Related papers: A Fast and Practical Method to Estimate Volumes of…
We tackle the problem of efficiently approximating the volume of convex polytopes, when these are given in three different representations: H-polytopes, which have been studied extensively, V-polytopes, and zonotopes (Z-polytopes). We…
The computational cost in evaluation of the volume of a body using numerical integration grows exponentially with dimension of the space $n$. The most generally applicable algorithms for estimating $n$-volumes and integrals are based on…
Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to…
We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…
We provide two algorithms for computing the volume of a convex polytope with half-space representation {x>=0; Ax <=b} for some (m,n) matrix A and some m-vector b. Both algorithms have a O(n^m) computational complexity which makes them…
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-concave distributions supported on convex bodies, we need at…
We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differential equations. Our approach rests on…
We examine volume computation of general-dimensional polytopes and more general convex bodies, defined as the intersection of a simplex by a family of parallel hyperplanes, and another family of parallel hyperplanes or a family of…
A method for calculating the pressure tensor in constant-volume Monte Carlo simulations of convex bodies is presented. In contrast to other approaches, the method requires only an isotropic scaling of the simulation box, and the counting of…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…
Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within…
We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett…
Sampling from high dimensional distributions and volume approximation of convex bodies are fundamental operations that appear in optimization, finance, engineering, artificial intelligence and machine learning. In this paper we present…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
Accurate body weight estimation is critical in emergency medicine for proper dosing of weight-based medications, yet direct measurement is often impractical in urgent situations. This paper presents a non-invasive method for estimating body…
In this letter, we introduce a novel message-passing algorithm for a class of problems which can be mathematically understood as estimating volume-related properties of random polytopes. Unlike the usual approach consisting in approximating…
We study the maximum weight convex polytope problem, in which the goal is to find a convex polytope maximizing the total weight of enclosed points. Prior to this work, the only known result for this problem was an $O(n^3)$ algorithm for the…
We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural…