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This article first presents a short historical perpective of the importance splitting approach to simulate and estimate rare events, with a detailed description of several variants. We then give an account of recent theoretical results on these algorithms, including a central limit theorem for Adaptive Multilevel Splitting (AMS). Considering the asymptotic variance in the latter, the choice of the importance function, called the reaction coordinate in molecular dynamics, is also discussed. Finally, we briefly mention some worthwhile applications of AMS in various domains.
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We present a novel optical transmission system to experimentally demonstrate the possibility of mode division multiplexing. Its key components are mode multiplexer and demultiplexer based on a programmable liquid crystal on silicon panel, a prototype few-mode fiber, and a 4×4 multiple input multiple output algorithm processing the information of two polarization diversity coherent receivers. Using this system, we transmit two 100 Gb/s PDM-QPSK data streams modulated on two different modes of the prototype few-mode fiber. After 40 km, we obtain Q(2)-factors about 1 dB above the limit for forward error correction.
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A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the replicas which have reached the highest values along a chosen one-dimensional reaction coordinate. This reaction coordinate does not need to precisely describe all the metastabilities of the system for the method to give reliable results. An extension of the algorithm to compute transition times from one metastable state to another one is also presented. We demonstrate the interest of the method on two simple cases: A one-dimensional two-well potential and a two-dimensional potential exhibiting two channels to pass from one metastable state to another one.