Synthesis and Redox and Photophysical Properties of Benzodifuran-Spiropyran Ensembles

Two benzodifuran (BDF)-coupled spiropyran (SP) systems and their BDF reference compounds were obtained in good yields through HuisgenMeldalSharpless click chemistry and then subjected to investigation of their electrochemical and photophysical properties. In both SP and merocyanine (MC) forms of the coupled molecules, the BDF-based emission is quenched to around 1 of the quantum yield of emission from the BDF reference compounds. Based on electrochemical data, this quenching is attributed to oxidative electron-transfer quenching. Irradiation at 366nm results in ring opening to the MC forms of the BDF-coupled SP compounds and the SP reference compound with a quantum efficiency of about 50. The rate constants for the thermal ring closing are approximately 3.4x103s1. However, in the photostationary states the MC fractions of the coupled molecules are substantially lower than that of the reference SP compound, attributed to the observed acceleration of the ring-closing reaction upon irradiation. As irradiation at 366nm invariably also excites higher-energy transitions of the BDF units in the coupled compounds, the ring-opening reaction is accelerated relative to the SP reference, which results in lower MC fractions in the photostationary state. Reversible photochromism of these BDF-coupled SP compounds renders them promising in the field of molecular switches.

Fast Update of Conditional Simulation Ensembles

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.