Related papers: Asymmetric Convex Intersection Testing
In these proceedings, the measurements of the $\Xi^-$, $\overline{\Xi}^+$, $\Omega^-$, $\overline{\Omega}^+$ masses and the mass differences between particle and anti-particle have been measured in pp collisions collected by the ALICE…
We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms…
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call "homotopic curve shortening" (HCS), starts with a closed curve (which might self-intersect) in the…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point…
We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex…
Acousto-optical coherence tomography (AOCT) consists in using random phase jumps on ultrasound and light to achieve a millimeter resolution when imaging thick scattering media. We combined this technique with heterodyne off-axis digital…
The goal of the ALICE experiment at LHC is to study strongly interacting matter at high energy densities as well as the signatures and properties of the quark-gluon plasma. This goal manifests itself in a rich physics program. Although…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
The Hirsch Conjecture stated that any $d$-dimensional polytope with n facets has a diameter at most equal to $n - d$. This conjecture was disproved by Santos (A counterexample to the Hirsch Conjecture, Annals of Mathematics, 172(1) 383-412,…
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
We present a framework to obtain valid inequalities for a reverse convex set: the set of points in a polyhedron that lie outside a given open convex set. Reverse convex sets arise in many models, including bilevel optimization and…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are generally characterized and distinguished by the width of the transparency created in the absorption profile of a weak probe in presence of a strong…
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…
Piecewise Linear Interface Construction (PLIC) is frequently used to geometrically reconstruct fluid interfaces in Computational Fluid Dynamics (CFD) modeling of two-phase flows. PLIC reconstructs interfaces from a scalar field that…
The Elvis problem has been studied in [2], which proves existence of solutions. However, their computation in the non-smooth case remains unsolved. A bisection method is proposed to solve the Elvis problem in two space dimensions for…