Related papers: Multivariate Power Series in Maple

We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to…

We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

With the increasing penetration of renewable energy, traditional physics-based power system operation faces growing challenges in achieving economic efficiency, stability, and robustness. Machine learning (ML) has emerged as a powerful tool…

Context: Machine learning (ML) may enable effective automated test generation. Objective: We characterize emerging research, examining testing practices, researcher goals, ML techniques applied, evaluation, and challenges. Methods: We…

Efficient algorithms are known for many operations on truncated power series (multiplication, powering, exponential, ...). Composition is a more complex task. We isolate a large class of power series for which composition can be performed…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for…

Interpretable Machine Learning (IML) is expected to remove significant barriers for the application of Machine Learning (ML) algorithms in power systems. This letter first seeks to showcase the benefits of SHapley Additive exPlanations…

Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…

We propose two improvements to the well-known power series method for confined one-dimensional quantum-mechanical problems. They consist of the addition of a variational step were the energy plays the role of a variational parameter. We…

A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for…

The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…

Power ISA(TM) Version 3.1 has introduced a new family of matrix math instructions, collectively known as the Matrix-Multiply Assist (MMA) facility. The instructions in this facility implement numerical linear algebra operations on small…

Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WILFPLUS,…

Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

We study Bessel processes on Weyl chambers of types A and B on $\mathbb R^N$. Using elementary symmetric functions, we present several space-time-harmonic functions and thus martingales for these processes $(X_t)_{t\ge0}$ which are…

Time-series prediction or forecasting is critical across many real-world dynamic systems, and recent studies have proposed using Large Language Models (LLMs) for this task due to their strong generalization capabilities and ability to…

Integrating multiple observational studies for meta-analysis has sparked much interest. The presented R package WMAP (Weighted Meta-Analysis with Pseudo-Population) addresses a critical gap in the implementation of integrative weighting…