Related papers: Mnesors for automatic control

Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define…

We realize the embedding functor from pseudotensor category to tensor category in a purely algebraic setting when the pseudotensor category is the category $\mathcal{M}(H)$ of left $H$-modules, which is originally defined by Beilinson and…

When designing new materials, it is often necessary to tailor the material design (with respect to its design parameters) to have some desired properties (e.g. Young's modulus). As the set of design parameters grow, the search space grows…

For a numerical semigroup, we encode the set of primitive elements that are larger than its Frobenius number and show how to produce in a fast way the corresponding sets for its children in the semigroup tree. This allows us to present an…

Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…

We define the notion of an aligned null direction, a Lorentz-signature analogue of the eigenvector concept that is valid for arbitrary tensor types. The set of aligned null directions is described by a a system of alignment polynomials…

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also…

In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…

Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…

Nowadays, Neural Networks represent a major expectation for the realization of powerful Deep Learning algorithms, which can determine several physical systems' behaviors and operations. Computational resources required for model, training,…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

One proves that each almost local-global semihereditary ring has the stacked basis property and is almost Bezout. If M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annhilators is…

The classic three-terminal electronic transistors and the emerging two-terminal ion-based memristors are complementary to each other in various nonconventional information processing systems in a heterogeneous integration approach, such as…

Once referred to as the missing circuit component, memristor has come long way across to be recognized and taken as important to future circuit designs. The memristor due to its ability to memorize the state, switch between different…

The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed…

This book chapter describes a novel approach to training machine learning systems by means of a hybrid computer setup i.e. a digital computer tightly coupled with an analog computer. As an example a reinforcement learning system is trained…

The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded…

Tensor2Tensor is a library for deep learning models that is well-suited for neural machine translation and includes the reference implementation of the state-of-the-art Transformer model.

Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…