Context. Numerous complex organic molecules have been detected in the universe and among them are amides, which are considered as prime models for species containing a peptide linkage. In its backbone, acrylamide (CH 2 CHC(O)NH 2 ) bears not only the peptide bond, but also the vinyl functional group that is a common structural feature in many interstellar compounds. This makes acrylamide an interesting candidate for searches in the interstellar medium. In addition, a tentative detection of the related molecule propionamide (C 2 H 5 C(O)NH 2 ) has been recently claimed toward Sgr B2(N). Aims. The aim of this work is to extend the knowledge of the laboratory rotational spectrum of acrylamide to higher frequencies, which would make it possible to conduct a rigorous search for interstellar signatures of this amide using millimeter wave astronomy. Methods. We measured and analyzed the rotational spectrum of acrylamide between 75 and 480 GHz. We searched for emission of acrylamide in the imaging spectral line survey ReMoCA performed with the Atacama Large Millimeter/submillimeter Array toward Sgr B2(N). We also searched for propionamide in the same source. The astronomical spectra were analyzed under the assumption of local thermodynamic equilibrium. Results. We report accurate laboratorymore »
A priori generalization error analysis of twolayer neural networks for solving high dimensional Schrödinger eigenvalue problems
This paper analyzes the generalization error of twolayer neural networks for computing the ground state of the Schrödinger operator on a d d dimensional hypercube with Neumann boundary condition. We prove that the convergence rate of the generalization error is independent of dimension d d , under the a priori assumption that the ground state lies in a spectral Barron space. We verify such assumption by proving a new regularity estimate for the ground state in the spectral Barron space. The latter is achieved by a fixed point argument based on the KreinRutman theorem.
 Publication Date:
 NSFPAR ID:
 10324294
 Journal Name:
 Communications of the American Mathematical Society
 Volume:
 2
 Issue:
 1
 Page Range or eLocationID:
 1 to 21
 ISSN:
 26923688
 Sponsoring Org:
 National Science Foundation
More Like this


This work concerns the asymptotic behavior of solutions to a (strictly) subcritical fluid model for a data communication network, where file sizes are generally distributed and the network operates under a fair bandwidthsharing policy. Here we consider fair bandwidthsharing policies that are a slight generalization of the [Formula: see text]fair policies introduced by Mo and Walrand [Mo J, Walrand J (2000) Fair endtoend windowbased congestion control. IEEE/ACM Trans. Networks 8(5):556–567.]. Since the year 2000, it has been a standing problem to prove stability of the data communications network model of Massoulié and Roberts [Massoulié L, Roberts J (2000) Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems 15(1):185–201.], with general file sizes and operating under fair bandwidth sharing policies, when the offered load is less than capacity (subcritical conditions). A crucial step in an approach to this problem is to prove stability of subcritical fluid model solutions. In 2012, Paganini et al. [Paganini F, Tang A, Ferragut A, Andrew LLH (2012) Network stability under alpha fair bandwidth allocation with general file size distribution. IEEE Trans. Automatic Control 57(3):579–591.] introduced a Lyapunov function for this purpose and gave an argument, assuming that fluid model solutions are sufficiently smooth in timemore »

Context. Glycinamide (NH 2 CH 2 C(O)NH 2 ) is considered to be one of the possible precursors of the simplest amino acid, glycine. Its only rotational spectrum reported so far has been in the centimetrewave region on a laserablation generated supersonic expansion sample. Aims. The aim of this work is to extend the laboratory spectrum of glycinamide to the millimetre (mm) wave region to support searches for this molecule in the interstellar medium and to perform the first check for its presence in the highmass star forming region Sagittarius B2(N). Methods. Glycinamide was synthesised chemically and was studied with broadband rotational spectroscopy in the 90–329 GHz region with the sample in slow flow at 50°C. Tunnelling across a lowenergy barrier between two symmetry equivalent configurations of the molecule resulted in splitting of each vibrational state and many perturbations in associated rotational energy levels, requiring careful coupled state fits for each vibrational doublet. We searched for emission of glycinamide in the imaging spectral line survey ReMoCA performed with the Atacama Large Millimetre/submillimetre Array towards Sgr B2(N). The astronomical spectra were analysed under the assumption of local thermodynamic equilibrium. Results. We report the first analysis of the mmwave rotational spectrum ofmore »

The classic Generative Adversarial Net (GAN) and its variants can be roughly categorized into two large families: the unregularized versus regularized GANs. By relaxing the nonparametric assumption on the discriminator in the classic GAN, the regularized GANs have better generalization ability to produce new samples drawn from the real distribution. Although the regularized GANs have shown compelling performances, there still exist some unaddressed problems. It is well known that the real data like natural images are not uniformly distributed over the whole data space. Instead, they are often restricted to a lowdimensional manifold of the ambient space. Such a manifold assumption suggests the distance over the manifold should be a better measure to characterize the distinct between real and fake samples. Thus, we define a pullback operator to map samples back to their data manifold, and a manifold margin is defined as the distance between the pullback representations to distinguish between real and fake samples and learn the optimal generators. We justify the proposed model from both theoretical and empirical perspectives, demonstrating it can produce high quality images as compared with the other stateoftheart GAN models.

ABSTRACT Strongly lensed quasars can provide measurements of the Hubble constant (H0) independent of any other methods. One of the key ingredients is exquisite highresolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptiveoptics (AO) imaging from groundbased telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three timedelay lenses with AO imaging (RX J1131−1231, HE 0435−1223, and PG 1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck telescope, obtained as part of the Strong lensing at High Angular Resolution Program (SHARP) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat Λ cold dark matter (ΛCDM) model with fixed Ωm = 0.3, we show that by marginalizing over two different kinds of mass models (powerlaw and composite models) and their transformed mass profiles via a masssheet transformation, we obtain $\Delta t_{\rm BA}=6.89\substack{+0.8\\0.7}\, h^{1}\hat{\sigma }_{v}^{2}$ d, $\Delta t_{\rm CA}=10.7\substack{+1.6\\1.2}\, h^{1}\hat{\sigma }_{v}^{2}$ d, and $\Delta t_{\rm DA}=7.70\substack{+1.0\\0.9}\, h^{1}\hat{\sigma }_{v}^{2}$ d, where $h=H_{0}/100\,\rm km\, s^{1}\, Mpc^{1}$ is the dimensionless Hubble constant and $\hat{\sigma }_{v}=\sigma ^{\rm ob}_{v}/(280\,\rm km\, s^{1})$ is the scaled dimensionless velocity dispersion. Future measurements of timemore »