We address the problem of reasoning about interleavings in safety verification of concurrent processes. We start with a systematic search tree depicting the program states across all possible interleavings. While this setting is totally general, a naive implementation based on explicit enumeration is clearly impractical. We then consider an algorithm schema which can prune the search space. The...

We introduce a new family of matrix norms, the “local max” norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this new family can be used to interpolate between the (weighted or unweighted) t...

We propose a novel metal artifact reduction (MAR) algorithm for CT images that completes a corrupted sinogram along the metal trace region. When metal implants are located inside a field of view, they create a barrier to the transmitted X-ray beam due to the high attenuation of metals, which significantly degrades the image quality. To fill in the metal trace region efficiently, the proposed al...

Seismic data are often inadequately or irregularly sampled along spatial axes. Irregular sampling can produce artifacts in seismic imaging results. We present a new approach to interpolate aliased seismic data based on adaptive predictionerror filtering (PEF) and regularized nonstationary autoregression. Instead of cutting data into overlapping windows (patching), a popular method for handling ...

We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there is statebased interpolation where a collection of formulas can be generalized by taking into account the property to be verified. Second, there are tracebased methods, collectively known as “Partia...

Seismic trace interpolation can be formulated as an underdetermined least squares inverse problem. In order to force interpolation to follow the directions of seismic events, the weighting function is designed to build the interpolated energy along the desired direction. Usually, such a weighting function is built in the Fourier domain. However, when Fourier spectra are aliased, especially in t...

Interpolation of missing seismic data (such as missing nearoffset data, gaps, etc.) is an important issue in seismic surveys. Here we show that interferometry can be used to fill in some gaps in the data. The interferometric method creates virtual traces in the gaps by crosscorrelation of traces in a shot gather followed by summation over all shot positions. Compared to other interpolation meth...

Interpolation inequalities of Gagliardo-Nirenberg type and compactness results for self-adjoint trace-class operators with finite kinetic energy are established. Applying these results to the minimization of various free energy functionals, we determine for instance stationary states of the Hartree problem with temperature corresponding to various statistics. Key-words. Compact self-adjoint ope...

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interface, the others for the Neumann trace. In this paper we provide several interpretations of the method and we car...