor and lung tumor) at 13 Hz over 49 s to demonstrate the impact of high speed motion monitoring over multiple breathing cycles. For each subject, the authors compared the tumor centroid trajectory as well as the deformable motion during free breathing. Results: In the rigid and deformable phantom studies, the RMS error of target tracking at the acquisition speed of 19 Hz was approximately 0.3–0.4 mm, which was smaller than the reconstructed pixel resolution of 0.67 mm. In the patient study, the dynamic 2D MRI enabled the monitoring of cycle-to-cycle respiratory variability present in the tumor position. It was seen that the range of centroid motion as well as the area covered due to target motion during each individual respiratory cycle was underestimated compared to the entire motion range observed over multiple breathing cycles. Conclusions: The authors’ initial results demonstrate that sparse-sampling- and reconstruction-based dynamic MRI can be used to achieve adequate image acquisition speeds without significant information loss for the task of radiotherapy guidance. Such monitoring can yield spatial and temporal information superior to conventional offline and online motion capture methods used in thoracic and abdominal radiotherapy.

60 APPLIED LIFE SCIENCES↗

From Data to Discovery: AI's Transformative Role in Thin Film Research

The advancement of thin film technologies is pivotal for progress in numerous fields, including energy, electronics, and quantum computing. However, the traditional trial-and-error approach to materials discovery is inherently slow and inefficient. This presentation will showcase how artificial intelligence (AI) is transforming thin film research by enabling a data-driven paradigm shift. We will highlight our past successes in applying AI to understand radiation damage in thin film oxides, demonstrating how graph analytics can unravel complex material behavior. Additionally, we will provide insights into our current work at the National Renewable Energy Laboratory, where we are leading the charge in autonomous materials science. Backed by a $14M investment in our characterization facility, we are developing AI-guided workflows that seamlessly integrate experimentation and AI-guided decision-making. By harnessing the power of AI, we aim to accelerate the discovery and design of high-performance thin films, propelling innovation across a multitude of industries.

36 MATERIALS SCIENCE↗

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗

On approaches to analyze the sensitivity of simulated hydrologic fluxes to model parameters in the community land model

Here, effective sensitivity analysis approaches are needed to identify important parameters or factors and their uncertainties in complex Earth system models composed of multi-phase multi-component phenomena and multiple biogeophysical-biogeochemical processes. In this study, the impacts of 10 hydrologic parameters in the Community Land Model on simulations of runoff and latent heat flux are evaluated using data from a watershed. Different metrics, including residual statistics, the Nash-Sutcliffe coefficient, and log mean square error, are used as alternative measures of the deviations between the simulated and field observed values. Four sensitivity analysis (SA) approaches, including analysis of variance based on the generalized linear model, generalized cross validation based on the multivariate adaptive regression splines model, standardized regression coefficients based on a linear regression model, and analysis of variance based on support vector machine, are investigated. Results suggest that these approaches show consistent measurement of the impacts of major hydrologic parameters on response variables, but with differences in the relative contributions, particularly for the secondary parameters. The convergence behaviors of the SA with respect to the number of sampling points are also examined with different combinations of input parameter sets and output response variables and their alternative metrics. This study helps identify the optimal SA approach, provides guidance for the calibration of the Community Land Model parameters to improve the model simulations of land surface fluxes, and approximates the magnitudes to be adjusted in the parameter values during parametric model optimization.

58 GEOSCIENCES↗

Model-based verification of I and C specifications - 184

In the field of nuclear I and C (Instrumentation and Control), the late detection of errors in the specifications and the design of I and C has a strong impact in terms of time and money. The early verification in the V cycle of I and C functions is a key issue to capture inconsistencies and errors before the implementation and on-site tests. EDF, in the framework of the collaborative project CONNEXION, has investigated methods based on simulation to formalize I and C requirements and to evaluate them at the conceptual and basic design phases. Behavioral models of the physic parts of the system and I and C functions, described as functional diagrams, are co-simulated in an integration environment based on the FMI (Functional Mockup Interface) standard. In this specific environment, test scenarios are performed on these models. These scenarios are defined on the basis of a high level model of the studied system that takes into account the states to cover (in normal and degraded situations). Requirements, once formalized, are translated into observers that evaluate their fulfillment during the simulations. Simulation logs are then a tool for the designer to analyze the causes of the possible non-fulfillment of requirements and to fix the corresponding errors in the specifications. The proposed methodology enables to detect errors in the specifications of I and C functions, to generate automatically functional test scenarios taking into account the coverage of the requirements and all the different operational modes of the system. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Electric field dependence of the Curie temperature of ferroelectric poly(vinylidenefluoride-trifluoroethylene) co-polymers for pyroelectric energy harvesting

We experimentally study pyroelectric energy harvesting in a ferroelectric co-polymer thin film, with a particular focus on the electric field dependence of its Curie temperature. Liquid-based switchable thermal interfaces are employed to achieve fast thermal cycling and reduce potential measurement errors resulting from leakage currents. Our work confirms that pyroelectric energy harvesting is most effective around the Curie temperature and that the Curie temperature does not depend strongly on electric fields, at least up to 500 kV cm(-1). These results are consistent with a recent study of the electrocaloric effect in co-polymer films of a similar composition.

Cha, G↗

Error and Correction Analysis for the FFA@CEBAF Energy Upgrade

An energy upgrade design for the Continuous Electron Beam Accelerator Facility (CEBAF) is under development, using fixed field alternating gradient (FFA) return arcs to recirculate electron beam up to an additional five times through the accelerating structures at CEBAF. A necessary component of any large accelerator is a beam steering and optical correction system. Small environmental changes and system errors can lower beam quality or even shut down the machine; and in pursuit of the scientific mission of JLab, high quality electron beams must be delivered to the experimental halls on a predictable schedule. Correction in the novel FFA arcs of the current upgrade design is complicated by several factors. These complexities inform the choice of correction algorithm structure and parameter values. A baseline algorithm in addition to diagnostic and correction hardware configuration is presented. The effect of this correction protocol is shown with respect to estimated errors, and several possible extensions of the algorithm are discussed. This work presents an important proof of concept for the FFA@CEBAF design effort, and provides a functional correction strategy which may be simply adjusted and optimized for future design changes.

Coxe, Alex [Old Dominion Univ., Norfolk, VA (Unite↗

Evaluation of pressure reconstruction techniques for Model Order Reduction in incompressible convective heat transfer

This paper compares pressure reconstruction strategies in Model Order Reduction for incompressible flows with convective heat transfer. The Navier-Stokes equation are reduced along with the passive scalar transport equation for the temperature using the POD-Galerkin technique. Six different pressure reconstruction methods are evaluated, two of which are novel to the best of the authors’ knowledge. Accurate pressure reconstruction is key to avoid error buildup in when solving for the conservation of linear momentum at the reduced level. The six approaches are compared using Direct Numerical Simulations of convective heat exchange processes in a 3D Backward Facing Step with a heated cylinder. Additionally, when comparing time-averaged metrics, we observe that the reconstruction methods that approximate the reduced pressure field using techniques borrowed from full order models (mechanical analogy, pressure Poisson, and velocity supremizers) yield higher errors than the methods that seek to stabilize the reduced systems (reduced residual stabilization, artificial divergence, and Uzawa operator).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies have employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.

60 APPLIED LIFE SCIENCES↗

IMPROVING CORRELATION FUNCTION FITTING WITH RIDGE REGRESSION: APPLICATION TO CROSS-CORRELATION RECONSTRUCTION

Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to obtain secure redshifts for 30%-50% or more of the galaxies targeted). In this paper, we improve on the redshift distribution reconstruction methods from our previous work by incorporating full covariance information into our correlation function fits. Correlation function measurements are strongly covariant between angular or spatial bins, and accounting for this in fitting can yield substantial reduction in errors. However, frequently the covariance matrices used in these calculations are determined from a relatively small set (dozens rather than hundreds) of subsamples or mock catalogs, resulting in noisy covariance matrices whose inversion is ill-conditioned and numerically unstable. We present here a method of conditioning the covariance matrix known as ridge regression which results in a more well behaved inversion than other techniques common in large-scale structure studies. We demonstrate that ridge regression significantly improves the determination of correlation function parameters. We then apply these improved techniques to the problem of reconstructing redshift distributions. By incorporating full covariance information, applying ridge regression, and changing the weighting of fields in obtaining average correlation functions, we obtain reductions in the mean redshift distribution reconstruction error of as much as {approx}40% compared to previous methods. We provide a description of POWERFIT, an IDL code for performing power-law fits to correlation functions with ridge regression conditioning that we are making publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗