Related papers: RandomPoints package for Macaulay2
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We…
This exposition presents nimblewomble, a software package to perform wombling, or boundary analysis, using the nimble Bayesian hierarchical modeling language in the R statistical computing environment. Wombling is used widely to track…
This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta.…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
One of the contemporary challenges in anomaly detection is the ability to detect, and differentiate between, both point and collective anomalies within a data sequence or time series. The anomaly package has been developed to provide users…
We introduce $\texttt{RandomMeas$.$jl}$, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a…
We introduce PyChEst, a Python package which provides tools for the simultaneous estimation of multiple changepoints in the distribution of piece-wise stationary time series. The nonparametric algorithms implemented are provably consistent…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…
This article introduces the package MatchingFields for Macaulay2 and highlights some open problems. A matching field is a combinatorial object whose data encodes a candidate toric degeneration of a Grassmannian or partial flag variety of…
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…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
PyUnfold is a Python package for incorporating imperfections of the measurement process into a data analysis pipeline. In an ideal world, we would have access to the perfect detector: an apparatus that makes no error in measuring a desired…
We introduce our package '+Ideals' for Magma, designed to perform the basic tasks related to ideals in number fields without pre-computing integral bases. It is based on Montes algorithm and a number of local techniques that we have…
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…