that the polynomial-time hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for ǫ = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several

to an equivalent instance, of an arbitrary problem, with bitsize O(n 2−ε ) for ε > 0, unless NP ⊆ coNP/poly and the polynomial-time hierarchy collapses. These results imply that existing linear-vertex kernels for k-Nonblocker and k-Max Leaf Spanning Tree (the parametric duals of (Connected) Dominating Set

different behaviors exhibited by universal plans. We show that universal plans which run in polynomial time and are of polynomial size cannot satisfy even the weakest type of completeness unless the polynomial hierarchy collapses. By relaxing either the polynomial time or the polynomial space

[∗], and (2) when restricted to monotone queries, the problem is complete for the fundamental parametric complexity class W[1]. The practical significance of these results is that unless the parameterized complexity hierarchy collapses, there are unlikely to be algorithms that solve this problem (even under

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-tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark: a mathematical

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.

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

. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low

and backchase