SEARCH · Engineering Papers

Results for “Variational inference”

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 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1979

Volatiles in Chainpur chondrules

A study of volatile element concentrations in individual chondrules in the Chainpur LL3 chondrite is presented. Volatile elements differing in geochemical behavior tended to vary randomly and correlated variations were observed only for those elements inferred to occupy similar mineral sites. Variations in Co and Ni in kamacite show that metal in chondrule interiors has not approached equilibrium, and that postformational element distribution has mainly altered siderophile concentrations in surface metal grains, and has probably left ionic species unaltered. Etching to remove 3 to 5% of the chondrule dissolved siderophiles, enhanced Zn and Na volatiles relative to nonvolatile Cr in the etch, and produced a large Cd enhancement. If metamorphic redistribution of nonsiderophile volatiles was neglible, their high concentrations are inconsistent with chondrule formation by direct condensation, and models involving sudden melting of preexisting solids can explain the observations but require rapid cooling to prevent volatile loss.

Grossman, J. N.↗

NASA NTRS1997

A Survey of Large-Scale Variations in Thermospheric Oxygen Column Density with Magnetic Activity as Inferred from Observations of the FUV Dayglow

Brightness of the terrestrial far-ultraviolet (FUV) dayglow is dominated by the 130.4-nm emission of neutral atomic oxygen, OI, and variations in the brightness observed from altitudes high above the emitting region reflect variations in thermospheric oxygen density. This paper summarizes the results of an initial survey of the Dynamics Explorer 1 observations of the FUV dayglow through a presentation of 13 representative events selected to demonstrate the spatial extent and short-term temporal stability of the brightness perturbations. The emphasis here is on the morning sector of local time and the polar cap for observations obtained in the time interval from September 23, 1981, through January 19, 1982. An analytic expression is derived for the average response of the FUV photometer to the dayglow during periods of high-latitude magnetic quiescence. The remaining observations in this time interval are then analyzed for their deviations from the established quiet time values. Deviations of -40% to +30% are found following intervals of increased magnetic activity. The most significant decreases (-30% to -40%) are observed equatorward of the instantaneous aurora] oval only after sustained periods (approx. 6 hours) of intense magnetic activity (average AE greater than approx. 700 nT). Decreases extend equatorward from the aurora to geographic latitudes as low as approx. 30 deg N. Decreases of lesser magnitude that do not extend as far equatorward are associated with sustained periods of more moderate activity in which the average value of AE is smaller (approx. 300-400 nT). Also, the spatial extent and magnitude of the decreases in the morning sector appear greater when the IMF B(sub y) component is positive. In both cases, decreases are readily observed within the polar cap. Localized enhancements of +20% to +30% occur much less frequently and are detected at the middle latitudes, well equator-ward of the auroral oval.

Nicholas, A. C.↗

DOE OSTI2022

Graph link prediction in computer networks using Poisson matrix factorisation

Graph link prediction is an important task in cybersecurity: relationships between entities within a computer network, such as users interacting with computers or system libraries and the corresponding processes that use them, can provide key insights into adversary behaviour. Poisson matrix factorisation (PMF) is a popular model for link prediction in large networks, particularly useful for its scalability. In this article PMF is extended to include scenarios that are commonly encountered in cybersecurity applications. Specifically, an extension is proposed to explicitly handle binary adjacency matrices and include known categorical covariates associated with the graph nodes. A seasonal PMF model is also presented to handle seasonal networks. To allow the methods to scale to large graphs, variational methods are discussed for performing fast inference. The results show an improved performance over the standard PMF model and other statistical network models.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Mantle viscosity - A comparison of models from postglacial rebound and from the geoid, plate driving forces, and advected heat flux

Models of the radial variation of effective viscosity inferred from the earth's response to surface loads associated with Pleistocene deglaciation are compared to structures inferred from models of geodynamic phenomena associated with convection: the geoid, plate-driving forces, and advected heat flux. While observations of the earth's response to surface loads do not have sufficient resolution to justify more than two viscous layers, adequately matching the observed long-wavelength geoid anomalies associated with density contrasts in the lower mantle (inferred from seismic tomography) and in the upper mantle (inferred from a model of subducted slabs) requires more structure. It is possible to explain the geoid, observed plate velocities, the advected heat flux in the lower mantle, and relative sea-level variations in oceanic regions, all with a mantle with a high-viscosity/elastic lid, an asthenospheric channel of 2 x 10 exp 19 Pa s from 100 to 400-km depth, a 6 x 10 exp 20 Pa s transition zone, and a lower mantle of 6 x 10 exp 21 Pa s. The uplift history of Australia, Fennoscandia, and Laurentia can be explained with an asthenospheric viscosity less than a factor of 10 higher. Lateral variations in lower mantle viscosity are not required. Transient creep appears to be unimportant for the recent response-to-surface loads from Pleistocene deglaciation.

Hager, Bradford H.↗

NASA NTRS1994

Compositional Variation in Apollo 16 Impact-Melt Breccias and Inferences for the Geology and Bombardment History of the Central Highlands of the Moon

High-precision data for the concentrations of a number of lithophile and siderophile elements were obtained on multiple subsamples from 109 impact-melt rocks and breccias (mostly crystalline) from the Apollo 16 site. Compositions of nearly all Apollo 16 melt rocks fall on one of two trends of increasing Sm concentration with increasing Sc concentration. The Eastern trend (lower Sm/Sc, Mg/Fe, and Sm/Yb ratios) consists of compositional groups 3 and 4 of previous classification schemes. These melt rocks are feldspathic, poor in incompatible and siderophile elements, and appear to have provenance in the Descartes formation to the east of the site. The Western trend (higher Sm/Sc. Mg/Fe, and Sm/ Yb ratios) consists of compositional groups 1 and 2. These relatively mafic, KREEP-bearing breccias are a major component (approx.35%) of the Cayley plains west of the site and are unusual, compared to otherwise similar melt breccias from other sites, in having high concentrations of Fe-Ni metal ( 1-2 %). The metal is the carrier of the low-Ir/Au (approx. 0.3 x chondritic) siderophile-element signature that is characteristic of the Apollo 16 site. Four compositionally distinct groups (1M, 1F, 2DB, and 2NR) of Western-trend melt breccias occur that are each represented by at least six samples. Compositional group 1 or previous classification schemes (the 'poikilitic' or 'LKFM' melt breccias) can be subdivided into two groups. Group 1M (represented by six samples, including 60315) is characterized by lower Al2O3 concentrations, higher MgO and alkali concentrations, and higher Mg/Fe and Cr/Sc ratios than group 1F (represented by fifteen samples, including 65015). Group 1M also has siderophile-element concentrations averaging about twice those of group lF and Ir/Au and Ir/Ni ratios that are even lower than those of other Western-trend melt rocks (Ir/Au = 0.24 +/- 0.03. CI-normalized). At the mafic extreme of group 2 ('VHA' melt breccias), the melt lithology occurring as clasts in feldspathic fragmental breccias from North Ray crater (group 2NR) is compositionally distinct from the melt lithology ofdimict breccias from the Cayley plains (group 2DB) in having higher concentrations of Sc, Cr, and heavy rare earth elements and lower concentrations of siderophile elements. The distinct siderophile-element signature (high absolute abundances, low Ir/Au ratio) suggest that the four groups ofmafic melt breccia are all somehow related. Ratios ofsome lithophile elements also suggest that they are more closely related to each other than then, are to melt breccias from other Apoll sites. However, none of the breccia compositions can be related to any of the others by any simple process of igneous fractionation or mixing involving common lunar materials. Thus, the origin of the four groups of mafic melt breccia is enigmatic. If they were produced in only one or two impacts, then a mechanism exists for generating regimes of impact-melt breccia in a single impact that are substantially different from each other in composition. For various reasons, including the problem of delivering large volumes of four different types of melt to the Apollo 16 site, it is unlikely that any of these breccias were produced in basin-forming impacts. If they were produced in as many as four crater-forming impacts, then the unusual siderophile-element signature is difficult to explain. Possible explanations are (1) the four groups of melt breccia all contain metal from a single, earlier impact, (2) they were each formed by related metal-rich meteoroids, or (3) some common postimpact process has resulted in metal of similar composition in each of four melt pools. Within a compositional group, most intrasample and intersample variation in lithophile element concentrations is caused by differences among samples in the proportion of a component of normative anorthosite or noritic anorthosite. In most cases, this compositional variation probably reflects variation in clast abundance. For group 2DB (and probably 2NR), differences in abundance of a component of ferroan anorthosite (estimated Al2O3 approx. 32%) accounts for the compositional variation. For groups 1M and 1F, the anorthositic component is more mafic (estimated Al203 approx. 26%). Some group-2 samples may be related by a troctolitic component of varying abundance.

Korotev, Randy L.↗

NASA NTRS1993

Latitudinal Variation of Solar Wind Speed and Mass Flux in the Acceleration Region of the Solar Wind during Solar Minimum Inferred from Spectral Broadening measurements

In this paper, we use an aggregate of S-band 2.3 GHz (13 cm) spectral broadening observations conducted during solar minimum conditions by the Mariner 4, Pioneer 10, Mariner 10, Helios 1 & 2 and Viking spacecraft to infer the first measurements of the latitudinal variation of solar wind speed and mass flux in the acceleration region of the solar wind at 3-8 R(sub o).

latitudinal variation of solar wind mass flux in a↗

NASA NTRS1996

ATMOS/ATLAS-3 Observations of Long-Lived Tracers and Descent in the Antarctic Vortex in November 1994

Observations of the long-lived tracers N2O, CH4 and HF obtained by the Atmospheric Trace Molecule Spectroscopy (ATMOS) instrument in early November 1994 are used to estimate average descent rates during winter in the Antarctic polar vortex of 0.5 to 1.5 km/month in the lower stratosphere, and 2.5 to 3.5 km/month in the middle and upper stratosphere. Descent rates inferred from ATMOS tracer observations agree well with theoretical estimates obtained using radiative heating calculations. Air of mesospheric origin (N2O less than 5 ppbV) was observed at altitudes above about 25 km within the vortex. Strong horizontal gradients of tracer mixing ratios, the presence of mesospheric air in the vortex in early spring, and the variation with altitude of inferred descent rates indicate that the Antarctic vortex is highly isolated from midlatitudes throughout the winter from approximately 20 km to the stratopause. The 1994 Antarctic vortex remained well isolated between 20 and 30 km through at least mid-November.

Abrams, M. C.↗

NASA NTRS1982

Short-term EUV flux variations from AE-E He/+/ abundances

The ionization rate of helium in the thermosphere is inferred from AE-E ion and neutral particle composition measurements made on 20 days from January 1979 to June 1980. The variations in the inferred rate are consistent with variations in the UV flux measured during the same period by the AE-E UV spectrometer. The approximately 27-day modulation of the calculated ionization rate is the result of cyclical variations in the UV flux, which are in turn coupled to the rotation period of the sun. Results indicate that the ionization structure of helium in the thermosphere is closely coupled to both the long and short term EUV flux variations.

Sternberg, A.↗

NASA NTRS2017

On the Relationship Between Sub-Daily Instantaneous and Daily Total Gross Primary Production: Implications for Interpreting Satellite-Based SIF Retrievals

Spatially and temporally continuous estimation of plant photosynthetic carbon fixation (or gross primary production, GPP) is crucial to our understanding of the global carbon cycle and the impact of climate change. Besides spatial, seasonal and interannual variations, GPP also exhibits strong diurnal variations. Satellite retrieved solar-induced chlorophyll fluorescence (SIF) provides a spatially continuous, but temporally discrete measurement of plant photosynthesis, and has the potential to be used to estimate GPP at global scale. However, it remains unclear whether the seasonal time series of SIF snapshots taken at a fixed time of the day can be used to infer daily total GPP variation at spatial and seasonal scales. In this study, we first used GPP estimates from 135 eddy covariance flux sites, covering a wide range of geographic locations and biome types, to investigate the relationship between the instantaneous GPP (GPP(sub inst)) and daily GPP (GPP(sub daily)) on the seasonal course for different times of the day. Latitudinal and diurnal patterns were found to correspond to variations in photosynthetically active radiation (PAR) and light use efficiency (LUE), respectively. We then used the Soil-Canopy Observation Photosynthesis and Energy Balance (SCOPE) model and the FluxCom GPP product to investigate the instantaneous and daily SIF-GPP relationships at five flux tower sites along a latitudinal gradient and at a global scale for different biome types. The results showed that daily SIF had a stronger linear correlation with daily GPP than instantaneous SIF at the seasonal scale, with an instantaneous to daily SIF conversion factor following the latitudinal and seasonal pattern driven by PAR. Our study highlights the necessity to take the latitudinal and diurnal factors into consideration for SIF-GPP relationship analyses or for physiological phenology analyses based on SIF.

photosynthesis model↗

DOE OSTI2022

Testing Hidden Assumptions of Representativeness in Reach-Scale Studies of Hyporheic Exchange

Field studies of hyporheic exchange in mountain systems are often conducted using short study reaches and a limited number of observations. It is common practice to assume these study reaches represent hyporheic exchange at larger scales or different sites and to infer general relationships among potential causal mechanisms from the limited number of observations. However, these assumptions of representativeness are rarely tested. In this study, we develop numerical models from four segments of mountain streams in different geomorphologic settings and extract shorter reaches to test how representative exchange metrics are in shorter reaches compared to their reference segments. We also map the locations of the representative reaches to determine if a pattern exists based on location. Finally, we compare variance of these shorter within-site reaches to 29 additional reaches across the same basin to understand the impacts of inferring causal mechanisms, for example, the expectation that wide and narrow valley bottoms will yield different hyporheic exchange patterns. Our results show that the location and length strategy of the study reach must be considered before assuming an exchange metric to be representative of anything other than the exact segment studied. Further, it is necessary to quantify within and between site variations before making causal inferences based on observable characteristics, such as valley width or stream morphology. Our findings have implications for future field practices and how those practices are translated into models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits

Quantum bits, or qubits, are an example of coherent circuits envisioned for next-generation computers and detectors. A robust superconducting qubit with a coherent lifetime of O (100 µs) is the transmon: a Josephson junction functioning as a non-linear inductor shunted with a capacitor to form an anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap between neighboring circuits. Simply transplanting our recipe optimized for single, stand-alone devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer) initially resulted in global drifts in room-temperature tunneling resistance of ± 30%. Inferring a critical current variation from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in < 3.5% relative standard deviation (RSD) in critical current ( ) for 3000 Josephson junctions (both single-junctions and asymmetric SQUIDs) across an area of 49 cm 2 . Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown = 1.8% within 1x1 cm, on average, with a few 1x1 cm areas having < 1.0% (equivalent to < 0.5%). Such stability would drastically improve the yield of multi-junction chips with strict critical current requirements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2007

Equatorial Annual Oscillation with QBO-driven 5-year Modulation in NCEP Data

An analysis is presented of the zonal wind and temperature variations supplied by the National Center for Environmental Prediction (NCEP), which have been assimilated in the Reanalysis and the Climate Prediction Center (CCP) data sets. The derived zonal-mean variations are employed. Stimulated by modeling studies, the data are separated into the hemispherically symmetric and anti-symmetric components, and spectral analysis is applied to study the annual 12-month oscillation and Quasi-biennial Oscillation (QBO). For data samples that cover as much as 40 years, the results reveal a pronounced 5-year modulation of the symmetric AO in the lower stratosphere, which is confined to equatorial latitudes. This modulation is also inferred for the temperature variations but extends to high latitudes, qualitatively consistent with published model results. A comparison between different data samples indicates that the signature of the 5-year oscillation is larger when the QBO of 30 months is more pronounced. Thus there is circumstantial evidence that this periodicity of the QBO is involved in generating the oscillation. The spectral analysis shows that there is a weak anti-symmetric 5-year oscillation in the zonal winds, which could interact with the large antisymmetric A0 to produce the modulation of the symmetric AO as was shown in earlier modeling studies. According to these studies, the 30-month QBO tends to be synchronized by the equatorial Semi-annual Oscillation (SAO), and this would explain why the inferred 5-year modulation is observed to persist and is phase locked over several cycles.

Mayr, H. G.↗

DOE OSTI2024

Can the Rate of a Catalytic Turnover Be Altered by Ligands in the Absence of Direct Binding Interactions?

Second sphere coordination effects ubiquitous in enzymatic catalysis occur through direct interactions, either covalent or non-covalent, with reaction intermediates and transition states. Here, we present herein evidence of indirect second sphere coordination effects in which ligation of water/alkanols far removed from the primary coordination sphere of the active site nevertheless alter energetic landscapes within catalytic redox cycles in the absence of direct physicochemical interactions with surface species mediating catalytic turnovers. Density functional theory, in situ X-ray absorption and infrared spectroscopy, and a wide array of steady-state and transient CO oxidation rate data suggest that the presence of peripheral water renders oxidation half-cycles within two-electron redox cycles over μ m -oxo-bridged trimers in MIL-100(M) more kinetically demanding. Communication between ligated water and the active site appears to occur through the Fe-O-Fe backbone, as inferred from spin density variations on the central μ m -oxygen 'junction'. Evidence is provided for the generality of these second sphere effects in that they influence different types of redox half-cycles or metals, and can be amplified or attenuated through choice of coordinating ligand. Specifically in the case of MIL-100(M) materials, the Cr isostructure can be made to kinetically mimic the Fe variant by disproportionately hindering oxidation half-cycles relative to the reduction half-cycles. Kinetic and spectroscopic inferences presented here significantly expand both the conceptual definition of second sphere effects as well as the palette of synthetic levers available for tuning catalytic redox performance through chemical ligation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

42 ENGINEERING↗

DOE OSTI2021

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Resource selection functions based on hierarchical generalized additive models provide new insights into individual animal variation and species distributions

Habitat selection studies are designed to generate predictions of species distributions or inference regarding general habitat associations and individual variation in habitat use. Such studies frequently involve either individually indexed locations gathered across limited spatial extents and analyzed using resource selection functions (RSFs) or spatially extensive locational data without individual resolution typically analyzed using species distribution models. Both analytical methodologies have certain desirable features, but analyses that combine individual- and population-level inference with flexible non-linear functions may provide improved predictions while accounting for individual variation. Here, we describe how RSFs can be fit using hierarchical generalized additive models (HGAMs) using widely available software, providing a means to explore individual variation in habitat associations and to generate species distribution maps. We used GPS tracking data from golden eagles Aquila chrysaetos from across eastern North America with four environmental predictors to generate monthly distribution models. We considered three model structures that assumed different amounts of individual variation in the functional relationship between predictors and habitat use and used k-fold cross-validation to compare model performance. Models accounting for individual variability in shape and smoothness of functional responses performed best. Eagles exhibited the least amount of individual variation in response to land cover variables during winter months, with most individuals more closely adhering to the population-level trend. During the summer months, eagles exhibited more substantial individual variation in shape and smoothness of the functional relationships, suggesting some need to account for individual variation in eagle habitat use for both inferential and predictive purposes, during this time of year. Because they allow users to blend flexible functions with random effects structures and are well-supported by a variety of software platforms, we believe that HGAMs provide a useful addition to the suite of analyses used for modeling habitat associations or predicting species distributions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Measurements of low-mode asymmetries in the areal density of laser-direct-drive deuterium–tritium cryogenic implosions on OMEGA using neutron spectroscopy

Areal density is one of the key parameters that determines the confinement time in inertial confinement fusion experiments, and low-mode asymmetries in the compressed fuel are detrimental to the implosion performance. The energy spectra from the scattering of the primary deuterium–tritium (DT) neutrons off the compressed cold fuel assembly are used to investigate low-mode nonuniformities in direct-drive cryogenic DT implosions at the Omega Laser Facility. For spherically symmetric implosions, the shape of the energy spectrum is primarily determined by the elastic and inelastic scattering cross sections for both neutron-deuterium and neutron-tritium kinematic interactions. Two highly collimated lines of sight, which are positioned at nearly orthogonal locations around the OMEGA target chamber, record the neutron time-of-flight signal in the current mode. An evolutionary algorithm is being used to extract a model-independent energy spectrum of the scattered neutrons from the experimental neutron time-of-flight data and is used to infer the modal spatial variations (l = 1) in the areal density. Experimental observations of the low-mode variations of the cold-fuel assembly (ρL 0 + ρL 1 ) show good agreement with a recently developed model, indicating a departure from the spherical symmetry of the compressed DT fuel assembly. As a result, another key signature that has been observed in the presence of a low-mode variation is the broadening of the kinematic end-point due to the anisotropy of the dense fuel conditions.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

SDSS-IV MaNGA: Bayesian analysis of the star formation history of low-mass galaxies in the local Universe

ABSTRACT We measure the star formation histories (SFHs) of a sample of low-mass galaxies with M* < 109 M⊙ from the SDSS-IV MaNGA survey. The large number of IFU spectra for each galaxy are either combined to reach a high signal to noise ratio or used to investigate spatial variations. We use Bayesian inferences based on full spectrum fitting. Our analysis based on Bayesian evidence ratio indicates a strong preference for a model that allows the presence of an old stellar population, and that an improper model for the SFH can significantly underestimate the old population in these galaxies. The addition of near-infrared photometry to the constraining data can further distinguish between different SFH model families and significantly tighten the constraints on the mass fraction in the old population. On average more than half of the stellar mass in present-day low-mass galaxies formed at least 8 Gyr ago, while about 30 per cent within the past 4 Gyr. Satellite galaxies on average have formed their stellar mass earlier than central galaxies. The radial dependence of the SFH is quite weak. Our results suggest that most of the low-mass galaxies have an early episode of active star formation that produces a large fraction of their present stellar mass.

Zhou, Shuang↗