Higher-order tensors are generalizations of vectors and matrices to thirdor even higher-order arrays of numbers. We consider a generalization of column and row rank of a matrix to tensors, called multilinear rank. Given a higher-order tensor, we are looking for another tensor, as close as possible to the original one and with multilinear rank bounded by prespecified numbers. In this paper, we g...

In this article we study the Gross-Schoen diagonal cycle on a triple product of Shimura curves at place bad reduction. We relate image under Abel-Jacobi map to certain period integral that governs central critical value Garrett-Rankin type $L$-function via level raising congruences. As an application prove rank $0$ case Bloch-Kato conjecture for symmetric cube motive weight $2$ modular form.

velocity analysis is one of the most important step in seismic data processing. it affects not only many processing steps directly and indirectly, but also is known as a primary interpretation of the data. however, it can also be assumed as one of the most time consuming processing step. the conventional velocity analysis method measures the energy amplitude along hyperbolic trajectories within...

We introduce Neural Choice by Elimination, a new framework that integrates deep neural networks into probabilistic sequential choice models for learning to rank. Given a set of items to chose from, the elimination strategy starts with the whole item set and iteratively eliminates the least worthy item in the remaining subset. We prove that the choice by elimination is equivalent to marginalizin...

We introduce Neural Choice by Elimination, a new framework that integrates deep neural networks into probabilistic sequential choice models for learning to rank. Given a set of items to chose from, the elimination strategy starts with the whole item set and iteratively eliminates the least worthy item in the remaining subset. We prove that the choice by elimination is equivalent to marginalizin...

In this paper we address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank pen...

The proposed study addresses a two-echelon sustainable supply chain (SC) model with single-vendor and single-buyer by considering the detrimental impacts of environmental pollution due to production. Moreover, an estimation function measure production is developed through separate modelling. In entire chain, we assume deterioration rate increases time it also depends on product’s expiration dat...

Here we calculate the value distribution of the first derivative of characteristic polynomials of matrices from SO(2N + 1) at the point 1, the symmetry point on the unit circle of the eigenvalues of these matrices. The connection between the values of random matrix characteristic polynomials and values of the L-functions of families of elliptic curves implies that this calculation in random mat...