The q-gradient method for global optimization

The q-gradient is an extension of the classical gradient vector based on the concept of Jackson's derivative. Here we introduce a preliminary version of the q-gradient method for unconstrained global optimization. The main idea behind our approach is the use of the negative of the q-gradient of the objective function as the search direction. In this sense, the method here proposed is a generalization of the well-known steepest descent method. The use of Jackson's derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient method is complemented with strategies to generate the parameter q and to compute the step length in a way that the search process gradually shifts from global in the beginning to almost local search in the end. For testing this new approach, we considered six commonly used test functions and compared our results with three Genetic Algorithms (GAs) considered effective in optimizing multidimensional unimodal and multimodal functions. For the multimodal test functions, the q-gradient method outperformed the GAs, reaching the minimum with a better accuracy and with less function evaluations.Comment: 12 pages, 1 figur

Small angle neutron scattering contrast variation reveals heterogeneities of interactions in protein gels

The structure of model gluten protein gels prepared in ethanol/water is investigated by small angle X-ray (SAXS) and neutrons (SANS) scattering. We show that gluten gels display radically different SAXS and SANS profiles when the solvent is (at least partially) deuterated. The detailed analysis of the SANS signal as a function of the solvent deuteration demonstrates heterogeneities of sample deuteration at different length scales. The progressive exchange between the protons (H) of the proteins and the deuteriums (D) of the solvent is inhomogeneous and 60 nm large zones that are enriched in H are evidenced. In addition, at low protein concentration, in the sol state, solvent deuteration induces a liquid/liquid phase separation. Complementary biochemical and structure analyses show that the denser protein phase is more protonated and specifically enriched in glutenin, the polymeric fraction of gluten proteins. These findings suggest that the presence of H-rich zones in gluten gels would arise from the preferential interaction of glutenin polymers through a tight network of non-exchangeable intermolecular hydrogen bonds.Comment: Soft Matter, Royal Society of Chemistry, 201