that the second largest block contains only ˜ Θ(n 2/3) vertices, and prove sharp concentration results for b(ℓ; Pn), for all 2 ≤ ℓ ≤ n 2/3 (here ˜ Θ(.) stands for “up to logarithmic factors”). In fact, we obtain this result as a consequence of a much more general result that we prove in this paper. Let C be a

I am grateful to Luc Segoufin who kindly accepted me to be his PhD student. He introduced me to the problem of query enumeration and encouraged me to look for the answers to all the questions that emerged during our collaboration. He was a truly great advisor, always supportive and available for discussions and advice. I would like to thank Arnaud Durand and Patrice Ossona de Mendez for accepting to review this thesis and for their constructive comments on the earlier versions of this manuscript. Many thanks to Nicole Bidoit and Victor Vianu for accepting to be in my jury. Special thanks go to my Parents, who directed me to follow the scientific path and where fully supportive at all times. Thanks to all the members of LSV – it was a pleasure working with You. I would like to thank the awesome people whom I have been working with in the same office on the 4th floor. Without all the nice riddles and the magnificent French lessons my time there wouldn’t be as chouette as it was. Big thanks go to my son Boris, who was kind enough to sleep through the whole nights, allowing his dad to actually write the thesis down.

of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond

2010 to my wife, Joyce, and my family...- Résumé-

Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmologi-cal inhomogeneities that can be used to study the eect of inhomogeneities on the universe's expansion. In this thesis, new

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove that a weak limit of biharmonic maps into a sphere is again bihar-monic. The proof of regularity can be adapted to biharmonic maps on the Heisenberg group, and to other functionals leading to fourth order elliptic equations with critical nonlinearities in lower order derivatives. Mathematics Subject Classification (2000): 35J60, 35H20 1.

Cell balance equation for chemotactic bacteria with a biphasic tumbling frequency

the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.

ii iii CHRISTOPHER CHARLES WEIGLE: Displays for Exploration and Comparison of Nested

symmetric structures in nature and engineering’. Subject Areas: geometry Keywords: overconstrained mechanism, Grünbaum framework, Kokotsakis mesh, flexible bipartite framework, Burmester’s focal mechanism Author for correspondence: