Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm (HEA) from Galinier and Hao (1999). The proposed algorithm, denoted HEAD -for HEA in Duet -works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD. These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81colorings for and even 47-colorings for and 82-colorings for .
We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent wave function. Because the evolution of the probability density of the wave packet just after it exits the slits raises the issue of interpreting the wave/particle dualism, we also simulate trajectories in the de Broglie-Bohm interpretation.
We show how energy flow lines answer the question about diffraction phenomena posed in 1818 by the French Academy: “Deduce by mathematical induction the movements of the rays during their crossing near the bodies.” The use of energy flow lines provides a complementary answer to Fresnel’s wave theory of light. A numerical simulation of the energy flow lines shows that they can reach the bright spot of Poisson–Arago in the shadow center of a circular opaque disk. For a monochromatic wave in vacuum, these energy flow lines correspond to the diffracted rays of Newton’s Opticks.
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