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 »
This content will become publicly available on January 31, 2023
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
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