Related papers: Multivariate Power Series in Maple
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact…
We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensors-to-image which enables us to take advantage of Computer…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
We introduce multi-scale energy models to learn the prior distribution of images, which can be used in inverse problems to derive the Maximum A Posteriori (MAP) estimate and to sample from the posterior distribution. Compared to the…
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is…
Wavelets and Multiwavelets have lately been adopted in Quantum Chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high…
The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale…
Significant advances have recently been achieved in Multi-Agent Reinforcement Learning (MARL) which tackles sequential decision-making problems involving multiple participants. However, MARL requires a tremendous number of samples for…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
In recent years, power analysis has become widely used in applied sciences, with the increasing importance of the replicability issue. When distribution-free methods, such as Partial Least Squares (PLS)-based approaches, are considered,…
Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…
Multi-agent reinforcement learning (MARL) algorithms have accomplished remarkable breakthroughs in solving large-scale decision-making tasks. Nonetheless, most existing MARL algorithms are model-free, limiting sample efficiency and…
We introduce a family of unital associative algebras A which are multiparameter analogues of the Weyl algebras and determine the simple weight modules and the Whittaker modules for them. All these modules can be regarded as spaces of…
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large…
Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
Our research aims to propose a new performance-explainability analytical framework to assess and benchmark machine learning methods. The framework details a set of characteristics that systematize the performance-explainability assessment…