Deep-seismic-prior-based reconstruction of seismic data using convolutional neural networks. (arXiv:1911.08784v1 [cs.LG])

Reconstruction of seismic data with missing traces is a long-standing issue in seismic data processing. In recent years, rank reduction operations are being commonly utilized to overcome this problem, which require the rank of seismic data to be a prior. However, the rank of field data is unknown; usually it requires much time to manually…

Non-local to local transition for ground states of fractional Schr\”{o}dinger equations on $\mathbb{R}^N$. (arXiv:1911.08570v1 [math.AP])

We consider the nonlinear fractional problem \begin{align*} (-\Delta)^{s} u + V(x) u = f(x,u) &\quad \hbox{in $\mathbb{R}^N$} \end{align*} We show that ground state solutions converge (along a subsequence) in $L^2_{\mathrm{loc}} (\mathbb{R}^N)$, under suitable conditions on $f$ and $V$, to a \emph{very weak} solution of the local problem as $s \to 1^-$.

Optimized Raman pulses for atom interferometry. (arXiv:1911.08789v1 [quant-ph])

We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of $^{85}$Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with…

Enantiomeric excess determination based on nonreciprocal transition induced spectral line elimination. (arXiv:1911.08804v1 [quant-ph])

The spontaneous emission spectrum of a multi-level atom or molecule with nonreciprocal transition is investigated. It is shown that the nonreciprocal transition can lead to the elimination of a spectral line in the spontaneous emission spectrum. As an application, we show that nonreciprocal transition arises from the phase-related driving fields in chiral molecules with cyclic…

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols. (arXiv:1911.08573v1 [math.CA])

In this paper we prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the…

Unitary calculus: model Categories and convergence. (arXiv:1911.08575v1 [math.AT])

We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description of the intricacies in the equivariance and homotopy theory involved. The subtle differences between real and complex geometry lead to subtle differences between orthogonal and unitary calculus. To address these differences we construct unitary spectra –…

Power-law decay of weights and recurrence of the two-dimensional VRJP. (arXiv:1911.08579v1 [math.PR])

The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker is biased towards returning to previously visited vertices with the bias depending linearly on the local time at these vertices. We prove that, for any initial bias, the weights sampled from the magic formula on a two-dimensional graph decay…

Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control. (arXiv:1911.08751v1 [eess.SY])

his paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear…