Breaking the Nanoparticle Loading-Dispersion Dichotomy in Polymer Nanocomposites with the Art of Croissant-Making.

The intrinsic properties of nanomaterials offer promise for technological revolutions in many fields, including transportation, soft robotics, and energy. Unfortunately, the exploitation of such properties in polymer nanocomposites is extremely challenging due to the lack of viable dispersion routes when the filler content is high. We usually face a dichotomy between the degree of nanofiller loading and the degree of dispersion (and, thus, performance) because dispersion quality decreases with loading.

OCReP: An Optimally Conditioned Regularization for pseudoinversion based neural training.

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability.