Related papers: A computer algebra system for R: Macaulay2 and the…
This paper explores an innovative approach to teaching data wrangling skills to students through hands-on activities before transitioning to coding. Data wrangling, a critical aspect of data analysis, involves cleaning, transforming, and…
A graphical model is an undirected network representing the conditional independence properties between random variables. Graphical modeling has become part and parcel of systems or network approaches to multivariate data, in particular…
Clustering of longitudinal data is used to explore common trends among subjects over time for a numeric measurement of interest. Various R packages have been introduced throughout the years for identifying clusters of longitudinal patterns,…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides…
With the current emphasis on reproducibility and replicability, there is an increasing need to examine how data analyses are conducted. In order to analyze the between researcher variability in data analysis choices as well as the aspects…
Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones, 1977). Cohen (1982) described an adaptation with less explicit competition suitable for…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…
We introduce the package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by producing the fiber graph of the toric ideal. The package uses…
Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…
This paper presents maplet, an open-source R package for the creation of highly customizable, fully reproducible statistical pipelines for omics data analysis, with a special focus on metabolomics-based methods. It builds on the…
We investigate the use of machine learning for solving analytic problems in theoretical physics. In particular, symbolic regression (SR) is making rapid progress in recent years as a tool to fit data using functions whose overall form is…
Although various forms of linkage map construction software are widely available, there is a distinct lack of packages for use in the R statistical computing environment. This article introduces the ASMap linkage map construction R package…
Robust estimation provides essential tools for analyzing data that contain outliers, ensuring that statistical models remain reliable even in the presence of some anomalous data. While robust methods have long been available in R, users of…