SEARCH · Search NASA

Results for “randomized methods”

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.

SourceResearch connectionFrom yearThrough year

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

At least 1,027 records · Page 57

All sources NASA NTRS DOE OSTI

DOE OSTI2016

Statistical-learning strategies generate only modestly performing predictive models for urinary symptoms following external beam radiotherapy of the prostate: A comparison of conventional and machine-learning methods

Purpose: Given the paucity of available data concerning radiotherapy-induced urinary toxicity, it is important to ensure derivation of the most robust models with superior predictive performance. This work explores multiple statistical-learning strategies for prediction of urinary symptoms following external beam radiotherapy of the prostate. Methods: The performance of logistic regression, elastic-net, support-vector machine, random forest, neural network, and multivariate adaptive regression splines (MARS) to predict urinary symptoms was analyzed using data from 754 participants accrued by TROG03.04-RADAR. Predictive features included dose-surface data, comorbidities, and medication-intake. Four symptoms were analyzed: dysuria, haematuria, incontinence, and frequency, each with three definitions (grade ≥ 1, grade ≥ 2 and longitudinal) with event rate between 2.3% and 76.1%. Repeated cross-validations producing matched models were implemented. A synthetic minority oversampling technique was utilized in endpoints with rare events. Parameter optimization was performed on the training data. Area under the receiver operating characteristic curve (AUROC) was used to compare performance using sample size to detect differences of ≥0.05 at the 95% confidence level. Results: Logistic regression, elastic-net, random forest, MARS, and support-vector machine were the highest-performing statistical-learning strategies in 3, 3, 3, 2, and 1 endpoints, respectively. Logistic regression, MARS, elastic-net, random forest, neural network, and support-vector machine were the best, or were not significantly worse than the best, in 7, 7, 5, 5, 3, and 1 endpoints. The best-performing statistical model was for dysuria grade ≥ 1 with AUROC ± standard deviation of 0.649 ± 0.074 using MARS. For longitudinal frequency and dysuria grade ≥ 1, all strategies produced AUROC>0.6 while all haematuria endpoints and longitudinal incontinence models produced AUROC<0.6. Conclusions: Logistic regression and MARS were most likely to be the best-performing strategy for the prediction of urinary symptoms with elastic-net and random forest producing competitive results. The predictive power of the models was modest and endpoint-dependent. New features, including spatial dose maps, may be necessary to achieve better models.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-G-BRB-03: Assessing the Sensitivity and False Positive Rate of the Integrated Quality Monitor (IQM) Large Area Ion Chamber to MLC Positioning Errors

Purpose: To examine both the IQM’s sensitivity and false positive rate to varying MLC errors. By balancing these two characteristics, an optimal tolerance value can be derived. Methods: An un-modified SBRT Liver IMRT plan containing 7 fields was randomly selected as a representative clinical case. The active MLC positions for all fields were perturbed randomly from a square distribution of varying width (±1mm to ±5mm). These unmodified and modified plans were measured multiple times each by the IQM (a large area ion chamber mounted to a TrueBeam linac head). Measurements were analyzed relative to the initial, unmodified measurement. IQM readings are analyzed as a function of control points. In order to examine sensitivity to errors along a field’s delivery, each measured field was divided into 5 groups of control points, and the maximum error in each group was recorded. Since the plans have known errors, we compared how well the IQM is able to differentiate between unmodified and error plans. ROC curves and logistic regression were used to analyze this, independent of thresholds. Results: A likelihood-ratio Chi-square test showed that the IQM could significantly predict whether a plan had MLC errors, with the exception of the beginning and ending control points. Upon further examination, we determined there was ramp-up occurring at the beginning of delivery. Once the linac AFC was tuned, the subsequent measurements (relative to a new baseline) showed significant (p <0.005) abilities to predict MLC errors. Using the area under the curve, we show the IQM’s ability to detect errors increases with increasing MLC error (Spearman’s Rho=0.8056, p<0.0001). The optimal IQM count thresholds from the ROC curves are ±3%, ±2%, and ±7% for the beginning, middle 3, and end segments, respectively. Conclusion: The IQM has proven to be able to detect not only MLC errors, but also differences in beam tuning (ramp-up). Partially supported by the Susan Scott Foundation.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Futility

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes; 8) Misc: random number generator, water saturation properties, sorting algorithms.

Collins, BenjaminS.↗

DOE OSTI2018

Metabolic Response of the Immature Right Ventricle to Acute Pressure Overloading

Background Surgical palliation or repair of complex congenital heart disease in early infancy can produce right ventricular (RV) pressure overload, often leading to acute hemodynamic decompensation. The mechanisms causing this acute RV dysfunction remain unclear. We tested the hypothesis that the immature right ventricle lacks the ability to modify substrate metabolism in order to meet increased energy demands induced by acute pressure overloading. Methods and Results Twenty-two infant male mixed breed Yorkshire piglets were randomized to a sham operation (Control) or pulmonary artery banding yielding >2-fold elevation over baseline RV systolic pressure. We used carbon 13 ( 13 C)-labeled substrates and proton nuclear magnetic resonance to assess RV energy metabolism. [Phosphocreatine]/[ATP] was significantly lower after pulmonary artery banding. [Phosphocreatine]/[ATP] inversely correlated with energy demand indexed by maximal sustained RV systolic pressure/left ventricular systolic pressure. Fractional contributions of fatty acids to citric acid cycle were significantly lower in the pulmonary artery banding group than in the Control group (medium-chain fatty acids; 14.5±1.6 versus 8.2±1.0%, long-chain fatty acids; 9.3±1.5 versus 5.1±1.1%). 13 C-flux analysis showed that flux via pyruvate decarboxylation did not increase during RV pressure overloading. Conclusions Acute RV pressure overload yielded a decrease in [phosphocreatine]/[ATP] ratio, implying that ATP production did not balance the increasing ATP requirement. Relative fatty acids oxidation decreased without a reciprocal increase in pyruvate decarboxylation. The data imply that RV inability to adjust substrate oxidation contributes to energy imbalance, and potentially to contractile failure. The data suggest that interventions directed at increasing RV pyruvate decarboxylation flux could ameliorate contractile dysfunction associated with acute pressure overloading.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Selective cerebral perfusion prevents abnormalities in glutamate cycling and neuronal apoptosis in a model of infant deep hypothermic circulatory arrest and reperfusion

Rationale: Deep hypothermic circulatory arrest (DHCA) is often required for the repair of complex congenital cardiac defects in infants. However, DHCA induces neuroapoptosis associated with later development of neurocognitive abnormalities. Selective cerebral perfusion (SCP) theoretically provides superior neural protection possibly through modifications in cerebral substrate oxidation and closely integrated glutamate cycling. Objectives: We tested the hypothesis that SCP modulates glucose entry into the citric acid cycle, and ameliorates abnormalities in glutamate flux which occur in association neuroapoptosis during DHCA. Methods and Results: Eighteen male Yorkshire piglets (age 34-44 days) were assigned randomly to 2 groups of 7 (DHCA or DHCA with SCP for 60 minutes at 18 °C) and 4 control pigs without cardiopulmonary bypass support. After the completion of rewarming from DHCA, 13-Carbon-labeled (13C) glucose as a metabolic tracer was infused. We used gas chromatography-mass spectrometry (GCMS) and nuclear magnetic resonance for metabolic analysis in the frontal cortex. Following 2.5 hours of cerebral reperfusion, we observed similar cerebral ATP levels, absolute levels of lactate and citric acid cycle intermediates, and 13C-enrichment. However, DHCA induced significant abnormalities in glutamate cycling resulting in reduced glutamate/glutamine and elevated γ-aminobutyric acid (GABA)/glutamate along with neuroapoptosis (TUNEL), which were all prevented by SCP. Conclusions: DHCA alone induces abnormalities in cycling of the major neurotransmitters in association with neuroapoptosis, but does not alter cerebral glucose utilization during reperfusion. The data suggest that SCP prevents these modifications in glutamate/glutamine/GABA cycling and protects the cerebral cortex from neuroapoptosis.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

Utilizing Highly Scattered Light for Intelligence through Aerosols

This communication is the final report for the project Utilizing Highly Scattered Light for Intelligence through Aerosols funded by the Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories and lasting six months in 2019. Aerosols like fog reduce visibility and cause down-time that for critical systems or operations are unacceptable. Information is lost due to the random scattering and absorption of light by tiny particles. Computational diffuse optical imaging methods show promise for interpreting the light transmitted through fog, enabling sensing and imaging to improve situational awareness at depths 10 times greater than current methods. Developing this capability first requires verification and validation of diffusion models of light propagation in fog. For this reason, analytical models were developed and compared to experimental data captured at the Sandia National Laboratory Fog Chamber facility. A methodology was developed to incorporate the propagation of scattered light through the imaging optics to a pixel array. The diffusion approximation to the radiative transfer equation was found to predict light propagation in fog under the appropriate conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Development of Short-Term Forecasting Models Using Plant Asset Data and Feature Selection

Nuclear power plants collect and store large volumes of heterogeneous data from various components and systems. With recent advances in machine learning (ML) techniques, these data can be leveraged to develop diagnostic and short-term forecasting models to better predict future equipment condition. Maintenance operations can then be planned in advance whenever degraded performance is predicted, thus resulting in fewer unplanned outages and the optimization of maintenance activities. This enables lower maintenance costs and improves the overall economics of nuclear power. This paper focuses on developing a short-term forecasting process that leverages a feature selection process to distill large volumes of heterogeneous data and predict specific equipment parameters. A variety of feature selection methods, including Shapley Additive Explanations (SHAP) and variance inflation factor (VIF), were used to select the optimal features as inputs for three ML methods: long short-term memory (LSTM) networks, support vector regression (SVR), and random forest (RF). Each combination of model and input features was used to predict a pump bearing temperature both 1 and 24 hours in advance, based on actual plant system data. The optimal inputs for the LSTM and SVR were selected using the SHAP values, while the optimal input for the RF consisted solely of the response variable itself. Each model produced similar 1-hour-ahead predictions, with root mean square errors (RMSEs) of roughly 0.006. For the 24-hour-ahead predictions, differences could be seen between LSTM, SVR, and RF, as reflected by model performances of 0.036 +- 0.014, 0.0026 +- 0, and 0.063 +- 0.004 RMSE, respectively. As big data and continuous online monitoring become more widely available, the proposed feature selection process can be used for many applications beyond the prediction of process parameters within nuclear infrastructure.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Futility

Collins, Benjamin S.↗

DOE OSTI2016

Impact of Sequencing Radiation Therapy and Chemotherapy on Long-Term Local Toxicity for Early Breast Cancer: Results of a Randomized Study at 15-Year Follow-Up

Purpose: To compare long-term late local toxicity after either concomitant or sequential chemoradiation therapy after breast-conserving surgery. Methods and Materials: From 1997 to 2002, women aged 18 to 75 years who underwent breast-conserving surgery and axillary dissection for early breast cancer and in whom CMF (cyclophosphamide, methotrexate, and 5-fluorouracil) chemotherapy was planned were randomized between concomitant and sequential radiation therapy. Radiation therapy was delivered to the whole breast through tangential fields to 50 Gy in 20 fractions over a period of 4 weeks, followed by an electron boost. Surviving patients were tentatively contacted and examined between March and September 2014. Patients in whom progressive disease had developed or who had undergone further breast surgery were excluded. Local toxicity (fibrosis, telangiectasia, and breast atrophy or retraction) was scored blindly to the treatment received. A logistic regression was run to investigate the effect of treatment sequence after correction for several patient-, treatment-, and tumor-related covariates on selected endpoints. The median time to cross-sectional analysis was 15.7 years (range, 12.0-17.8 years). Results: Of 206 patients randomized, 154 (74.8%) were potentially eligible. Of these, 43 (27.9%) refused participation and 4 (2.6%) had been lost to follow-up, and for 5 (3.2%), we could not restore planning data; thus, the final number of analyzed patients was 102. No grade 4 toxicity had been observed, whereas the number of grade 3 toxicity events was low (<8%) for each item, allowing pooling of grade 2 and 3 events for further analysis. Treatment sequence (concomitant vs sequential) was an independent predictor of grade 2 or 3 fibrosis according to both the National Cancer Institute Common Terminology Criteria for Adverse Events (odds ratio [OR], 4.05; 95% confidence interval [CI], 1.34-12.2; P=.013) and the SOMA (Subjective, Objective, Management and Analytic) scale (OR, 3.75; 95% CI, 1.19-11.79; P=.018), as well as grade 2 or 3 breast atrophy or retraction (OR, 3.87; 95% CI, 1.42-10.56; P=.008). No effect on telangiectasia was detected. Conclusions: At long-term follow-up, concomitant chemoradiation therapy has a detrimental effect on both fibrosis and retraction with an approximately 4-fold increase in the odds of grade 2 or 3 toxicity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2021

On the Feynman-alpha method for reflected fissile assemblies

The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the k eff multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve k eff values of 0.83–0.94 and prompt periods of 5–75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for k eff < 0.92, whereas the Rossi-alpha method is generally more accurate for higher multiplications. Here, the uncertainty propagation developed in this work should be used for all Feynman-alpha measurements and will therein improve fitting accuracy and appropriate precision estimates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2015

Flattening of fuel importance for heterogeneous system to estimate maximal multiplication factor - 14595

In order to quantify risks of re-criticality incidents associated with loss of coolant accidents (LOCA), the maximum reactivity insertion by relocation of damaged fuel should be quantified. As the first step for the quantification, an automated search scheme is studied for an optimal geometry of damaged fuel in the coolant channel where the neutron multiplication factor k{sub eff} takes a maximal value. The scheme is based on the flattening of the fuel importance. The importance can be recognized as the substitution reactivity from fuel to water in heterogeneous systems. The flattening is achieved by substitution of water and the fuel so as to raise the k{sub eff} referring the local substitution reactivities. To calculate the reactivities efficiently, the first order perturbation scheme is adopted. In the scheme, the adjoint flux is calculated with the PARTISN code. The multi group constants used for the calculation and the perturbed reaction rates are estimated with the continuous energy Monte Carlo code MCNP-5. The proposed methods are tested for a quarter pin cell model that is constructed using Cartesian mesh. From a random distribution of a given amount of fragmented fuel, an optimal geometry is found where the fragmented fuels are aggregated. The multiplication factor in the geometry is greater than that in the original random distribution by 1.4%Δk/k. That indicates the significance of this study. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Accuracy of Robotic Radiosurgical Liver Treatment Throughout the Respiratory Cycle

Purpose: To quantify random uncertainties in robotic radiosurgical treatment of liver lesions with real-time respiratory motion management. Methods and Materials: We conducted a retrospective analysis of 27 liver cancer patients treated with robotic radiosurgery over 118 fractions. The robotic radiosurgical system uses orthogonal x-ray images to determine internal target position and correlates this position with an external surrogate to provide robotic corrections of linear accelerator positioning. Verification and update of this internal–external correlation model was achieved using periodic x-ray images collected throughout treatment. To quantify random uncertainties in targeting, we analyzed logged tracking information and isolated x-ray images collected immediately before beam delivery. For translational correlation errors, we quantified the difference between correlation model–estimated target position and actual position determined by periodic x-ray imaging. To quantify prediction errors, we computed the mean absolute difference between the predicted coordinates and actual modeled position calculated 115 milliseconds later. We estimated overall random uncertainty by quadratically summing correlation, prediction, and end-to-end targeting errors. We also investigated relationships between tracking errors and motion amplitude using linear regression. Results: The 95th percentile absolute correlation errors in each direction were 2.1 mm left–right, 1.8 mm anterior–posterior, 3.3 mm cranio–caudal, and 3.9 mm 3-dimensional radial, whereas 95th percentile absolute radial prediction errors were 0.5 mm. Overall 95th percentile random uncertainty was 4 mm in the radial direction. Prediction errors were strongly correlated with modeled target amplitude (r=0.53-0.66, P<.001), whereas only weak correlations existed for correlation errors. Conclusions: Study results demonstrate that model correlation errors are the primary random source of uncertainty in Cyberknife liver treatment and, unlike prediction errors, are not strongly correlated with target motion amplitude. Aggregate 3-dimensional radial position errors presented here suggest the target will be within 4 mm of the target volume for 95% of the beam delivery.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2024

Generalized representative structures for atomistic systems

A new method is presented to generate atomic structures that reproduce the essential characteristics of arbitrary material systems, phases, or ensembles. Previous methods allow one to reproduce the essential characteristics (e.g. the chemical disorder) of a large random alloy within a small crystal structure. The ability to generate small representations of random alloys, along with the restriction to crystal systems, results from using the fixed-lattice cluster correlations to describe structural characteristics. A more general description of the structural characteristics of atomic systems is obtained using complete sets of atomic environment descriptors. These are used within for generating representative atomic structures without restriction to fixed lattices. A general data-driven approach is provided here utilizing the atomic cluster expansion (ACE) basis. The N-body ACE descriptors are a complete set of atomic environment descriptors that span both chemical and spatial degrees of freedom and are used within for describing atomic structures. The generalized representative structure (GRS) method presented within generates small atomic structures that reproduce ACE descriptor distributions corresponding to arbitrary structural and chemical complexity. It is shown that systematically improvable representations of crystalline systems on fixed parent lattices, amorphous materials, liquids, and ensembles of atomic structures may be produced efficiently through optimization algorithms. With the GRS method, we highlight reduced representations of atomistic machine-learning training datasets that contain similar amounts of information and small 40–72 atom representations of liquid phases. The ability to use GRS methodology as a driver for informed novel structure generation is also demonstrated. The advantages over other data-driven methods and state-of-the-art methods restricted to high-symmetry systems are highlighted.

atomic cluster expansion↗

DOE OSTI2017

Assessment of genome annotation using gene function similarity within the gene neighborhood

Functional annotation of bacterial genomes is an obligatory and crucially important step of information processing from the genome sequences into cellular mechanisms. However, there is a lack of computational methods to evaluate the quality of functional assignments. Results: We developed a genome-scale model that assigns Bayesian probability to each gene utilizing a known property of functional similarity between neighboring genes in bacteria. Conclusions: Our model clearly distinguished true annotation from random annotation with Bayesian annotation probability >0.95. Our model will provide a useful guide to quantitatively evaluate functional annotation methods and to detect gene sets with reliable annotations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

On the Estimation of Circumbinary Orbital Properties

We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity—the random motion of a satellite relative to a dynamically cool orbit—from oscillatory modes driven by the central binary’s time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto–Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to promote mergers and growth. These results illustrate how dynamical cooling can set the stage for the formation of Tatooine-like planets around stellar binaries and the small moons around the Pluto–Charon binary planet.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Multi-fidelity Gaussian process regression for prediction of random fields

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

A Hierarchical Feature-Based Methodology to Perform Cervical Cancer Classification

Prevention of cervical cancer could be performed using Pap smear image analysis. This test screens pre-neoplastic changes in the cervical epithelial cells; accurate screening can reduce deaths caused by the disease. Pap smear test analysis is exhaustive and repetitive work performed visually by a cytopathologist. This article proposes a workload-reducing algorithm for cervical cancer detection based on analysis of cell nuclei features within Pap smear images. We investigate eight traditional machine learning methods to perform a hierarchical classification. We propose a hierarchical classification methodology for computer-aided screening of cell lesions, which can recommend fields of view from the microscopy image based on the nuclei detection of cervical cells. We evaluate the performance of several algorithms against the Herlev and CRIC databases, using a varying number of classes during image classification. Results indicate that the hierarchical classification performed best when using Random Forest as the key classifier, particularly when compared with decision trees, k-NN, and the Ridge methods.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

The information content of projected galaxy fields

ABSTRACT The power spectrum of the non-linearly evolved large-scale mass distribution recovers only a minority of the information available on the mass fluctuation amplitude. We investigate the recovery of this information in 2D ‘slabs’ of the mass distribution averaged over ≈100 h−1 Mpc along the line of sight, as might be obtained from photometric redshift surveys. We demonstrate a Hamiltonian Monte Carlo method to reconstruct the non-Gaussian mass distribution in slabs, under the assumption that the projected field is a point-transformed Gaussian random field, Poisson-sampled by galaxies. When applied to the Quijote N-body suite at z = 0.5 and at a transverse resolution of 2 h−1 Mpc, the method recovers ∼30 times more information than the 2D power spectrum in the well-sampled limit, recovering the Gaussian limit on information. At a more realistic galaxy sampling density of 0.01 h3 Mpc−3, shot noise reduces the information gain to a factor of 5 improvement over the power spectrum at resolutions of 4 h−1 Mpc or smaller.

79 ASTRONOMY AND ASTROPHYSICS↗