11,732 research outputs found

    Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training

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    In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.Comment: arXiv admin note: text overlap with arXiv:2002.0823

    The scaling relations of early--type galaxies in clusters I. Surface photometry in seven nearby clusters

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    This is the first paper of a series investigating the scaling relations of early-type galaxies in clusters. Here we illustrate the multi-band imagery and the image reduction and calibration procedures relative to the whole sample of 22 clusters at 0.05 < z < 0.25. We also present the detailed surface photometry of 312 early-type galaxies in 7 clusters in the first redshift bin, z~0.025-0.075. We give for each galaxy the complete set of luminosity and geometrical profiles, and and a number of global, photometric and morphological parameters. They have been evaluated taking into account the effects of seeing. Internal consistency checks and comparisons with data in the literature confirm the quality of our analysis. These data, together with the spectroscopic ones presented in the second paper of the series, will provide the local calibration of the scaling relations.Comment: 36 pages, 13 figures, 7 tables, accepted for publication in A&

    Cultivar and Year-to-Year Variation of Phytosterol Content in Rye (Secale cereale L.)

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    Intake of phytosterols (and -stanols) has been shown to decrease the level of low-density lipoprotein cholesterol and thus protect against development of cardiovascular diseases. Therefore, studies on the cultivar and year-to-year variation in phytosterol content in rye grains have been performed. The phytosterol content and composition of different rye cultivars, grown under identical conditions on the same field in three consecutive years, were analyzed. Both cultivar and year-to-year variation in sterol content were statistically significant (p < 0.0001). The total sterol content varied from 1007 ± 21 mg/kg in the highest yielding cultivar, Tsulpan 3, to 761 ± 10 mg/kg in the lowest yielding cultivar (Amando in the 1999 harvest). Because the meteorological conditions varied substantially between the different years, it was possible to deduce the impact of varying weather conditions on phytosterol content in the different cultivars. The studied cultivars had all the lowest phytosterol contents in the dry and warm harvest season of 1999. Although there were statistically significant cultivar and year-to-year variations in the sterol composition (p < 0.0001), these were only between 2 and 4% of the total sterol content

    An estimating equations approach to fitting latent exposure models with longitudinal health outcomes

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    The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudinal health outcomes which is robust to misspecification of the outcome variance. We show that compared to maximum likelihood, the loss of efficiency of the proposed method is relatively small when the model is correctly specified. The proposed equations formalize the ad-hoc regression on factor scores procedure, and generalize regression calibration. We propose two weighting schemes for the equations, and compare their efficiency. We apply this method to a study of the effects of in-utero lead exposure on child development.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS226 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Subarcsecond resolution observations of warm water towards three deeply embedded low-mass protostars

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    Water is present during all stages of star formation: as ice in the cold outer parts of protostellar envelopes and dense inner regions of circumstellar disks, and as gas in the envelopes close to the protostars, in the upper layers of circumstellar disks and in regions of powerful outflows and shocks. In this paper we probe the mechanism regulating the warm gas-phase water abundance in the innermost hundred AU of deeply embedded (Class~0) low-mass protostars, and investigate its chemical relationship to other molecular species during these stages. Millimeter wavelength thermal emission from the para-H2-18O 3(1,3)-2(2,0) (Eu=203.7 K) line is imaged at high angular resolution (0.75"; 190 AU) with the IRAM Plateau de Bure Interferometer towards the deeply embedded low-mass protostars NGC 1333-IRAS2A and NGC 1333-IRAS4A. Compact H2-18O emission is detected towards IRAS2A and one of the components in the IRAS4A binary; in addition CH3OCH3, C2H5CN, and SO2 are detected. Extended water emission is seen towards IRAS2A, possibly associated with the outflow. The detections in all systems suggests that the presence of water on <100 AU scales is a common phenomenon in embedded protostars. We present a scenario in which the origin of the emission from warm water is in a flattened disk-like structure dominated by inward motions rather than rotation. The gas-phase water abundance varies between the sources, but is generally much lower than a canonical abundance of 10^-4, suggesting that most water (>96 %) is frozen out on dust grains at these scales. The derived abundances of CH3OCH3 and SO2 relative to H2-18O are comparable for all sources pointing towards similar chemical processes at work. In contrast, the C2H5CN abundance relative to H2-18O is significantly lower in IRAS2A, which could be due to different chemistry in the sources.Comment: 12 pages, 9 figure

    On C*-algebras generated by pairs of q-commuting isometries

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    We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

    Disk and Envelope Structure in Class 0 Protostars: I. The Resolved Massive Disk in Serpens FIRS 1

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    We present the first results of a program to characterize the disk and envelope structure of typical Class 0 protostars in nearby low-mass star forming regions. We use Spitzer IRS mid-infrared spectra, high resolution CARMA 230 GHz continuum imaging, and 2-D radiative transfer models to constrain the envelope structure, as well as the size and mass of the circum-protostellar disk in Serpens FIRS 1. The primary envelope parameters (centrifugal radius, outer radius, outflow opening angle, and inclination) are well constrained by the spectral energy distribution (SED), including Spitzer IRAC and MIPS photometry, IRS spectra, and 1.1 mm Bolocam photometry. These together with the excellent uv-coverage (4.5-500 klam) of multiple antenna configurations with CARMA allow for a robust separation of the envelope and a resolved disk. The SED of Serpens FIRS 1 is best fit by an envelope with the density profile of a rotating, collapsing spheroid with an inner (centrifugal) radius of approximately 600 AU, and the millimeter data by a large resolved disk with Mdisk~1.0 Msun and Rdisk~300 AU. These results suggest that large, massive disks can be present early in the main accretion phase. Results for the larger, unbiased sample of Class~0 sources in the Perseus, Serpens, and Ophiuchus molecular clouds are needed to determine if relatively massive disks are typical in the Class 0 stage.Comment: Comments: 13 pages, 8 figures, 3 tables; accepted for publication in the Ap

    C18O (3-2) observations of the Cometary Globule CG 12: a cold core and a C18O hot spot

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    The feasibility of observing the C18O (3-2) spectral line in cold clouds with the APEX telescope has been tested. As the line at 329.330 GHz lies in the wing of a strong atmospheric H2O absorption it can be observed only at high altitude observatories. Using the three lowest rotational levels instead of only two helps to narrow down the physical properties of dark clouds and globules. The centres of two C18O maxima in the high latitude low mass star forming region CG 12 were mapped in C18O (3-2) and the data were analyzed together with spectral line data from the SEST. The T_MB(3-2)/T_MB(2-1) ratio in the northern C18O maximum, CG 12 N, is 0.8, and in the southern maximum, CG 12 S, ~2. CG 12 N is modelled as a 120'' diameter (0.4pc) cold core with a mass of 27 Msun. A small size maximum with a narrow, 0.8 kms-1, C18O (3-2) spectral line with a peak temperature of T_MB ~11 K was detected in CG 12 S. This maximum is modelled as a 60'' to 80'' diameter (~0.2pc) hot (80 K < Tex < 200 K) ~1.6 Msun clump. The source lies on the axis of a highly collimated bipolar molecular outflow near its driving source. This is the first detection of such a compact, warm object in a low mass star forming region.Comment: APEX A&A special issue, accepte
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