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Motivation: Elastic net regression is a form of penalized regression that lies between ridge and least absolute shrinkage and selection operator (LASSO) regression. The elastic net penalty is a powerful tool controlling the impact of…
Everything that exists in R is an object [Chambers2016]. This article examines what would be possible if we kept copies of all R objects that have ever been created. Not only objects but also their properties, meta-data, relations with…
Discovering patterns of the complex high-dimensional data is a long-standing problem. Dimension Reduction (DR) and Intrinsic Dimension Estimation (IDE) are two fundamental thematic programs that facilitate geometric understanding of the…
The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional and projectivity. Examples and closure properties are…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…
This article introduces the R package hermiter which facilitates estimation of univariate and bivariate probability density functions and cumulative distribution functions along with full quantile functions (univariate) and nonparametric…
In this short article I introduce the mvp package, which provides some functionality for handling multivariate polynomials. The package uses the C++ Standard Template Library's map class to store and retrieve elements; it conforms to…
{\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological…
With the advent of modern statistical software, complex experimental designs are now routinely employed in many areas of research. Failing to correctly identify the structure of the experimental design can lead to incorrect model selection…
In this short article I introduce the knotR package, which creates two dimensional knot diagrams optimized for visual appearance using the R programming language. The knotR package is a systematic R-centric suite of software for the…
Despite several deficiencies, the use of spreadsheets in statistics courses is increasingly common. In this paper we discuss many shortcomings resulting from this approach. We suggest a technique integrating a spreadsheet and a dedicated…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…
The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a…
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…
R packages are the fundamental units of reproducible code in R, providing a mechanism for distributing user-developed code, documentation, and data. Docker is a virtualization technology that allows applications and their dependencies to be…
Algebraic differentiators have attracted much interest in recent years. Their simple implementation as classical finite impulse response digital filters and systematic tuning guidelines may help to solve challenging problems, including, but…
The R package innsight offers a general toolbox for revealing variable-wise interpretations of deep neural networks' predictions with so-called feature attribution methods. Aside from the unified and user-friendly framework, the package…