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Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present a new flexible algorithmic framework that targets nonsmooth level-set constraints, including L1, Linf, and even L0 norms. These constraints give greater flexibility for modeling deviations in observation and denoising, and have significant impact on the solution. Measuring error in the L1 and L0 norms makes the result more robust to large outliers, while matching many observations exactly. We demonstrate the approach for basis pursuit denoise (BPDN) problems as well as for extensions of BPDN to matrix factorization, with applications to interpolation and denoising of 5D seismic data. The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models., Comment: 11 pages, 10 figures

Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. We show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve these joint problems. In the seismology setting, we use the approach to interpolate missing stations and de-noise observed stations. The new approach is competitive with alternative algorithms, and offers new functionality to interpolate observed data using both smoothness and low rank structure in the presence of data fitting constraints., Comment: 22 pages, 10 figures

We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates ($r, \theta, \phi$) and obtained explicitly flow variables in $r-$ and $\theta -$directions around black holes (BHs). We investigated global transonic advection-dominated accretion flow (ADAF) solutions in $r-$direction on an equatorial plane with using Paczy\'nski-Wiita potential. We used radial flow variables of ADAFs with symmetric conditions on the equatorial plane, as initial values for integration in $\theta-$direction. In the study of 2D disk structure, we used two-azimuthal components of viscous stress tensors namely, $\tau_{\rm r\phi}$ and $\tau_{\rm\theta\phi}$. Interestingly, we found that the whole advective disk is not participating in outflow generation and the outflows form close to the BHs. Normally, outflow strength increased with increasing viscosity parameter ($\alpha_1$), mass-loss parameter ($s$) and decreasing gas pressure ratio ($\beta$). Outflow region increased with increasing $s$, $\alpha_1$ for $\tau_{\rm r\phi}$ and decreasing $\alpha_2$ for $\tau_{\rm\theta\phi}$. The $\tau_{\rm\theta\phi}$ is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry since it changes polar velocity ($v_{\rm\theta}$) of the flow. The outflow emission is also affected by the ADAF size and decreased with decreasing it. Transonic surfaces formed for both inflows ($v_{\rm r}<0$, very close to BH) and outflows ($v_{\rm r}>0$). We also explored no outflows, outflows and failed outflows regions, which mainly depend on the viscosity parameters., Comment: 22 pages, 9 figures, Accepted for publication in ApJ

Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach., Comment: 16 pages, 10 figures

The Cohen-Macaulay property of a graph arising from a poset has been studied by various authors. In this article, we study the Cohen-Macaulay property of a graph arising from a family of reflexive and antisymmetric relations on a set. We use this result to find classes of multipartite graphs which are Cohen-Macaulay.

Outflows launched from a remnant disc of compact binary merger may have essential contribution to the kilonova emission. Numerical calculations are conducted in this work to study the structure of accretion flows and outflows. By the incorporation of limited-energy advection in the hyper-accretion discs, outflows occur naturally from accretion flows due to imbalance between the viscous heating and the sum of the advective and radiative cooling. Following this spirit, we revisit the properties of the merger outflow ejecta. Our results show that around $10^{-3} \sim 10^{-1} M_\odot$ of the disc mass can be launched as powerful outflows. The amount of unbound mass varies with the disc mass and the viscosity. The outflow-contributed peak luminosity is around $10^{40} \sim 10^{41}$ erg/s. Such a scenario can account for the observed kilonovae associated with short gamma-ray bursts, including the recent event AT2017gfo (GW170817)., Comment: 8 pages, 6 figures, accepted for publication in MNRAS