Related papers: Computing Convex Hulls of Trajectories
We obtain local and global results on polynomially convex hulls of Lagrangian and totally real submanifolds of $C^n$ with self-intersections and open Whitney umbrella points.
In this paper we look for the convex hull of a set using the geometric evolution by minimal curvature of a hypersurface that surrounds the set. To find the convex hull, we study the large time behavior of solutions to an obstacle problem…
In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…
This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain…
The cut polytope ${\rm CUT}(n)$ is the convex hull of the cut vectors in a complete graph with vertex set $\{1,\ldots,n\}$. It is well known in the area of combinatorial optimization and recently has also been studied in a direct relation…
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…
A novel 2-D method for computing the convex hull of a sufficiently dense set of n integer points is introduced. The approach employs a ranking function that avoids sorting the points directly thus reducing the overall time complexity. The…
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin…
This paper summarises works carried out for defining tool trajectory formats well adapted to High Speed Machining (HSM). Advantages in using native polynomial formats, calculated directly from the CAD model, are highlighted. In particular,…
This article provides an overview of our joint work on binary polynomial optimization over the past decade. We define the multilinear polytope as the convex hull of the feasible region of a linearized binary polynomial optimization problem.…
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material,…
We describe algorithms for computing the intersection numbers of divisors and of Chern classes of the Hodge bundle on the moduli spaces of stable pointed curves. We also discuss the implementations and the results obtained. There are…
We study the numerical computation of an expectation of a bounded function with respect to a measure given by a non-normalized density on a convex body. We assume that the density is log-concave, satisfies a variability condition and is not…
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time…
Given a set of disjoint simple polygons $\sigma_1, \ldots, \sigma_n$, of total complexity $N$, consider a convexification process that repeatedly replaces a polygon by its convex hull, and any two (by now convex) polygons that intersect by…
In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…
The finely tuned structures of membrane channels allow selective passage of ions through the available aqueous pores. In order to understand channel function, it is crucial to locate the pore and study its physical and chemical properties.…
Let $P$ be a crossing-free polygon and $\mathcal C$ a set of shortcuts, where each shortcut is a directed straight-line segment connecting two vertices of $P$. A shortcut hull of $P$ is another crossing-free polygon that encloses $P$ and…
Thermodynamic constraints on reactions directions are inherent in the structure of a given biochemical network. However, concrete procedures for determining feasible reaction directions for large-scale metabolic networks are not well…
We give an overview of the 2020 Computational Geometry Challenge, which targeted the problem of partitioning the convex hull of a given planar point set P into the smallest number of convex faces, such that no point of P is contained in the…