Related papers: RandomPoints package for Macaulay2
This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization…
Instance Space Analysis is a methodology to evaluate algorithm performance across diverse problem fields. Through visualisation and exploratory data analysis techniques, Instance Space Analysis offers objective, data-driven insights into…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
We develop a new variational scheme to approximate the position dependent spatial probability distribution of a zero dimensional manifold in a random medium. This celebrated 'toy-model' is associated via a mapping with directed polymers in…
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…
We introduce the CpMackeyFunctors package for Macaulay2, which allows for computations with Mackey functors over a cyclic group of prime order.
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from…
For a map $f:X \to M$ into a manifold $M$, we study the sets of deficient and multiple points of $f$. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in $X$, and we also provide…
A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. Frequently, it is desirable to go beyond scalar…
We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold…
We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which…
This manuscript outlines a software package that facilitates working with probability distributions by means of Monte-Carlo methods, in a way that allows for propagation of multivariate probability distributions through arbitrary functions.…