Publications

2013

• Anaglyphe d'un hypercube
  
  • Colonna Jean-François
  , 2013. Anaglyph of an hypercube (Anaglyphe d'un hypercube)
• Un pavage de Penrose pseudo-périodique fractal
  
  • Colonna Jean-François
  , 2013. A fractal pseudo-periodical Penrose tiling (Un pavage de Penrose pseudo-périodique fractal)
• Un hypercube fractal
  
  • Colonna Jean-François
  , 2013. A fractal hypercube (Un hypercube fractal)
• Un hypercube fractal
  
  • Colonna Jean-François
  , 2013. A fractal hypercube (Un hypercube fractal)
• Un ruban de Möbius fractal
  
  • Colonna Jean-François
  , 2013. A fractal Möbius strip (Un ruban de Möbius fractal)
• Une bouteille de Klein fractale
  
  • Colonna Jean-François
  , 2013. A fractal Klein bottle (Une bouteille de Klein fractale)
• Le ruban de Möbius
  
  • Colonna Jean-François
  , 2013. The Möbius strip (Le ruban de Möbius)
• La bouteille de Klein
  
  • Colonna Jean-François
  , 2013. The Klein bottle (La bouteille de Klein)
• Un tore
  
  • Colonna Jean-François
  , 2013. A torus (Un tore)
• Une sphère
  
  • Colonna Jean-François
  , 2013. A sphere (Une sphère)
• Une sphère fractale
  
  • Colonna Jean-François
  , 2013. A fractal sphere (Une sphère fractale)
• Un tore fractal
  
  • Colonna Jean-François
  , 2013. A fractal torus (Un tore fractal)
• Un 'tapis' de Sierpinski tridimensionnel obtenu à l'aide de la méthode des 'Iterated Function Systems' -IFS
  
  • Colonna Jean-François
  , 2013. A tridimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS- (Un 'tapis' de Sierpinski tridimensionnel obtenu à l'aide de la méthode des 'Iterated Function Systems' -IFS-)
• Un 'tapis' de Sierpinski bidimensionnel obtenu à l'aide de la méthode des 'Iterated Function Systems' -IFS
  
  • Colonna Jean-François
  , 2013. A bidimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS- (Un 'tapis' de Sierpinski bidimensionnel obtenu à l'aide de la méthode des 'Iterated Function Systems' -IFS-)
• Une fougère bidimensionnelle obtenue à l'aide de la méthode des 'Iterated Function Systems' -IFS
  
  • Colonna Jean-François
  , 2013. A bidimensional fern computed by means of an 'Iterated Function System' -IFS- (Une fougère bidimensionnelle obtenue à l'aide de la méthode des 'Iterated Function Systems' -IFS-)
• How regular can maxitive measures be?
  
  • Poncet Paul
  Topology and its Applications, Elsevier, 2013, 160 (4), pp.606-619. We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every regular maxitive measure is completely maxitive, this yields sufficient conditions for the existence of a cardinal density. We also show that every outer-continuous maxitive measure can be decomposed as the supremum of a regular maxitive measure and a maxitive measure that vanishes on compact subsets under appropriate conditions. (10.1016/j.topol.2013.01.007)
  DOI : 10.1016/j.topol.2013.01.007
• Semi-smooth Newton methods for optimal control of the dynamical Lamé system with control constraints.
  
  • Kröner Axel
  Numerical Functional Analysis and Optimization, Taylor & Francis, 2013. Optimal control problems governed by the dynamical Lamé system with additional constraints on the controls are analyzed. Different types of control action are considered: distributed, Neumann boundary and Dirichlet boundary control. To treat the inequality control constraints semi-smooth Newton methods are applied and their convergence is analyzed. Although semi-smooth Newton methods are widely studied in the context of PDE-constrained optimization little has been done in the context of the dynamical Lamé system. The novelty of the article is the proof that in case of distributed and Neumann boundary control the Newton method converges superlinearly. In case of Dirichlet control superlinear convergence is shown for a strongly damped Lamé system. The results are an extension of [A. Kröner , K. Kunisch , and B. Vexler ( 2011 ), SIAM J. Control Optim. 49 : 830 – 858], where optimal control problems of the classical wave equation are considered. The control problems are discretized by finite elements and numerical examples are presented.
• Variation artistique d'une visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments
  
  • Colonna Jean-François
  , 2013. Artistic view of a tridimensional visualization of the Mandelbrot set with mapping of the arguments (Variation artistique d'une visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments)
• Dobrushin ergodicity coefficient for Markov operators on cones, and beyond
  
  • Gaubert Stéphane
  • Qu Zheng
  , 2013. The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in quantum information theory. In particular, we show that the contraction rate of such operators, with respect to the Hopf oscillation seminorm, is given by an analogue of Dobrushin's ergodicity coefficient. We derive from this result a characterization of the contraction rate of a non-linear flow, with respect to Hopf's oscillation seminorm and to Hilbert's projective metric.
• Visualisation tridimensionnelle de l'Univers inflationnaire
  
  • Colonna Jean-François
  , 2013. Tridimensional display of the inflationary Universe (Visualisation tridimensionnelle de l'Univers inflationnaire)
• Visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments -le Mont Saint Michel
  
  • Colonna Jean-François
  , 2013. Tridimensional visualization of the Mandelbrot set with mapping of the arguments -the Mont Saint Michel- (Visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments -le Mont Saint Michel-)
• Multi-input Schrödinger equation: controllability, tracking, and application to the quantum angular momentum
  
  • Boscain Ugo
  • Caponigro Marco
  • Sigalotti Mario
  , 2013. We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schrödinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability, approximate controllability in $H^s$, and tracking in modulus. The result is more general than those present in the literature even in the case of one control and permits to treat situations in which the spectrum of the uncontrolled operator is very degenerate (e.g. it has multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum preventing the application of the results in the literature.
• Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs
  
  • Allamigeon Xavier
  • Gaubert Stéphane
  • Goubault Eric
  Discrete and Computational Geometry, Springer Verlag, 2013, 49, pp.247-279. We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches. (10.1007/s00454-012-9469-6)
  DOI : 10.1007/s00454-012-9469-6
• Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -section tridimensionnelle
  
  • Colonna Jean-François
  , 2013. A foggy pseudo-octonionic Julia set ('MandelBulb' like : a 'JuliaBulb') computed with A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -tridimensional cross-section- (Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -section tridimensionnelle-)
• Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -section tridimensionnelle
  
  • Colonna Jean-François
  , 2013. A foggy pseudo-octonionic Julia set ('MandelBulb' like : a 'JuliaBulb') computed with A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -tridimensional cross-section- (Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(-0.5815147625160462,+0.6358885017421603,0,0,0,0,0,0) -section tridimensionnelle-)