Related papers: Computational procedures for weighted projective s…

The photonic lantern (PL) is a tapered waveguide that can efficiently couple light into multiple single-mode optical fibers. Such devices are currently being considered for a number of tasks, including the coupling of telescopes and…

We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm…

Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for…

In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with…

Given a hypersurface in the complex projective $n$-space we prove several known formulas for the degree of its polar map by purely algebro-geometric methods. Furthermore, we give formulas for the degree of its polar map in terms of the…

We generalize methods to compute various kinds of rank to the case of a toric variety $X$ embedded into projective space using a very ample line bundle $\mathcal{L}$. We find an upper bound on the cactus rank. We use this to compute rank,…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

This paper is about a machine learning approach based on the multilinear projection of an unknown function (or probability distribution) to be estimated towards a linear (or multilinear) dimensional space E'. The proposal transforms the…

This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…

We introduce admissible Minkowski decomposition data (amd) for a 3-dimensional reflexive polytope P. This notion is defined purely in terms of the combinatorics of P. Denoting by X the Gorenstein toric Fano 3-fold whose fan is the spanning…

Any integral convex polytope $P$ in $\mathbb{R}^N$ provides a $N$-dimensional toric variety $X_P$ and an ample divisor $D_P$ on this variety. This paper gives an explicit construction of the algebraic geometric error-correcting code on…

We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood…

This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…

In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…

We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…

We describe MPSE: a Multi-Perspective Simultaneous Embedding method for visualizing high-dimensional data, based on multiple pairwise distances between the data points. Specifically, MPSE computes positions for the points in 3D and provides…