Related papers: Navigating Around Convex Sets
In this note, we propose some open problems and questions about bounded convex domains in $\mathbb C^N$, specifically about visibility and iteration theory.
A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields…
Knowing the distance of an astrophysical object is key to understanding it. However, at present, comparisons of theory and observations are hampered by precision (or lack thereof) in distance measurements or estimates. Putting the many…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
Cette these etudie l'aspect metrique de la geometrie non commutative a travers la formulation de Connes de la distance entre etats d'une algebre. Sont etudies des exemples d'espaces finis et le modele standard ou le champs de Higgs…
The flight of a quadcopter drone, readily available as a toy, is analyzed using simple physics concepts. A smartphone with built-in accelerometer and gyroscope was attached to the drone to register the accelerations and angular velocities…
The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…
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…
In this paper we discuss a classical geometrical problem of estimating an unknown point's location in $\Real{n}$ from several noisy measurements of the Euclidean distances from this point to a set of known reference points (anchors). We…
Convex geometry and complex geometry have long had fascinating interactions. This survey offers a tour of a few.
In this paper we outline the framework of mathematical statistics with which one may study the properties of galaxy distance estimators. We describe, within this framework, how one may formulate the problem of distance estimation as a…
The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic…
In this paper we study some relationships between polyhedral convex sets (PCS) and generalized polyhedral convex sets (GPCS). In particular, we clarify by a counterexample that the necessary and sufficient conditions for the separation of a…
This paper addresses the fundamental question of when convex sets remain disjoint after random projection. We provide an analysis using ideas from high-dimensional convex geometry. For ellipsoids, we provide a bound in terms of the distance…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.
Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very-high control accuracy, and…
Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which…
The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential…