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Order Types of Convex Bodies

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Between the Pattern and the Type: A short parallel story

Vasileios Chanis

Historically speaking, the notion of the type was reintroduced to the larger architectural discourse as a direct consequence of the crisis of the Modern. The task of revisiting the forms of the past also dictated the return of architectural methods that ha ...

2023

Quantum yield and brightness

Jean-Claude Bünzli

Brightness has different meaning in different contexts and some of these are reviewed. The scientific definition of brightness does not represent our perception. The current definition is that from the IUPAC Gold Book and is mainly restricted to solutions. ...

2020

Entropic Matroids and Their Representation

Emmanuel Abbé

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw ...

2019

Cross-sections of line configurations in R-3 and (d-2)-flat configurations in R-d

Andres Jacinto Ruiz Vargas

We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the order types of point sets {p(1),..., p(n)} that stem from the intersections of the lines in L with (directed) planes Pi, not parallel to any line of L, that ...

ELSEVIER SCIENCE BV2019

An Improved Analysis of Local Search for Max-Sum Diversification

Friedrich Eisenbrand, Rico Zenklusen, Alfonso Bolívar Cevallos Manzano

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

INFORMS2019

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2019

On the reverse isodiametric problem and Dvoretzky-Rogers-type volume bounds

Matthias Schymura

The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr. on the reverse question: Every convex body has a linear image whose isodiametric quot ...

2018

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM PUBLICATIONS2018

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Subdeterminant Maximization via Nonconvex Relaxations and Anti-Concentration

Nisheeth Vishnoi, Javad Ebrahimi Boroojeni, Damian Mateusz Straszak

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the sim ...

Ieee2017