Publications related to Construction of the real numbers

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

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 ...

2021

Test and lower bound modeling of keyed shear connections in RC shear walls

Aurelio Muttoni, Cao Linh Hoang, Jesper Harrild Sorensen

This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests sho ...

Engineering Structures2018

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

Simultaneous Approximation of Polynomials

János Pach, Andrei Kupavskii

Let P-d denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers x(1)

Springer Int Publishing Ag2016

On The Number Of Ordinary Conics

Frank de Zeeuw, Adrian Claudiu Valculescu

We prove a lower bound on the number of ordinary conics determined by a finite point set in R-2. An ordinary conic for S subset of R-2 is a conic that is determined by five points of S and contains no other points of S. Wiseman and Wilson proved the Sylves ...

SIAM Publications2016

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

Constitutive gray hair in Mice induced by Melanocyte-specific deletion of c-Myc

Friedrich Beermann, Karine Schouwey, Marzia Armaro

c-Myc is involved in the control of diverse cellular processes and implicated in the maintenance of different tissues including the neural crest. Here we report that c-Myc is particularly important for pigment cell development and homeostasis. Targeting c- ...

2012

Trustworthy Numerical Computation in Scala

Viktor Kuncak, Eva Darulova

Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures. However, rigorous reasoning about the resulting ...

2011

Overlap properties of geometric expanders

The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...

De Gruyter2011

Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

Philippe Müllhaupt, Basile Graf

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combi- nation of free coor ...

IEEE2010

Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

Philippe Müllhaupt, Basile Graf

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combination of the free co ...

2010

Ordered Sets in the Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...

Springer2010

Contribution to the ergodic theory of piecewise monotone continuous maps

Bastien Faller

This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dy ...

EPFL2008

Fractional Collections with Cardinality Bounds, and Mixed Integer Linear Arithmetic with Stars

Viktor Kuncak, Ruzica Piskac

We present decision procedures for logical constraints that support reasoning about collections of elements such as sets, multisets, and fuzzy sets. Element membership in such collections is given by a characteristic function from a finite universe (of unk ...

2008

Recent evolution of the simulation tools for computer aided design of electron-optical systems for powerful gyrotrons

Jean-Philippe Hogge, Trach-Minh Tran, Ioannis Pagonakis

Computer aided design of powerful gyrotrons for electron cyclotron resonance heating and current drive of fusion plasmas requires adequate physical models and efficient software packages for analysis, comparison and optimization of their electron-optical s ...

2007