Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor funct...

The structure tensor of $\mathfrak{sl}_n$, denoted $T_{\mathfrak{sl}_n}$, is the tensor arising from the Lie bracket bilinear operation on the set of traceless $n \times n$ matrices over $\mathbb{C}$....

We derive the Green tensor of Mindlin's anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient el...

We show that positive elements of a Pedersen ideal of a tensor product can be approximated in a particularly strong sense by sums of tensor products of positive elements. This has a range of applicati...

We aim to provably complete a sparse and highly-missing tensor in the presence of covariate information along tensor modes. Our motivation comes from online advertising where users click-through-rates...

We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral $G$-Mackey fun...

We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minim...

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We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of space. The latter are associated to rank $d$ te...

We use the transfer tensor method to analyze localization and transport in simple disordered systems, specifically the Anderson and Aubry-André-Harper models. Emphasis is placed on the memory effects...

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse natural language tasks but suffer from extremely large memory footprints and computational costs. In this paper, w...

Markov Chain Monte Carlo (MCMC), and Tensor Networks (TN) are two powerful frameworks for numerically investigating many-body systems, each offering distinct advantages. MCMC, with its flexibility and...

In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discret...

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For each positive integer $n$, the basic classical complex Lie superalgebra $\mathfrak{osp}(1|2n)$ has a unique equivalence class of infinite-dimensional completely-pointed modules, those weight modul...

Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potent...

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Speci...

Continuing our investigation of the regularization of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001 (2001)] we adopt the modified point separation s...

In Paper II [N. G. Phillips and B. L. Hu, previous abstract] we presented the details for the regularization of the noise kernel of a quantum scalar field in optical spacetimes by the modified point s...