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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…
We present MGPU, a C++ programming library targeted at single-node multi-GPU systems. Such systems combine disproportionate floating point performance with high data locality and are thus well suited to implement real-time algorithms. We…
This paper presents a high-level description of the R software package mixdistreg to fit mixture of experts distributional regression models. The proposed framework is implemented in R using the deepregression software template, which is…
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…
Investigating processes in complex molecular systems, which are characterized by many variables, is a crucial problem in computational physics. These systems can be reduced to a few meaningful degrees of freedom known as collective…
Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…
The Fleet Size and Mix Vehicle Routing Problem (FSMVRP) is a prominent variant of the Vehicle Routing Problem (VRP), extensively studied in operations research and computational science. FSMVRP requires simultaneous decisions on fleet…
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a…
Rgtsvm provides a fast and flexible support vector machine (SVM) implementation for the R language. The distinguishing feature of Rgtsvm is that support vector classification and support vector regression tasks are implemented on a…
The R package multgee implements the local odds ratios generalized estimating equations (GEE) approach proposed by Touloumis et al. (2013), a GEE approach for correlated multinomial responses that circumvents theoretical and practical…
We generalize univariate multipoint evaluation of polynomials of degree n at sublinear amortized cost per point. More precisely, it is shown how to evaluate a bivariate polynomial p of maximum degree less than n, specified by its n^2…
Program analysis requires the generation of program properties expressing conditions to hold at intermediate program locations. When it comes to programs with loops, these properties are typically expressed as loop invariants. In this paper…
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of spatial dimension $m$. Here, we analyze the FNT in the…
Marginal MAP problems are notoriously difficult tasks for graphical models. We derive a general variational framework for solving marginal MAP problems, in which we apply analogues of the Bethe, tree-reweighted, and mean field…
We present PlanetPack, a new software tool that we developed to facilitate and standardize the advanced analysis of radial velocity (RV) data for the goal of exoplanets detection, characterization, and basic dynamical $N$-body simulations.…
The mean and variance of the number of appearances of a given subgraph $H$ in an Erd\H{o}s--R\'enyi random graph over $n$ nodes are rational polynomials in $n$. We present a piece of software named Polcovar (from "polynomial" and…
When performing an aggregate data meta-analysis of a continuous outcome, researchers often come across primary studies that report the sample median of the outcome. However, standard meta-analytic methods typically cannot be directly…
Bayesian inference has become an important tool to solve inverse problems and to quantify uncertainties in their solutions. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently by using optimization.…
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
We introduce $\mathcal{V}$-polyhedral disjunctive cuts (VPCs) for generating valid inequalities from general disjunctions. Cuts are critical to integer programming solvers, but the benefit from many families is only realized when the cuts…