Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

Differentiation of electrophilic and ambiphilic carbenes

Comparative selectivities toward alkenes of CH₃CCl, CCl₂, and CH₃OCCl establish the former two carbenes as electrophiles; the latter is an ambiphile.     

Intermolecular additions of cyclobutylchlorocarbene

Cyclobutylchlorocarbene can be intercepted by simple alkenes in successful competition with intramolecular ring expansion and hydride migration reactions.     

Synthesis,X-ray crystal structure,DFT calculations,spectroscopic characterization and redox behaviour of a rhodium(III) complex of an anthracene–pyridylhydrazone ligand

Transition Metal Chemistry - A pyridylhydrazone incorporating an anthracene moiety, designated as HLAnc, has been synthesized in order to examine its coordination behaviour towards rhodium(III)....