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Wavelet transform on manifolds: old and new approaches

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A Magnetic Procedure for the Stability Number

Dominique de Werra

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new verte ...

2009

Graph transformations preserving the stability number

Dominique de Werra

We analyse the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...

2009

Quotient method for controlling the acrobot

Dominique Bonvin, Philippe Müllhaupt

This paper describes a two-sweep control design method to stabilize the acrobot, an input-afﬁne under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensiona ...

2009

Drawing cubic graphs with at most five slopes

János Pach, Balázs Keszegh

We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice. ...

2008

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

The continous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the ...

2008

On Polyhedral Projection and Parametric Programming

Colin Neil Jones

This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the ...

2008

Robust Routing for Dynamic Wireless Networks Based on Stable Embeddings

Matthias Grossglauser, Suhas Diggavi, Dominique Florian Tschopp, Jörg Widmer

Routing packets is a central function of multi-hop wireless networks. Traditionally, there have been two paradigms for routing, either based on the geographical coordinates of the nodes (geographic routing), or based on the connectivity graph (topology-bas ...

2007

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

Complex data processing: fast wavelet analysis on the sphere

Yves Wiaux, Jason Douglas McEwen

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sph ...

2007