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At least 235 records · Page 13

Objective Phenotyping of Root System Architecture Using Image Augmentation and Machine Learning in Alfalfa (Medicago sativa L.)

Active breeding programs specifically for root system architecture (RSA) phenotypes remain rare; however, breeding for branch and taproot types in the perennial crop alfalfa is ongoing. Phenotyping in this and other crops for active RSA breeding has mostly used visual scoring of specific traits or subjective classification into different root types. While image-based methods have been developed, translation to applied breeding is limited. This research is aimed at developing and comparing image-based RSA phenotyping methods using machine and deep learning algorithms for objective classification of 617 root images from mature alfalfa plants collected from the field to support the ongoing breeding efforts. Our results show that unsupervised machine learning tends to incorrectly classify roots into a normal distribution with most lines predicted as the intermediate root type. Encouragingly, random forest and TensorFlow-based neural networks can classify the root types into branch-type, taproot-type, and an intermediate taproot-branch type with 86% accuracy. With image augmentation, the prediction accuracy was improved to 97%. Coupling the predicted root type with its prediction probability will give breeders a confidence level for better decisions to advance the best and exclude the worst lines from their breeding program. This machine and deep learning approach enables accurate classification of the RSA phenotypes for genomic breeding of climate-resilient alfalfa.

59 BASIC BIOLOGICAL SCIENCES↗

THE X-RAY LUMINOSITY FUNCTION OF LOW MASS X-RAY BINARIES IN EARLY-TYPE GALAXIES, THEIR METAL-RICH, AND METAL-POOR GLOBULAR CLUSTERS

We present the X-ray luminosity function (XLF) of low-mass X-ray binaries (LMXBs) in the globular clusters (GCs) and fields of seven early-type galaxies. These galaxies are selected to have both deep Chandra observations, which allow their LMXB populations to be observed to X-ray luminosities of 10{sup 37}–10{sup 38} erg s{sup −1}, and Hubble Space Telescope optical mosaics that enable the X-ray sources to be separated into field LMXBs, GC LMXBs, and contaminating background and foreground sources. We find that at all luminosities the number of field LMXBs per stellar mass is similar in these galaxies. This suggests that the field LMXB populations in these galaxies are not effected by the GC specific frequency, and that properties such as binary fraction and the stellar initial mass function are either similar across the sample or change in a way that does not affect the number of LMXBs. We compare the XLF of the field LMXBs to that of the GC LMXBs and find that they are significantly different with a p-value of 3 × 10{sup −6} (equivalent to 4.7σ for a normal distribution). The difference is such that the XLF of the GC LMXBs is flatter than that of the field LMXBs, with the GCs hosting relatively more bright sources and fewer faint sources. A comparison of the XLF of the metal-rich and metal-poor GCs hints that the metal-poor clusters may have more bright LMXBs, but the difference is not statistically significant.

79 ASTRONOMY AND ASTROPHYSICS↗

THE IONIZED GAS IN NEARBY GALAXIES AS TRACED BY THE [NII] 122 AND 205 μm TRANSITIONS

The [N ii] 122 and 205 μ m transitions are powerful tracers of the ionized gas in the interstellar medium. By combining data from 21 galaxies selected from the Herschel KINGFISH and Beyond the Peak surveys, we have compiled 141 spatially resolved regions with a typical size of ∼1 kpc, with observations of both [N ii] far-infrared lines. We measure [N ii] 122/205 line ratios in the ∼0.6–6 range, which corresponds to electron gas densities of n {sub e} ∼ 1–300 cm{sup −3}, with a median value of n {sub e} = 30 cm{sup −3}. Variations in the electron density within individual galaxies can be as high as a factor of ∼50, frequently with strong radial gradients. We find that n {sub e} increases as a function of infrared color, dust-weighted mean starlight intensity, and star-formation rate (SFR) surface density (Σ{sub SFR}). As the intensity of the [N ii] transitions is related to the ionizing photon flux, we investigate their reliability as tracers of the SFR. We derive relations between the [N ii] emission and SFR in the low-density limit and in the case of a log-normal distribution of densities. The scatter in the correlation between [N ii] surface brightness and Σ{sub SFR} can be understood as a property of the n {sub e} distribution. For regions with n {sub e} close to or higher than the [N ii] line critical densities, the low-density limit [N ii]-based SFR calibration systematically underestimates the SFR because the [N ii] emission is collisionally quenched. Finally, we investigate the relation between [N ii] emission, SFR, and n {sub e} by comparing our observations to predictions from the MAPPINGS-III code.

79 ASTRONOMY AND ASTROPHYSICS↗

Stellar Proper Motions in the Orion Nebula Cluster

The Orion Nebula Cluster (ONC) is the nearest site of ongoing massive star formation, which allows us to study the kinematics and dynamics of the region in detail and constrain star formation theories. Using HST ACS/WFPC2/WFC3IR and Keck II NIRC2 data, we have measured the proper motions of 701 stars within an ∼6′ × 6′ field of view around the center of the ONC. We have found more than 10 escaping star candidates, concentrated predominantly at the core of the cluster. The proper motions of the bound stars are consistent with a normal distribution, albeit elongated north–south along the Orion filament, with proper-motion dispersions of (σ{sub μ,α{sup ∗}},σ{sub μ,δ})=(0.83±0.02,1.12±0.03) mas yr{sup −1} or intrinsic velocity dispersions of (σ{sub v,α{sup ∗}},σ{sub v,δ})=(1.57±0.04,2.12±0.06) km s{sup −1} assuming a distance of 400 pc to the ONC. The cluster shows no evidence for tangential-to-radial anisotropy. Our velocity dispersion profile agrees with the prediction from the observed stellar + gas density profile from Da Rio et al., indicating that the ONC is in virial equilibrium. This finding suggests that the cluster was formed with a low star formation efficiency per dynamical timescale based on comparisons with current star formation theories. Our survey also recovered high-velocity IR sources BN, x and n in the BN/KL region. The estimated location of the first two sources ∼500 yr ago agrees with that of the radio source I, consistent with their proposed common origin from a multistellar disintegration. However, source n appears to have a small proper motion and is unlikely to have been involved in the event.

79 ASTRONOMY AND ASTROPHYSICS↗

Massive warm/hot galaxy coronae as probed by UV/X-ray oxygen absorption and emission. I. Basic model

We construct an analytic phenomenological model for extended warm/hot gaseous coronae of L{sub *} galaxies. We consider UV O vi Cosmic Origins Spectrograph (COS)-Halos absorption line data in combination with Milky Way (MW) X-ray O vii and O viii absorption and emission. We fit these data with a single model representing the COS-Halos galaxies and a Galactic corona. Our model is multi-phased, with hot and warm gas components, each with a (turbulent) log-normal distribution of temperatures and densities. The hot gas, traced by the X-ray absorption and emission, is in hydrostatic equilibrium in an MW gravitational potential. The median temperature of the hot gas is 1.5×10{sup 6} K and the mean hydrogen density is ∼5×10{sup −5} cm{sup −3}. The warm component as traced by the O vi, is gas that has cooled out of the high density tail of the hot component. The total warm/hot gas mass is high and is 1.2×10{sup 11} M{sub ⊙}. The gas metallicity we require to reproduce the oxygen ion column densities is 0.5 solar. The warm O vi component has a short cooling time (∼2×10{sup 8} years), as hinted by observations. The hot component, however, is ∼80% of the total gas mass and is relatively long-lived, with t{sub cool}∼7×10{sup 9} years. Our model supports suggestions that hot galactic coronae can contain significant amounts of gas. These reservoirs may enable galaxies to continue forming stars steadily for long periods of time and account for “missing baryons” in galaxies in the local universe.

79 ASTRONOMY AND ASTROPHYSICS↗

X-ray counterpart of gravitational waves due to binary neutron star mergers: light curves, luminosity function, and event rate density

Zhang proposed a type of GRB-less X-ray transient associated with double neutron star (NS–NS) mergers under the conjecture of a rapidly spinning magnetar merger product with the line of sight off the short gamma-ray burst (GRB) jet. We investigate possible light curves of these transients by considering different observers’ viewing angles. We perform Monte Carlo simulations to calculate the peak luminosity function (LF) and event rate density of these X-ray transients. By considering that a fraction of massive neutron stars may be supra-massive and later collapse into black holes after spinning down, we investigate how the predicted LF depends on the equation of state (EoS) of the central object and the geometry of the system. In general, the LF can be fit by two log-normal distributions peaking around 10{sup 46.4} and 10{sup 49.6} erg s{sup −1}, corresponding to the trapped and free zones, respectively. For the majority of the EoS models, the current non-detection is consistent with having a free zone solid angle, at most a few times the solid angle of the short GRB jet. The event rate density of these X-ray transients is around a few tens of Gpc{sup −3} yr{sup −1} for luminosity above 10{sup 45} erg s{sup −1}. We predict that future X-ray telescopes (such as Einstein Probe) with sensitivity ∼10{sup −11} erg s{sup −1} cm{sup −2} would detect as many as several tens of such transients per year per steradian. Within 200 Mpc, the aLIGO average range for NS–NS mergers, the estimated event rate of these transients is about 1 transient per year all sky.

79 ASTRONOMY AND ASTROPHYSICS↗

Are the Formation and Abundances of Metal-poor Stars the Result of Dust Dynamics?

Large dust grains can fluctuate dramatically in their local density, relative to the gas, in neutral turbulent disks. Small, high-redshift galaxies (before reionization) represent ideal environments for this process. We show via simple arguments and simulations that order-of-magnitude fluctuations are expected in local abundances of large grains (>100 Å) under these conditions. This can have important consequences for star formation and stellar metal abundances in extremely metal-poor stars. Low-mass stars can form in dust-enhanced regions almost immediately after some dust forms even if the galaxy-average metallicity is too low for fragmentation to occur. We argue that the metal abundances of these “promoted” stars may contain interesting signatures as the CNO abundances (concentrated in large carbonaceous grains and ices) and Mg and Si (in large silicate grains) can be enhanced and/or fluctuate almost independently. Remarkably, the otherwise puzzling abundance patterns of some metal-poor stars can be well fit by standard IMF-averaged core-collapse SNe yields if we allow for fluctuating local dust-to-gas ratios. We also show that the observed log-normal distribution of enhancements in pure SNe yields, shows very large enhancements and variations up to factors of ≳100 as expected in the dust-promoted model, preferentially in the [C/Fe]-enhanced metal-poor stars. Together, this suggests that (1) dust exists in second-generation star formation, (2) local dust-to-gas ratio fluctuations occur in protogalaxies and can be important for star formation, and (3) the light element abundances of these stars may be affected by the local chemistry of dust where they formed, rather than directly tracing nucleosynthesis from earlier populations.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing Large Galaxy Halos at Z ∼ 0 with Automated Lyα-absorption Matching

We present initial results from an ongoing large-scale study of the circumgalactic medium in the nearby Universe (cz ⩽ 10,000 km s{sup −1}), using archival Cosmic Origins Spectrograph spectra of background quasi-stellar objects. This initial sample contains 33 sightlines chosen for their proximity to large galaxies (D⩾25 kpc) and high signal-to-noise ratios (S/N ⩾ 10), yielding 48 Lyα absorption lines that we have paired with 33 unique galaxies, with 29 cases where multiple absorbers within a single sightline are paired with the same galaxy. We introduce a likelihood parameter to facilitate the matching of galaxies to absorption lines in a reproducible manner. We find the usual anti-correlation between Lyα equivalent width (EW) and impact parameter (ρ) when we normalize by galaxy virial radius (R {sub vir}). Galaxies associated with a Lyα absorber are found to be more highly inclined than galaxies in the survey volume at a > 99% confidence level (equivalent to ∼3.6σ for a normal distribution). In contrast with suggestions in other recent papers of a correlation with azimuth angle for Mg ii absorption, we find no such correlation for Lyα.

79 ASTRONOMY AND ASTROPHYSICS↗

High-resolution Observations of a White-light Flare with NST

Using high-resolution data from the New Solar Telescope, we studied fine spatial and temporal details of an M1.3 white-light (WL) flare, which was one of three homologous solar flares (C6.8, M1.3, and M2.3) observed in close proximity to the west solar limb on 2014 October 29 in NOAA active region 12192. We report that the TiO WL flare consists of compact and intense cores surrounded by less intense spatial halos. The strong and compact WL cores were measured to be ≈0.2 Mm across, with an area of about 10{sup 14} cm{sup 2}. Several TiO features were not cospatial with Hα flare ribbons and were displaced toward the disk center by about 500 km, which suggests that the TiO and Hα radiation probably did not originate in the same chromospheric volume. The observed TiO intensity enhancements are not normally distributed and are structured by the magnetic field of the penumbra.

79 ASTRONOMY AND ASTROPHYSICS↗

The Small Magellanic Cloud Investigation of Dust and Gas Evolution (SMIDGE): The Dust Extinction Curve from Red Clump Stars

We use Hubble Space Telescope (HST) observations of red clump stars taken as part of the Small Magellanic Cloud Investigation of Dust and Gas Evolution (SMIDGE) program to measure the average dust extinction curve in a ∼200 pc × 100 pc region in the southwest bar of the Small Magellanic Cloud (SMC). The rich information provided by our eight-band ultraviolet through near-infrared photometry allows us to model the color–magnitude diagram of the red clump accounting for the extinction curve shape, a log-normal distribution of A {sub V}, and the depth of the stellar distribution along the line of sight. We measure an extinction curve with R{sub 475} =A{sub 475}/(A{sub 475}--A{sub 814})=2.65±0.11. This measurement is significantly larger than the equivalent values of published Milky Way (MW) R {sub V} = 3.1 (R{sub 475}=1.83) and SMC Bar R {sub V} = 2.74 (R{sub 475}=1.86) extinction curves. Similar extinction curve offsets in the Large Magellanic Cloud (LMC) have been interpreted as the effect of large dust grains. We demonstrate that the line-of-sight depth of the SMC (and LMC) introduces an apparent “gray” contribution to the extinction curve inferred from the morphology of the red clump. We show that no gray dust component is needed to explain extinction curve measurements when FWHM depth of 10 ± 2 kpc in the stellar distribution of the SMC (5 ± 1 kpc for the LMC) is considered, which agrees with recent studies of Magellanic Cloud stellar structure. The results of our work demonstrate the power of broadband HST imaging for simultaneously constraining dust and galactic structure outside the MW.

79 ASTRONOMY AND ASTROPHYSICS↗

The 3D Kinematics of the Orion Nebula Cluster: NIRSPEC-AO Radial Velocities of the Core Population

The kinematics and dynamics of stellar and substellar populations within young, still-forming clusters provide valuable information for constraining theories of formation mechanisms. Using Keck II NIRSPEC+AO data, we have measured radial velocities for 56 low-mass sources within 4' of the core of the Orion Nebula Cluster (ONC). We also remeasure radial velocities for 172 sources observed with SDSS/APOGEE. These data are combined with proper motions measured using HST ACS/WFPC2/WFC3IR and Keck II NIRC2, creating a sample of 135 sources with all three velocity components. The velocities measured are consistent with a normal distribution in all three components. We measure intrinsic velocity dispersions of (${\sigma }_{{v}_{\alpha }}$, ${\sigma }_{{v}_{\delta }}$, ${\sigma }_{{v}_{r}}$) = (1.64 ± 0.12, 2.03 ± 0.13, ${2.56}_{-0.17}^{+0.16}$) km s –1 . Our computed intrinsic velocity dispersion profiles are consistent with the dynamical equilibrium models from Da Rio et al. (2014) in the tangential direction but not in the line-of-sight direction, possibly indicating that the core of the ONC is not yet virialized, and may require a nonspherical potential to explain the observed velocity dispersion profiles. We also observe a slight elongation along the north–south direction following the filament, which has been well studied in previous literature, and an elongation in the line-of-sight to tangential velocity direction. These 3D kinematics will help in the development of realistic models of the formation and early evolution of massive clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

Redshift Evolution of the Feedback–Cooling Equilibrium in the Core of 48 SPT Galaxy Clusters: A Joint Chandra–SPT–ATCA Analysis

We analyze the cooling and feedback properties of 48 galaxy clusters at redshifts 0.4 < z < 1.3 selected from the South Pole Telescope (SPT) catalogs to evolve like the progenitors of massive and well-studied systems at z ~ 0. We estimate the radio power at the brightest cluster galaxy (BCG) location of each cluster from an analysis of Australia Telescope Compact Array data. Assuming that the scaling relation between the radio power and active galactic nucleus (AGN) cavity power P cav observed at low redshift does not evolve with redshift, we use these measurements in order to estimate the expected AGN cavity power in the core of each system. We estimate the X-ray luminosity within the cooling radius L cool of each cluster from a joint analysis of the available Chandra X-ray and SPT Sunyaev–Zel'dovich (SZ) data. This allows us to characterize the redshift evolution of the P cav /L cool ratio. When combined with low-redshift results, these constraints enable investigations of the properties of the feedback–cooling cycle across 9 Gyr of cluster growth. We model the redshift evolution of this ratio measured for cool-core clusters by a log-normal distribution Log-N (α + βz, σ 2 ) and constrain the slope of the mean evolution to β = -0.05 ± 0.47. This analysis improves the constraints on the slope of this relation by a factor of two. We find no evidence of redshift evolution of the feedback–cooling equilibrium in these clusters, which suggests that the onset of radio-mode feedback took place at an early stage of cluster formation. High values of P cav /L cool are found at the BCG location of noncool-core clusters, which might suggest that the timescales of the AGN feedback cycle and the cool core–noncool core transition are different. This work demonstrates that the joint analysis of radio, SZ, and X-ray data solidifies the investigation of AGN feedback at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

BANYAN. IX. The Initial Mass Function and Planetary-mass Object Space Density of the TW HYA Association

A determination of the initial mass function (IMF) of the current, incomplete census of the 10 Myr-old TW Hya association (TWA) is presented. This census is built from a literature compilation supplemented with new spectra and 17 new radial velocities from ongoing membership surveys, as well as a reanalysis of Hipparcos data that confirmed HR 4334 (A2 Vn) as a member. Although the dominant uncertainty in the IMF remains census incompleteness, a detailed statistical treatment is carried out to make the IMF determination independent of binning while accounting for small number statistics. The currently known high-likelihood members are fitted by a log-normal distribution with a central mass of 0.21{sub −0.06}{sup +0.11} M {sub ⊙} and a characteristic width of 0.8{sub −0.1}{sup +0.2} dex in the 12 M {sub Jup}–2 M {sub ⊙} range, whereas a Salpeter power law with α=2.2{sub −0.5}{sup +1.1} best describes the IMF slope in the 0.1–2 M {sub ⊙} range. This characteristic width is higher than other young associations, which may be due to incompleteness in the current census of low-mass TWA stars. A tentative overpopulation of isolated planetary-mass members similar to 2MASS J11472421–2040204 and 2MASS J11193254–1137466 is identified: this indicates that there might be as many as 10{sub −5}{sup +13} similar members of TWA with hot-start model-dependent masses estimated at ∼5–7 M {sub Jup}, most of which would be too faint to be detected in 2MASS. Our new radial velocity measurements corroborate the membership of 2MASS J11472421–2040204, and secure TWA 28 (M8.5 γ), TWA 29 (M9.5 γ), and TWA 33 (M4.5 e) as members. The discovery of 2MASS J09553336–0208403, a young L7-type interloper unrelated to TWA, is also presented.

79 ASTRONOMY AND ASTROPHYSICS↗

The long-solved problem of the best-fit straight line: application to isotopic mixing lines

Abstract. It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.

58 GEOSCIENCES↗

Improved methodologies for Earth system modelling of atmospheric soluble iron and observation comparisons using the Mechanism of Intermediate complexity for Modelling Iron (MIMI v1.0)

Abstract. Herein, we present a description of the Mechanism of Intermediate complexity for Modelling Iron (MIMI v1.0). This iron processing module was developed for use within Earth system models and has been updated within a modal aerosol framework from the original implementation in a bulk aerosol model. MIMI simulates the emission and atmospheric processing of two main sources of iron in aerosol prior to deposition: mineral dust and combustion processes. Atmospheric dissolution of insoluble to soluble iron is parameterized by an acidic interstitial aerosol reaction and a separate in-cloud aerosol reaction scheme based on observations of enhanced aerosol iron solubility in the presence of oxalate. Updates include a more comprehensive treatment of combustion iron emissions, improvements to the iron dissolution scheme, and an improved physical dust mobilization scheme. An extensive dataset consisting predominantly of cruise-based observations was compiled to compare to the model. The annual mean modelled concentration of surface-level total iron compared well with observations but less so in the soluble fraction (iron solubility) for which observations are much more variable in space and time. Comparing model and observational data is sensitive to the definition of the average as well as the temporal and spatial range over which it is calculated. Through statistical analysis and examples, we show that a median or log-normal distribution is preferred when comparing with soluble iron observations. The iron solubility calculated at each model time step versus that calculated based on a ratio of the monthly mean values, which is routinely presented in aerosol studies and used in ocean biogeochemistry models, is on average globally one-third (34 %) higher. We redefined ocean deposition regions based on dominant iron emission sources and found that the daily variability in soluble iron simulated by MIMI was larger than that of previous model simulations. MIMI simulated a general increase in soluble iron deposition to Southern Hemisphere oceans by a factor of 2 to 4 compared with the previous version, which has implications for our understanding of the ocean biogeochemistry of these predominantly iron-limited ocean regions.

54 ENVIRONMENTAL SCIENCES↗

Uncertainty Reduction in Power Generation Forecast Using Coupled Wavelet-ARIMA

In this paper, we introduce a new approach without implying normal distributions and stationarity of power generation forecast errors. In addition, it is desired to more accurately quantify the forecast uncertainty by reducing prediction intervals of forecasts. We use automatically coupled wavelet transform and autoregressive integrated moving-average (ARIMA) forecasting to reflect multi-scale variability of forecast errors. The proposed analysis reveals slow-changing “quasi-deterministic” components of forecast errors. This helps improve forecasts produced by other means, e.g., using weather-based models, and reduce forecast errors prediction intervals.

Power system planning, uncertainty reduction, fore↗

Data Collection and Analysis Challenges and Mitigation Strategies for Quantitative Human Factors Research Studies in Nuclear Power Plant Modernization

The United States (U.S.) Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program Plant Modernization Pathway is conducting targeted research and development (R&D) to address aging and reliability concerns with the legacy instrumentation and control and related information systems of the U.S. LWR fleet. In this effort, the application of human factors engineering (HFE) provides an important role in ensuring new digital plant technologies enable broad innovation and business improvement with continued operational safety. Evaluation is a key activity in HFE, which often occurs iteratively through the system design lifecycle. While qualitative methods are important in collecting information of how users perform tasks through observations, quantitative methods are equally important in assessing system design based on performance. In collecting and analyzing this quantitative data, there are notable challenges in the nuclear HFE domain that may threaten the validity and reliability of the inferences made in these studies. Notable challenges include small sample size and limited resources, large error variance and small effect size, an “adding test features to losing degrees of freedom” dilemma, non-normal distribution, and heterogeneity of variance. The results in control room usability studies are often statistically non-significant, which makes it hard to interpret. This work discusses these challenges across different scientific viewpoints and provides real-world examples of these challenges in practice. Collectively, the objective of this work is to position these challenges to the larger data science community as a means of identifying future opportunities to address these issues.

99 GENERAL AND MISCELLANEOUS↗

Working with Bezier Curves as bases for Functional Expansion Tallies

Functional expansion tallies (FETs) are a powerful tool for getting more information per history from Monte Carlo simulations, but in the past they have been constrained to orthogonal bases. Bezier curves, from computer aided design (CAD), could be well suited for FET due to their ability to assume many arbitrary shapes, but are non-orthogonal. Recent development has made non-orthongal FET possible. The convergence of B ´ezier curve FETs in both polynomial order and number of samples is explored. These bases are well suited for representing normal distributions, and opens the door to possible other CAD derived FET bases.

97 MATHEMATICS AND COMPUTING↗