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

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

Sensitivity to Calibrated Parameters

Across many fields in economics, a common approach to estimation of economic models is to calibrate a sub-set of model parameters and keep them fixed when estimating the remaining parameters. Calibrated parameters likely affect conclusions based on the model but estimation time often makes a systematic investigation of the sensitivity to calibrated parameters infeasible. I propose a simple and computationally low-cost measure of the sensitivity of parameters and other objects of interest to the calibrated parameters. In the main empirical application, I revisit the analysis of life-cycle savings motives in Gourinchas and Parker (2002) and show that some estimates are sensitive to calibrations

The Evolution of Cluster Early-Type Galaxies over the Past 8 Gyr

We present the Fundamental Plane (FP) of early-type galaxies in the clusters of galaxies RXJ1415.1+3612 at z=1.013. This is the first detailed FP investigation of cluster early-type galaxies at redshift z=1. The distant cluster galaxies follow a steeper FP relation compared to the local FP. The change in the slope of the FP can be interpreted as a mass-dependent evolution. To analyse in more detail the galaxy population in high redshift galaxy clusters at 0.8<z<1, we combine our sample with a previous detailed spectroscopic study of 38 early-type galaxies in two distant galaxy clusters, RXJ0152.7-1357 at z=0.83 and RXJ1226.9+3332 at z=0.89. For all clusters Gemini/GMOS spectroscopy with high signal-to-noise and intermediate-resolution has been acquired to measure the internal kinematics and stellar populations of the galaxies. From HST/ACS imaging, surface brightness profiles, morphologies and structural parameters were derived for the galaxy sample. The least massive galaxies (M=2x10^{10}M_{\sun}) in our sample have experienced their most recent major star formation burst at z_{form}~1.1. For massive galaxies (M>2x10^{11}M_{\sun}) the bulk of their stellar populations have been formed earlier z_{form}>~1.6. Our results confirm previous findings by Jorgensen et al. This suggests that the less massive galaxies in the distant clusters have much younger stellar populations than their more massive counterparts. One explanation is that low-mass cluster galaxies have experienced more extended star formation histories with more frequent bursts of star formation with shorter duration compared to the formation history of high-mass cluster galaxies.Comment: 6 pages, 2 figures, Talk for "Matter Cycles of Galaxies in Clusters", presented at JENAM 2008, Vienna, to be published in Astronomische Nachrichten in Nov 2009 (proceedings of Symposium 6 of the JENAM 2008, Vienna

An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin

Exploring the Origins of Earth's Nitrogen: Astronomical Observations of Nitrogen-bearing Organics in Protostellar Environments

It is not known whether the original carriers of Earth's nitrogen were molecular ices or refractory dust. To investigate this question, we have used data and results of Herschel observations towards two protostellar sources: the high-mass hot core of Orion KL, and the low-mass protostar IRAS 16293-2422. Towards Orion KL, our analysis of the molecular inventory of Crockett et al. (2014) indicates that HCN is the organic molecule that contains by far the most nitrogen, carrying $74_{-9}^{+5}\%$ of nitrogen-in-organics. Following this evidence, we explore HCN towards IRAS 16293-2422, which we consider a solar analog. Towards IRAS 16293-2422, we have reduced and analyzed Herschel spectra of HCN, and fit these observations against "jump" abundance models of IRAS 16293-2422's protostellar envelope. We find an inner-envelope HCN abundance $X_{\textrm{in}} = 5.9\pm0.7 \times 10^{-8}$ and an outer-envelope HCN abundance $X_{\textrm{out}} = 1.3 \pm 0.1 \times 10^{-9}$. We also find the sublimation temperature of HCN to be $T_{\textrm{jump}} = 71 \pm 3$~K; this measured $T_{\textrm{jump}}$ enables us to predict an HCN binding energy $E_{\textrm{B}}/k = 3840 \pm 140$~K. Based on a comparison of the HCN/H2O ratio in these protostars to N/H2O ratios in comets, we find that HCN (and, by extension, other organics) in these protostars is incapable of providing the total bulk N/H2O in comets. We suggest that refractory dust, not molecular ices, was the bulk provider of nitrogen to comets. However, interstellar dust is not known to have 15N enrichment, while high 15N enrichment is seen in both nitrogen-bearing ices and in cometary nitrogen. This may indicate that these 15N-enriched ices were an important contributor to the nitrogen in planetesimals and likely to the Earth.Comment: Accepted to ApJ; 21 pages, 4 figure

Tun formation is not a prerequisite for desiccation tolerance in the marine tidal tardigrade Echiniscoides sigismundi

The so-called ‘tun’ state is best known from limno-terrestrial tardigrades and rotifers that rely on this compact body shape for anhydrobiotic survival. Little is known of tun formation in marine species and the evolutionary origin of the state is presently unknown. Here, we investigate desiccation tolerance and tun formation in the marine tidal echiniscoidean tardigrade, Echiniscoides sigismundi (M. Schultze, 1865). Groups of approximately 20 E. sigismundi sampled from Lynæs (Denmark) were dehydrated on filter paper from seawater as well as ultrapurified water and kept for 48 h at 5 °C, after which they were rehydrated in seawater. The activity and behaviour of the tardigrades was examined under a light microscope, whereas scanning electron microscopy was used for high-resolution three-dimensional imaging. When dehydrated from seawater, E. sigismundi enters a tun, however, when exposed to ultrapurified water, the tardigrade swells and becomes incapable of movement, and thus incapable of tun formation. Nonetheless, E. sigismundi tolerates being dehydrated from ultrapurified water, revealing an exceptional and unparalleled resilience towards losing structural integrity. Our results confirm previous investigations, which suggest that tun formation relies on a functional musculature. They further suggest that tun formation may have evolved as a response to elevated external pressure rather than desiccation per se