Concept

Definable real number

Related publications (32)

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...

EPFL2022

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

SPRINGER HEIDELBERG2020

The perceptual relevance of balance, evenness, and entropy in musical rhythms

Steffen Alexander Herff

There is an uncountable number of different ways of characterizing almost any given real-world stimulus. This necessitates finding stimulus features that are perceptually relevant - that is, they have distinct and independent effects on the perception and ...

ELSEVIER2020

Lonely Runner Polyhedra

Matthias Schymura

We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...

2018

Visualization, Adaptation, and Transformation of Procedural Grammars

Stefan Lienhard

Procedural shape grammars are powerful tools for the automatic generation of highly detailed 3D content from a set of descriptive rules. It is easy to encode variations in stochastic and parametric grammars, and an uncountable number of models can be gener ...

EPFL2017

Dynamic Graffiti Stylisation with Stochastic Optimal Control

Sylvain Calinon

We present a method for the interactive generation of stylised letters, curves and motion paths that are similar to the ones that can be observed in art forms such as graffiti and calligraphy. We define various stylisations of a letter form over a common g ...

ACM2017

Towards a Compiler for Reals

Viktor Kuncak, Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses a finite-precision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by finite-precision ...

2017

Embeddings of maximal tori in classical groups over local and global fields

Eva Bayer Fluckiger, Ting-Yu Lee

Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...

Turpion Ltd2016

Curve Graphs On Surfaces Of Infinite Type

Hugo Parlier, Ariadna Fossas Tenas

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the ...

Suomalainen Tiedeakatemia2015

Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...

ACM2014

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