On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Morphology Change of C60 Islands on Organic Crystals Observed by Atomic Force Microscopy

Organic-organic heterojunctions are nowadays highly regarded materials for light-emitting diodes, field-effect transistors, and photovoltaic cells with the prospect of designing low-cost, flexible, and efficient electronic devices.1-3 However, the key parameter of optimized heterojunctions relies on the choice of the molecular compounds as well as on the morphology of the organic-organic interface,4 which thus requires fundamental studies. In this work, we investigated the deposition of C60 molecules at room temperature on an organic layer compound, the salt bis(benzylammonium)bis(oxalato)cupurate(II), by means of noncontact atomic force microscopy. Three-dimensional molecular islands of C60 having either triangular or hexagonal shapes are formed on the substrate following a "Volmer-Weber" type of growth. We demonstrate the dynamical reshaping of those C60 nanostructures under the local action of the AFM tip at room temperature. The dissipated energy is about 75 meV and can be interpreted as the activation energy required for this migration process.