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In this thesis, we try to treat the problem of oriented paths in n-chromatic digraphs. We first treat the case of antidirected paths in 5-chromatic digraphs, where we explain El-Sahili’s theorem and provide an elementary and shorter proof of it. We then tr ...
We give a new, combinatorial proof for the necklace splitting problem for two thieves using only Tucker's lemma (a combinatorial version of the Borsuk-Ulam theorem). We show how this method can be applied to obtain a related recent result of Simonyi and ev ...
We consider models of N interacting objects, where the interaction is via a common resource and the distribution of states of all objects. We consider the case where the number of transitions per time slot per object vanishes as N grows. We show that, ...
What does a blind entity need in order to determine the geometry of the set of photocells that it carries through a changing lightfield? In this paper, we show that very crude knowledge of some statistical properties of the environment is sufficient for th ...
What does a blind entity need in order to determine the geometry of the set of photocells that it carries through a changing lightfield? In this paper, we show that very crude knowledge of some statistical properties of the environment is sufficient for th ...
We consider the recovery of an airline schedule after an unpredicted event, commonly called disruption, that makes the planned schedule unfeasible. In particular we consider the aircraft recovery problem for a heterogeneous fleet of aircrafts, made of regu ...
Any finite, separately convex, positively homogeneous function on R2 is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...
The main objective of the thesis is the study and the determination of an optimal navigation strategy, for a sailboat in an America's Cup race, by methods of stochastic optimization. Such methods are appropriate because the sailing team expects the wind to ...
Recently, Byrka, Grandoni, RothvoBand Sanita gave a 1.39 approximation for the Steiner tree problem, using a hypergraph-based linear programming relaxation. They also upper-bounded its integrality gap by 1.55. We describe a shorter proof of the same integr ...
Efficient mixing in bioreactors is essential in order to avoid concentration gradients which can be harmful for mammalian cells. To study mixing and its scalability in orbitally shaken cylindrical bioreactors, we measured mixing times in containers with no ...
