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At least 811 records · Page 45

NASA Tech Briefs, December 2009

Topics include: A Deep Space Network Portable Radio Science Receiver; Detecting Phase Boundaries in Hard-Sphere Suspensions; Low-Complexity Lossless and Near-Lossless Data Compression Technique for Multispectral Imagery; Very-Long-Distance Remote Hearing and Vibrometry; Using GPS to Detect Imminent Tsunamis; Stream Flow Prediction by Remote Sensing and Genetic Programming; Pilotless Frame Synchronization Using LDPC Code Constraints; Radiometer on a Chip; Measuring Luminescence Lifetime With Help of a DSP; Modulation Based on Probability Density Functions; Ku Telemetry Modulator for Suborbital Vehicles; Photonic Links for High-Performance Arraying of Antennas; Reconfigurable, Bi-Directional Flexfet Level Shifter for Low-Power, Rad-Hard Integration; Hardware-Efficient Monitoring of I/O Signals; Video System for Viewing From a Remote or Windowless Cockpit; Spacesuit Data Display and Management System; IEEE 1394 Hub With Fault Containment; Compact, Miniature MMIC Receiver Modules for an MMIC Array Spectrograph; Waveguide Transition for Submillimeter-Wave MMICs; Magnetic-Field-Tunable Superconducting Rectifier; Bonded Invar Clip Removal Using Foil Heaters; Fabricating Radial Groove Gratings Using Projection Photolithography; Gratings Fabricated on Flat Surfaces and Reproduced on Non-Flat Substrates; Method for Measuring the Volume-Scattering Function of Water; Method of Heating a Foam-Based Catalyst Bed; Small Deflection Energy Analyzer for Energy and Angular Distributions; Polymeric Bladder for Storing Liquid Oxygen; Pyrotechnic Simulator/Stray-Voltage Detector; Inventions Utilizing Microfluidics and Colloidal Particles; RuO2 Thermometer for Ultra-Low Temperatures; Ultra-Compact, High-Resolution LADAR System for 3D Imaging; Dual-Channel Multi-Purpose Telescope; Objective Lens Optimized for Wavefront Delivery, Pupil Imaging, and Pupil Ghosting; CMOS Camera Array With Onboard Memory; Quickly Approximating the Distance Between Two Objects; Processing Images of Craters for Spacecraft Navigation; Adaptive Morphological Feature-Based Object Classifier for a Color Imaging System; Rover Slip Validation and Prediction Algorithm; Safety and Quality Training Simulator; Supply-Chain Optimization Template; Algorithm for Computing Particle/Surface Interactions; Cryogenic Pupil Alignment Test Architecture for Aberrated Pupil Images; and Thermal Transport Model for Heat Sink Design.

Source record↗

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗

Elastic wave velocities in anorthosite and anorthositic gabbros from Apollo 15 and 16 landing sites

Laboratory measurements of ultrasonic velocities in lunar samples 15065, 15555, 15415, 60015, and 61016 as well as in synthetic materials corresponding to compositions of anorthositic gabbros are presented as a function of hydrostatic pressure to about 7 kb. The author examined the seismic velocity distributions in the moon with reference to the variations to be expected in a homogeneous medium. The lunar mantle begins about 60 km, and the velocity of P waves in this area is about 7.7 km/sec. Variation of the seismic parameter with depth in the upper crust (about 20 km thick) is much too rapid to be explained by compression of a uniform material and the departure from expectation is so great that no reasonable adjustment of the material parameters can bring agreement; therefore, this author concludes that this result in this region of the moon is not due to self-compression but to textural gradients. In the lower crust (about 40 km thick), the region is shown to be relatively homogeneous, consisting probably of anorthositic rocks.

Chung, D. H.↗

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael↗

A Bayesian Analysis of SDSS J0914+0853, a Low-mass Dual AGN Candidate

We present the first results from Bayesian AnalYsis of Multiple AGN in X-rays (BAYMAX), a tool that uses a Bayesian framework to quantitatively evaluate whether a given Chandra observation is more likely a single or dual point source. Although the most robust method of determining the presence of dual active galactic nuclei (AGNs) is to use X-ray observations, only sources that are widely separated relative to the instrumentʼs point-spread function are easy to identify. It becomes increasingly difficult to distinguish dual AGNs from single AGNs when the separation is on the order of Chandraʼs angular resolution (<1″). Using likelihood models for single and dual point sources, BAYMAX quantitatively evaluates the likelihood of an AGN for a given source. Specifically, we present results from BAYMAX analyzing the lowest-mass dual AGN candidate to date, SDSS J0914+0853, where archival Chandra data shows a possible secondary AGN ∼ 0"3 from the primary. Analyzing a new 50 ks Chandra observation, results from BAYMAX shows that SDSS J0914+0853 is most likely a single AGN with a Bayes factor of 13.5 in favor of a single point source model. Further, posterior distributions from the dual point source model are consistent with emission from a single AGN. We find a very low probability of SDSS J0914+0853 being a dual AGN system with a flux ratio f>0.3 and separation r>0"3. Overall, BAYMAX will be an important tool for correctly classifying candidate dual AGNs in the literature, as well as studying the dual AGN population where past spatial resolution limits have prevented systematic analyses.

Active galaxies↗

The spatial distribution of shocked gas in the Orion nebula

Observations of the spatial distribution of extinction and excitation temperature toward the molecular hydrogen emission in the Orion molecular cloud OMC-1 are presented. Most, although not all, of the observed structure in the near-infrared line intensities results from variations in the column density of vibrationally excited H2 and is not due to variable extinction or temperature. The extinction toward the center of the emission region is between 1 and 2 mag at 4712/cm, the frequency of the v = 1-0 S(1) line, but increases toward the edges. The lack of emission from the eastern part of the nebula may result from increased extinction in that direction. Variations in the extinction temperature are less than the observational uncertainties of + or - 200 K at all but one position observed. Therefore, the excitation temperature of the hydrogen molecules is probably not a strong function of either the shock velocity or the density of the gas. Observations of the v = 3-2 S(3) line in the direction of strongest emission indicate the presence of gas temperatures about 2700 K and place constraints on the column density of gas which is at higher temperature.

Beck, S. C.↗

Ni partitioning between diopside and silicate melt - A redetermination by ion microprobe and recognition of an experimental complication

The capabilities of and potential problems with ion microprobe analysis are illustrated in the determination of Ni distribution between silicate melt and diopside as a function of concentration. Samples of diopside and a melt in the albite-anorthite-diopside system were doped with Ni to levels of 5.22 and 1.08 wt % and 1060, 138, 42 and 30 ppm, and with 3 ppm of Ni-63, and characterized by both electron and ion microprobe techniques. Measurements of Ni-62 distribution by the ion probe method give a ratio of 1.87 for the ratio of count rates in the diopsides with the glass, which is slightly lower than the value of 2.05 obtained from beta-track mapping. The measurements required the secondary ion signal to be linear with concentration in the range measured, and a calibration to correct for differential secondary ion yields from different phases. It is found, however, that partition coefficients measured for Ni-58 and Ni-60 are not constant with Ni concentration, probably due to Ni migration during crystallization. The results thus show ion microprobe analyses to be feasible for simultaneous measurements of distributions of more than one element, and of elements inappropriate for beta-track mapping or electron probe analysis.

Steele, I. M.↗

An Overview of the NCC Spray/Monte-Carlo-PDF Computations

This paper advances the state-of-the-art in spray computations with some of our recent contributions involving scalar Monte Carlo PDF (Probability Density Function), unstructured grids and parallel computing. It provides a complete overview of the scalar Monte Carlo PDF and Lagrangian spray computer codes developed for application with unstructured grids and parallel computing. Detailed comparisons for the case of a reacting non-swirling spray clearly highlight the important role that chemistry/turbulence interactions play in the modeling of reacting sprays. The results from the PDF and non-PDF methods were found to be markedly different and the PDF solution is closer to the reported experimental data. The PDF computations predict that some of the combustion occurs in a predominantly premixed-flame environment and the rest in a predominantly diffusion-flame environment. However, the non-PDF solution predicts wrongly for the combustion to occur in a vaporization-controlled regime. Near the premixed flame, the Monte Carlo particle temperature distribution shows two distinct peaks: one centered around the flame temperature and the other around the surrounding-gas temperature. Near the diffusion flame, the Monte Carlo particle temperature distribution shows a single peak. In both cases, the computed PDF's shape and strength are found to vary substantially depending upon the proximity to the flame surface. The results bring to the fore some of the deficiencies associated with the use of assumed-shape PDF methods in spray computations. Finally, we end the paper by demonstrating the computational viability of the present solution procedure for its use in 3D combustor calculations by summarizing the results of a 3D test case with periodic boundary conditions. For the 3D case, the parallel performance of all the three solvers (CFD, PDF, and spray) has been found to be good when the computations were performed on a 24-processor SGI Origin work-station.

Raju, M. S.↗

Solar Wind Strahl Observations and Their Implication to the Core-Halo Formation due to Scattering

A study of the kinetic properties of the strahl electron velocity distribution functions (VDF?s) in the solar wind is presented. This study focuses on the mechanisms that control and regulate the electron VDF?s and the stability of the strahl electrons in the solar wind; mechanisms that are not yet well understood. Various parameters are investigated such as the strahl-electron density, temperature anisotropy, and electron heat-flux. These parameters are used to investigate the stability of the strahl population. The analysis check for whether the strahl electrons are constrained by some instability (e.g., the whistler or KAW instabilities), or are maintained by other types of processes. The electron heat-flux and temperature anisotropy are determined by modeling of the 3D-VDF?s from which the moments properties of the various populations are obtained. The results of this study have profound implication on the current hypothesis about the probable formation of the solar wind halo electrons produced from the scattering of the strahl population. This hypothesis is strengthened by direct observations of the strahl electrons being scattered into the core-halo in an isolated event. The observation implies that the scattering of the strahl is not a continuous process but occurs in bursts in regions where conditions for wave growth providing the scattering are optimum. Sometimes, observations indicate that the strahl component is anisotropic (Tper/Tpal approx. 2). This provides a possible free energy source for the excitation of whistler waves as a possible scattering mechanism, however this condition is not always observed. The study is based on high time resolution data from the Cluster/PEACE electron spectrometer.

Vinas, Adolfo F.↗

Theory and modeling of atmospheric turbulence, part 1

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Source record↗

Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves

Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using growth curves.

Mengshoel, Ole Jakob↗

Particle Filter Based Inference Testing

The primary intent of PAR-FIT (Particle Filter based Inference Testing) is to provide hard inductive evidence that a machine learning model is capable and proven for an individual test input. By examining training data used to form the underlying model functional correlation, an estimate of the reliability that a model will make the correct prediction can be made. The Sequential Probability Ratio Test is used to derive a qualitative evaluation for reliability based on hypothesis testing. The PAR-FIT framework achieves this by implementing a particle filter and the sequential probability ratio test algorithms on the machine learning model training data to determine relevancy of new individual test samples to the training dataset. The kernel function evaluates the local proximity and density of training data used to derive a prediction outcome. Particles are used to probabilistically determine which training data to evaluate for proximity. For test samples that are within a close proximity to and surrounded by multiple training data points, the evaluated reliability of the prediction is high. For test samples that are anomalies not represented by the training dataset, in low density data clusters, or are far from existing data points, the evaluated reliability is low as insufficient training evidence exists to suggest the model is capable of making the correct prediction. Sequential Probability Ratio Test is further used to determine when a hypothesis on whether a signal can be rejected or accepted for use. The ratio test collects sequence information from the particle filter to test whether the signal is anomalous or normal via hypothesis testing of the underlying distributions.

Chen, Edward [Idaho National Laboratory (INL), Ida↗

A compact x-ray spectrometer for measurements of electron temperature distributions in inertial confinement fusion implosions at OMEGA

The Wedge Range Filter (WRF), commonly used for proton spectroscopy at the OMEGA Laser Facility and National Ignition Facility, is adapted to measure the x-ray continuum spectrum through transmission measurement using a continuous-gradient filter. Continuum x rays emitted from the hotspot of an implosion contain information about the plasma composition and electron temperature. The WRF data are leveraged to probe this distribution, specifically the electron temperature distribution. In this work, the data recorded with the WRF are forward modeled using a temperature distribution model folded with the WRF response function. An uncertainty analysis is conducted through a Bayesian regression algorithm using a Hamiltonian Monte Carlo sampler. This analysis enables the uncertainties in the instrument response to be folded into the uncertainty estimation of the electron temperature and absolute x-ray emission. Data analysis for a series of OMEGA implosions is presented and compared with radiation hydrodynamic simulations.

Lasers↗

Aspects of silicon bulk lifetimes

The best lifetimes attained for bulk crytalline silicon as a function of doping concentrations are analyzed. It is assumed that the dopants which set the Fermi level do not contribute to the recombination traffic which is due to the unknown defect. This defect is assumed to have two charge states: neutral and negative, the neutral defect concentration is frozen-in at some temperature T sub f. The higher doping concentrations should include the band-band Auger effect by using a generalization of the Shockley-Read-Hall (SRH) mechanism. The generalization of the SRH mechanism is discussed. This formulation gives a straightforward procedure for incorporating both band-band and band-trap Auger effects in the SRH procedure. Two related questions arise in this context: (1) it may sometimes be useful to write the steady-state occupation probability of the traps implied by SRH procedure in a form which approximates to the Fermi-Dirac distribution; and (2) the effect on the SRH mechanism of spreading N sub t levels at one energy uniformly over a range of energies is discussed.

Landsberg, P. T.↗

Gas kinematics and ionization along the extended sight line to HD 116852

We present Goddard High-Resolution Spectrograph intermediate observations of the interstellar medium toward HD 116852, a low halo star at a distance of 4.8 kpc (z = -1.3 kpc) in the direction l = 304. deg 9, b = 16.deg 1. The small science aperture observations have signal-to-noise ratios ranging from 30 to 90 and resolutions of 11 to 18 km/s (FWHM). We confirm the optical MK classification of this star through an analysis of its ultraviolet photosperic and stellar wind profiles. We detect interstellar lines of Al III, Si IV, C IV, and N V together with lines of C I, C I*, C I**, Si II, Ge II, P II, and Ni II. We convert the Mg II, P II, S II, Al III, Si IV, C IV, and N V profiles into measure of apparent column density as a function of LSR velocity. Gas scale height, velocity dispersion, and differential Galactic rotation effects govern the profile shapes. A simple computer model of the expected sight line column density profiles for the low and high ion species indicates that the gas velocity dispersions and scale heights increase as the ionization level of the gas increases. We find scale heigts H greater than or = 1 kpc for the high ions, which are comparable to the z-distance of the star, whereas we find H approximatley = 0.6 to 0.7 kpc for A1 III and H approximatley 0.1 kpc for P II and Ge II. An enhancement in the Al II profile near -15 km/s accounts for approximately 25% of the A1 III column along the sight line and probably arises within gas located approximately 500 pc below the Sagittarius-Carina spiral arm link. Portions of the broad underlying A1 III distribution are associated with the higher ionization lines, perhaps in conductive interfaces. The presence of N V and the column density ratios of Si IV, C IV, and N V favor the interpretation that much of the high ion absorption is produced by collisional ionization in gas with T = 1-3 x 10(exp 5) K. An enhancement near -35 km/s in both the Si IV and C IV profiles may be due to an outflow from the Norma spiral arm at a z-distance of about -1 kpc. The smooth decrease of the N(C IV)/N(Si IV) ratio at negative velocities may be due to an ISM ionization structure for hot gas that changes distance from the Galactic plane or to a two phase gas distribution in which the relative contribution from each phase changes with distance from the Galactic plane.

Sembach, Kenneth R.↗

Image-Based Empirical Modeling of the Plasmasphere

A new suite of empirical models of plasmaspheric plasma based on remote, global images from the IMAGE EUV instrument is proposed for development. The purpose of these empirical models is to establish the statistical properties of the plasmasphere as a function of conditions. This suite of models will mark the first time the plasmaspheric plume is included in an empirical model. Development of these empirical plasmaspheric models will support synoptic studies (such as for wave propagation and growth, energetic particle loss through collisions and dust transport as influenced by charging) and serves as a benchmark against which physical models can be tested. The ability to know that a specific global density distribution occurs in response to specific magnetospheric and solar wind factors is a huge advantage over all previous in-situ based empirical models. The consequence of creating these new plasmaspheric models will be to provide much higher fidelity and much richer quantitative descriptions of the statistical properties of plasmaspheric plasma in the inner magnetosphere, whether that plasma is in the main body of the plasmasphere, nearby during recovery or in the plasmaspheric plume. Model products to be presented include statistical probabilities for being in the plasmasphere, near thermal He+ density boundaries and the complexity of its spatial structure.

Adrian, Mark L.↗

Assessing correlated truncation errors in modern nucleon-nucleon potentials

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

Bayesian methods↗

Photometric redshifts probability density estimation from recurrent neural networks in the DECam local volume exploration survey data release 2

Photometric wide-field surveys are imaging the sky in unprecedented detail. These surveys face a significant challenge in efficiently estimating galactic photometric redshifts while accurately quantifying associated uncertainties. In this work, we address this challenge by exploring the estimation of Probability Density Functions (PDFs) for the photometric redshifts of galaxies across a vast area of 17,000 square degrees, encompassing objects with a median 5 σ point-source depth of g = 24.3, r = 23 . 9 , i = 23.5, and z = 22.8 mag. Our approach uses deep learning, specifically integrating a Recurrent Neural Network architecture with a Mixture Density Network, to leverage magnitudes and colors as input features for constructing photometric redshift PDFs across the whole DECam Local Volume Exploration (DELVE) survey sky footprint. Subsequently, we rigorously evaluate the reliability and robustness of our estimation methodology, gauging its performance against other well-established machine learning methods to ensure the quality of our redshift estimations. Our best results constrain photometric redshifts with the bias of − 0 . 0013 , a scatter of 0.0293, and an outlier fraction of 5.1%. These point estimates are accompanied by well-calibrated PDFs evaluated using diagnostic tools such as Probability Integral Transform and Odds distribution. We also address the problem of the accessibility of PDFs in terms of disk space storage and the time demand required to generate their corresponding parameters.We present a novel Autoencoder model that reduces the size of PDF parameter arrays to one-sixth of their original length, significantly decreasing the time required for PDF generation to one-eighth of the time needed when generating PDFs directly from the magnitudes.

79 ASTRONOMY AND ASTROPHYSICS↗