Related papers: Hit-and-run for numerical integration
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…
Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different…
The need for efficient normal integration methods is driven by several computer vision tasks such as shape-from-shading, photometric stereo, deflectometry, etc. In the first part of this survey, we select the most important properties that…
We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However,…
This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal…
We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of the target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Our sampler performs well in…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling…
A Monte Carlo algorithm for computing quantum mechanical expectation values of coordinate operators in many body problems is presented. The algorithm, that relies on the forward walking method, fits naturally in a Green's Function Monte…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\mathbb R}^n$. We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant…