Concept
Polytope
Related publications (47)
Safe Motion Planning against Multimodal Distributions Based on a Scenario Approach
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicl ...
2022Robust numerical integration on curved polyhedra based on folded decompositions
Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...
ELSEVIER SCIENCE SA2022Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions
In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition ...
2022A Low-Parametric Rhombic Microstructure Family for Irregular Lattices
New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material prope ...
ASSOC COMPUTING MACHINERY2020The hamburger theorem
We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...
Elsevier Science Bv2018