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We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...
In recent years, light field technology has attracted the interest of academia and industry, thanks to the possibility of rendering 3D scenes in a more realistic and immersive way. In particular, light field displays have been consistently investigated for ...
This paper is concerned with low multilinear rank approximations to antisymmetric tensors, that is, multivariate arrays for which the entries change sign when permuting pairs of indices. We show which ranks can be attained by an antisymmetric tensor and di ...
This paper is concerned with low multilinear rank approximations to antisymmetric tensors, that is, multivariate arrays for which the entries change sign when permuting pairs of indices. We show which ranks can be attained by an antisymmetric tensor and di ...
Tensor completion aims to reconstruct a high-dimensional data set where the vast majority of entries is missing. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem rest ...
In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...
Tensor completion aims to reconstruct a high-dimensional data set with a large fraction of missing entries. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem restricte ...
Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...