Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “variance estimation”

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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Cosmic variance in the nanohertz gravitational wave background

We use large N-body simulations and empirical scaling relations between dark matter halos, galaxies, and supermassive black holes (SMBBHs) to estimate the formation rates of SMBBH binaries and the resulting low-frequency stochastic gravitational wave background (GWB). We find this GWB to be relatively insensitive (≲10%) to cosmological parameters, with only slight variation between wmap5 and Planck cosmologies. We find that uncertainty in the astrophysical scaling relations changes the amplitude of the GWB by a factor of ∼2. Current observational limits are already constraining this predicted range of models. We investigate the Poisson variance in the amplitude of the GWB for randomly generated populations of SMBBHs, finding a scatter of order unity per frequency bin below 10 nHz, and increasing to a factor of ∼10 near 100 nHz. This variance is a result of the rarity of the most massive binaries, which dominate the signal, and acts as a fundamental uncertainty on the amplitude of the underlying power law spectrum. This Poisson uncertainty dominates at ≳20 nHz, while at lower frequencies the dominant uncertainty is related to our poor understanding of the astrophysical scaling relations, although very low frequencies may be dominated by uncertainties related to the final parsec problem and the processes which drive binaries to the gravitational wave dominated regime. Cosmological effects are negligible at all frequencies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A Bayesian approach to multivariate measurement system assessment

This article considers system assessment for multivariate measurements and presents a Bayesian approach to analyzing gauge R&R study data. The evaluation of variances for univariate measurement becomes the evaluation of covariance matrices for multivariate measurements. The Bayesian approach ensures positive definite estimates of the covariance matrices and easily provides their uncertainty. Furthermore, various measurement system assessment criteria are easily evaluated. The approach is illustrated with data from a real gauge R&R study as well as simulated data.

random effects↗
NASA NTRS1991

Humidity profiles over the ocean

The variabilities of atmospheric humidity profile over oceans from daily to interannual time scales were examined using 9 years of daily and semidaily radiosonde soundings at island stations extending from the Arctic to the South Pacific. The relative humidity profiles were found to have considerable temporal and geographic variabilities, contrary to the prevalent assumption. Principal component analysis on the profiles of specific humidity were used to examine the applicability of a relation between the surface-level humidity and the integrated water vapor; this relation has been used to estimate large-scale evaporation from satellite data. The first principal component was found to correlate almost perfectly with the integrated water vapor. The fractional variance represented by this mode increases with increasing period. It reaches approximately 90 percent at two weeks and decreases sharply, below one week, down to approximately 60 percent at the daily period. At low frequencies, the integrated water vapor appeared to be an adequate estimator of the humidity profile and the surface-level humidity. At periods shorter than a week, more than one independent estimator is needed.

Liu, W. T.↗
NASA NTRS1981

The effects of missing data on global ozone estimates

The effects of missing data and model truncation on estimates of the global mean, zonal distribution, and global distribution of ozone are considered. It is shown that missing data can introduce biased estimates with errors that are not accounted for in the accuracy calculations of empirical modeling techniques. Data-fill techniques are introduced and used for evaluating error bounds and constraining the estimate in areas of sparse and missing data. It is found that the accuracy of the global mean estimate is more dependent on data distribution than model size. Zonal features can be accurately described by 7th order models over regions of adequate data distribution. Data variance accounted for by higher order models appears to represent climatological features of columnar ozone rather than pure error. Data-fill techniques can prevent artificial feature generation in regions of sparse or missing data without degrading high order estimates over dense data regions.

Drewry, J. W.↗
DOE OSTI2017

Vulnerability of US thermoelectric power generation to climate change when incorporating state-level environmental regulations

This study explores the interactions between climate and thermoelectric generation in the U.S. by coupling an Earth System Model with a thermoelectric power generation model. We validated model simulations of power production for selected power plants (~44% of existing thermoelectric capacity) against reported values. In addition, we projected future usable capacity for existing power plants under two different climate change scenarios. Results indicate that climate change alone may reduce average thermoelectric generating capacity by 2%-3% by the 2060s. Reductions up to 12% are expected if environmental requirements are enforced without waivers for thermal variation. This study concludes that the impact of climate change on the U.S. thermoelectric power system is less than previous estimates due to an inclusion of a spatially-disaggregated representation of environmental regulations and provisional variances that temporarily relieve power plants from permit requirements. This work highlights the significance of accounting for legal constructs in which the operation of power plants are managed, and underscores the effects of provisional variances in addition to environmental requirements.

climate change↗
DOE OSTI2015

INTERPRETING THE UNRESOLVED INTENSITY OF COSMOLOGICALLY REDSHIFTED LINE RADIATION

Intensity mapping experiments survey the spectrum of diffuse line radiation rather than detect individual objects at high signal-to-noise ratio. Spectral maps of unresolved atomic and molecular line radiation contain three-dimensional information about the density and environments of emitting gas and efficiently probe cosmological volumes out to high redshift. Intensity mapping survey volumes also contain all other sources of radiation at the frequencies of interest. Continuum foregrounds are typically ∼10{sup 2}–10{sup 3} times brighter than the cosmological signal. The instrumental response to bright foregrounds will produce new spectral degrees of freedom that are not known in advance, nor necessarily spectrally smooth. The intrinsic spectra of foregrounds may also not be well known in advance. We describe a general class of quadratic estimators to analyze data from single-dish intensity mapping experiments and determine contaminated spectral modes from the data themselves. The key attribute of foregrounds is not that they are spectrally smooth, but instead that they have fewer bright spectral degrees of freedom than the cosmological signal. Spurious correlations between the signal and foregrounds produce additional bias. Compensation for signal attenuation must estimate and correct this bias. A successful intensity mapping experiment will control instrumental systematics that spread variance into new modes, and it must observe a large enough volume that contaminant modes can be determined independently from the signal on scales of interest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2004

Amplitude Scintillation due to Atmospheric Turbulence for the Deep Space Network Ka-Band Downlink

Fast amplitude variations due to atmospheric scintillation are the main concerns for the Deep Space Network (DSN) Ka-band downlink under clear weather conditions. A theoretical study of the amplitude scintillation variances for a finite aperture antenna is presented. Amplitude variances for weak scattering scenarios are examined using turbulence theory to describe atmospheric irregularities. We first apply the Kolmogorov turbulent spectrum to a point receiver for three different turbulent profile models, especially for an exponential model varying with altitude. These analytic solutions then are extended to a receiver with a finite aperture antenna for the three profile models. Smoothing effects of antenna aperture are expressed by gain factors. A group of scaling factor relations is derived to show the dependences of amplitude variances on signal wavelength, antenna size, and elevation angle. Finally, we use these analytic solutions to estimate the scintillation intensity for a DSN Goldstone 34-m receiving station. We find that the (rms) amplitude fluctuation is 0.13 dB at 20-deg elevation angle for an exponential model, while the fluctuation is 0.05 dB at 90 deg. These results will aid us in telecommunication system design and signal-fading prediction. They also provide a theoretical basis for further comparison with other measurements at Ka-band.

Ho, C.↗
NASA NTRS2004

Air Mass Factor Formulation for Spectroscopic Measurements from Satellites: Application to Formaldehyde Retrievals from the Global Ozone Monitoring Experiment

We present a new formulation for the air mass factor (AMF) to convert slant column measurements of optically thin atmospheric species from space into total vertical columns. Because of atmospheric scattering, the AMF depends on the vertical distribution of the species. We formulate the AMF as the integral of the relative vertical distribution (shape factor) of the species over the depth of the atmosphere, weighted by altitude-dependent coefficients (scattering weights) computed independently from a radiative transfer model. The scattering weights are readily tabulated, and one can then obtain the AMF for any observation scene by using shape factors from a three dimensional (3-D) atmospheric chemistry model for the period of observation. This approach subsequently allows objective evaluation of the 3-D model with the observed vertical columns, since the shape factor and the vertical column in the model represent two independent pieces of information. We demonstrate the AMF method by using slant column measurements of formaldehyde at 346 nm from the Global Ozone Monitoring Experiment satellite instrument over North America during July 1996. Shape factors are cumputed with the Global Earth Observing System CHEMistry (GEOS-CHEM) global 3-D model and are checked for consistency with the few available aircraft measurements. Scattering weights increase by an order of magnitude from the surface to the upper troposphere. The AMFs are typically 20-40% less over continents than over the oceans and are approximately half the values calculated in the absence of scattering. Model-induced errors in the AMF are estimated to be approximately 10%. The GEOS-CHEM model captures 50% and 60% of the variances in the observed slant and vertical columns, respectively. Comparison of the simulated and observed vertical columns allows assessment of model bias.

Palmer, Paul I.↗
NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗
NASA NTRS2016

Interpreting The Unresolved Intensity Of Cosmologically Redshifted Line Radiation

Intensity mapping experiments survey the spectrum of diffuse line radiation rather than detect individual objects at high signal-to-noise ratio. Spectral maps of unresolved atomic and molecular line radiation contain three-dimensional information about the density and environments of emitting gas and efficiently probe cosmological volumes out to high redshift. Intensity mapping survey volumes also contain all other sources of radiation at the frequencies of interest. Continuum foregrounds are typically approximately 10(sup 2)-10(Sup 3) times brighter than the cosmological signal. The instrumental response to bright foregrounds will produce new spectral degrees of freedom that are not known in advance, nor necessarily spectrally smooth. The intrinsic spectra of fore-grounds may also not be well known in advance. We describe a general class of quadratic estimators to analyze data from single-dish intensity mapping experiments and determine contaminated spectral modes from the data themselves. The key attribute of foregrounds is not that they are spectrally smooth, but instead that they have fewer bright spectral degrees of freedom than the cosmological signal. Spurious correlations between the signal and foregrounds produce additional bias. Compensation for signal attenuation must estimate and correct this bias. A successful intensity mapping experiment will control instrumental systematics that spread variance into new modes, and it must observe a large enough volume that contaminant modes can be determined independently from the signal on scales of interest.

INTERPRETING↗
DOE OSTI2018

Measuring the scale dependence of intrinsic alignments using multiple shear estimates

We present a new method for measuring the scale dependence of the intrinsic alignment (IA) contamination to the galaxy–galaxy lensing signal, which takes advantage of multiple shear estimation methods applied to the same source galaxy sample. By exploiting the resulting correlation of both shape noise and cosmic variance, our method can provide an increase in the signal-to-noise of the measured IA signal as compared to methods which rely on the difference of the lensing signal from multiple photometric redshift bins. For a galaxy–galaxy lensing measurement which uses LSST sources and DESI lenses, the signal-to-noise on the IA signal from our method is predicted to improve by a factor of ~2 relative to the method of Blazek et al. (2012), for pairs of shear estimates which yield substantially different measured IA amplitudes and highly correlated shape noise terms. We show that statistical error necessarily dominates the measurement of IAs using our method. We also consider a physically motivated extension of the Blazek et al. (2012) method which assumes that all nearby galaxy pairs, rather than only excess pairs, are subject to IA. In this case, the signal-to-noise of the method of Blazek et al. (2012) is improved.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Tracking the GLOMR satellite

The task of day-to-day low orbiting satellite tracking utilizing the NAVSPASUR orbital elements is discussed and methods for improving pass time predictions are presented. Estimates are needed for preprogramming of satellite-initiated communications scheduling which requires an accuracy of approximately 30 seconds. This can be achieved by removing the variance associated with the NAVSPASUR D sub 2 (decay) term. Finally, the shock evidenced in GLOMR's orbit on February 7, 1986 is documented and attributed to a severe solar storm with immediately enhanced drag. GLOMR's life expectancy in orbit is now estimated to have dropped approximately 17% by the end of orbit in early February, 1987.

Reiss, Keith W.↗
DOE OSTI2016

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation

Purpose: To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. Methods: The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl{sub 2} aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe–Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. [“Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues,” Phys. Med. Biol. 55, 1343–1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Results: Based on the authors’ idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. Conclusions: The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

Bootstrapping outperforms community‐weighted approaches for estimating the shapes of phenotypic distributions

Abstract Estimating phenotypic distributions of populations and communities is central to many questions in ecology and evolution. These distributions can be characterized by their moments (mean, variance, skewness and kurtosis) or diversity metrics (e.g. functional richness). Typically, such moments and metrics are calculated using community‐weighted approaches (e.g. abundance‐weighted mean). We propose an alternative bootstrapping approach that allows flexibility in trait sampling and explicit incorporation of intraspecific variation, and show that this approach significantly improves estimation while allowing us to quantify uncertainty. We assess the performance of different approaches for estimating the moments of trait distributions across various sampling scenarios, taxa and datasets by comparing estimates derived from simulated samples with the true values calculated from full datasets. Simulations differ in sampling intensity (individuals per species), sampling biases (abundance, size), trait data source (local vs. global) and estimation method (two types of community‐weighting, two types of bootstrapping). We introduce the traitstrap R package, which contains a modular and extensible set of bootstrapping and weighted‐averaging functions that use community composition and trait data to estimate the moments of community trait distributions with their uncertainty. Importantly, the first function in the workflow, trait_fill , allows the user to specify hierarchical structures (e.g. plot within site, experiment vs. control, species within genus) to assign trait values to each taxon in each community sample. Across all taxa, simulations and metrics, bootstrapping approaches were more accurate and less biased than community‐weighted approaches. With bootstrapping, a sample size of 9 or more measurements per species per trait generally included the true mean within the 95% CI. It reduced average percent errors by 26%–74% relative to community‐weighting. Random sampling across all species outperformed both size‐ and abundance‐biased sampling. Our results suggest randomly sampling ~9 individuals per sampling unit and species, covering all species in the community and analysing the data using nonparametric bootstrapping generally enable reliable inference on trait distributions, including the central moments, of communities. By providing better estimates of community trait distributions, bootstrapping approaches can improve our ability to link traits to both the processes that generate them and their effects on ecosystems.

Maitner, Brian S.↗
DOE OSTI2013

Dimensionality and noise in energy selective x-ray imaging

Purpose: To develop and test a method to quantify the effect of dimensionality on the noise in energy selective x-ray imaging.Methods: The Cramèr-Rao lower bound (CRLB), a universal lower limit of the covariance of any unbiased estimator, is used to quantify the noise. It is shown that increasing dimensionality always increases, or at best leaves the same, the variance. An analytic formula for the increase in variance in an energy selective x-ray system is derived. The formula is used to gain insight into the dependence of the increase in variance on the properties of the additional basis functions, the measurement noise covariance, and the source spectrum. The formula is also used with computer simulations to quantify the dependence of the additional variance on these factors. Simulated images of an object with three materials are used to demonstrate the trade-off of increased information with dimensionality and noise. The images are computed from energy selective data with a maximum likelihood estimator.Results: The increase in variance depends most importantly on the dimension and on the properties of the additional basis functions. With the attenuation coefficients of cortical bone, soft tissue, and adipose tissue as the basis functions, the increase in variance of the bone component from two to three dimensions is 1.4 × 10{sup 3}. With the soft tissue component, it is 2.7 × 10{sup 4}. If the attenuation coefficient of a high atomic number contrast agent is used as the third basis function, there is only a slight increase in the variance from two to three basis functions, 1.03 and 7.4 for the bone and soft tissue components, respectively. The changes in spectrum shape with beam hardening also have a substantial effect. They increase the variance by a factor of approximately 200 for the bone component and 220 for the soft tissue component as the soft tissue object thickness increases from 1 to 30 cm. Decreasing the energy resolution of the detectors increases the variance of the bone component markedly with three dimension processing, approximately a factor of 25 as the resolution decreases from 100 to 3 bins. The increase with two dimension processing for adipose tissue is a factor of two and with the contrast agent as the third material for two or three dimensions is also a factor of two for both components. The simulated images show that a maximum likelihood estimator can be used to process energy selective x-ray data to produce images with noise close to the CRLB.Conclusions: The method presented can be used to compute the effects of the object attenuation coefficients and the x-ray system properties on the relationship of dimensionality and noise in energy selective x-ray imaging systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗