Related papers: Tensor distributions with covariance tensor or cor…

For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.

The n-th derivative of a tensor valued function of a tensor is defined by a finite number of coefficients each with closed form expression.

We introduce various notions of rank for a symmetric tensor, namely: rank, border rank, catalecticant rank, generalized rank, scheme length, border scheme length, extension rank and smoothable rank. We analyze the stratification induced by…

Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…

A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity…

High-dimensional tensor-valued data have recently gained attention from researchers in economics and finance. We consider the estimation and inference of high-dimensional tensor factor models, where each dimension of the tensor diverges.…

We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…

The J\"uttner (covariant Boltzmann) distribution is provided for anisotropic pressure (or temperature) tensors. Its manifestly covariant form follows from its scalar property.

This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…

We define super-energy tensors for arbitrary physical fields, including the gravitational, electromagnetic and massless scalar fields. We also define super-super-energy tensors, and so on. All these tensors satisfy the so-called "Dominant…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…

We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of…