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We study the smallest intersecting and enclosing ball problems in Euclidean spaces for input objects that are compact and convex. They link and unify many problems in computational geometry and machine learning. We show that both problems…
The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
We implement a shape optimization algorithm for body-assisted light-matter interactions described by the formalism of macroscopic quantum electrodynamics. The approach uses the level-set method to represent and incrementally evolve…
We consider the problem of quantifying the Pareto optimal boundary in the achievable rate region over multiple-input single-output (MISO) interference channels, where the problem boils down to solving a sequence of convex feasibility…
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their…
Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry…
Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…
We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed…
Electromagnetic metasurfaces have attracted significant interest recently due to their low profile and advantageous applications. Practically, many metasurface designs start with a set of constraints for the radiated far-field, such as…
We study partitions on three dimensional manifolds which minimize the total geodesic perimeter. We propose a relaxed framework based on a $\Gamma$-convergence result and we show some numerical results. We compare our results to those…
In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…