We establish a link between stabilizer states, rank, and higher-order Fourier analysis -- still-developing area of mathematics that grew out Gowers's celebrated Fourier-analytic proof Szemer\'edi's theorem \cite{gowers1998new}. observe $n$-qudit states are so-called nonclassical quadratic phase functions (defined on affine subspaces $\mathbb{F}_p^n$ where $p$ is the dimension qudit) which funda...

The steady trend of complication mining and geological factors in underground coal at the same time processes intensification cause growth dynamic manifestations natural mining, such as sudden gas outbursts, rock bursts, collapses, leading to dust explosions fires. This requires developing models different phenomena manifestation risks, which enable improving process safety a enterprise. In thi...

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

We construct a family of groups from suitable higher rank graphs which are dimensional generalizations the Thompson groups. introduce group invariants, inspired by K-theory C⁎-algebras, and show that many our not isomorphic to Brin-Thompson nV, when n≥2.

Abstract The tensor rank decomposition, or canonical polyadic is the decomposition of a into sum rank-1 tensors. condition number measures sensitivity summands with respect to structured perturbations. Those are perturbations preserving that decomposed. On other hand, angular up scaling. We show for random rank-2 tensors expected value infinite wide range choices density. Under mild additional ...

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. Nuclear-norm minimization models have been proposed for matrix separation and proved to yield exact separations under suitable conditions. These models, however, typically require...