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The lexico-smallest representation of convex polyhedra

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Diameter of Polyhedra: Limits of Abstraction

Friedrich Eisenbrand, Thomas Rothvoss, Nicolai Hähnle

We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Even if this abstraction is more general than other abstractions previously studied in the literature, known upper bounds on the diameter of polyhedra continue to hold her ...

2010

Differential geometry applied to crystallography

Philippe Kocian

The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...

EPFL2009

A note on the representation of parametric models for multivariate extremes

Marc-Olivier Boldi

In this note, the representations of extremal Dirichlet and logistic distributions are reviewed and extended. These new representations allow exact simulations of the spectral distribution functions and an extension of the extremal logistic case to dimensi ...

2009

Diameter of Polyhedra: Limits of Abstraction

Friedrich Eisenbrand, Thomas Rothvoss, Nicolai Hähnle

We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Although this abstraction is simpler than other abstractions that were previously studied in the literature, the best upper bounds on the diameter of polyhedra continue to ...

2009

Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

Victor Panaretos

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. ...

2008

Points surrounding the origin

János Pach, Andreas Fukami Holmsen

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

2008

Some Recovery Conditions for Basis Learning by L1-Minimization

Rémi Gribonval, Karin Schnass

Many recent works have shown that if a given signal admits a sufficiently sparse representation in a given dictionary, then this representation is recovered by several standard optimization algorithms, in particular the convex

\ell^1

minimization approac ...

2008

Analytical calculation of the inertia matrices of convex spheropolyhedra

Lionel Pournin

Spheropolyhedra are bodies obtained as Minkowski sums of polyhedra with spheres. They are simple, yet flexible models of non-spherical particles for granular media simulated with the Distinct Element Method (DEM). We here give an analytical method for the ...

2008

On the origin of the boson peak in globular proteins

Paolo De Los Rios, Francesco Piazza

We study the boson peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean random matrix theory, whose predictions can be numerica ...

Taylor & Francis2007

Controllability and Stability of Repetitive Batch Processes

Dominique Bonvin

Batch control has traditionally addressed the problems related to the absence of a steady state and the finite batch duration. Recently, batch control has added the dimension that arises naturally from the possibility of applying run-to-run control, i.e. i ...

2007

Some Recovery Conditions for Basis Learning by L1-Minimization

Rémi Gribonval, Karin Schnass

\ell^1

minimization approac ...

2008