Gradient design for liquid chromatography using multi-scale optimization

Recent applications of chemometrics in one‐ and two‐dimensional chromatography

“…Before and after, other optimization methods, such as predictive elution-window shifting and stretching (PEWS) [231] and "concentration pulses" have been developed. A concentration pulse is a temporary increase in modifier content when a compound elutes and is typically used in multistep isocratic measurements [282] and multistep gradients [283,284]. These optimization strategies may require a good deal of computational power to perform brute-force computations.…”

“…Using computer modelling to predict and optimize separation in GC × GC GC × GC 2008 [280] Benefits of solvent concentration pulses in retention time modelling of LC LC 2019 [282] Enhancement in the computation of gradient retention times in LC using root-finding methods LC 2019 [285] Gradient design for LC using multi-scale optimizations LC 2018 [284] (Continues) T A B L E 2 (Continued)…”

A Harten's Multiresolution Framework for Subdivision Schemes

“…Despite that the subdivision was conceived with a geometrical purpose in CAGD [12], other applications have been adopted it because of its easy implementation and flexibility to reach special properties. We are interested in the presence of subdivision in multiresolution algorithms, with applications in image processing [2,6], optimization [10,14] and uncertainty quantification [8], among others.…”

“…Originally, Harten's Mulitiresolution Framework (HMR-F) [13] provided a set of tools that allows to define a consistent multi-scale structure for numerical methods for conservation laws. Nevertheless, this theory is prepared for very general multi-scale scenarios and over the years it were found applications in other mathematical fields, for instance in the above mentioned applications [2,6,10,8,14], where it was combined with subdivision schemes.…”

“…In other applications, however, the prediction operators are subdivision schemes and they seem to be more relevant than the decimation operators. In fact, in [8,10,14], the decimation does not appear in the implementation of the methods, despite being needed to describe the multiresolution structure. The aim of this paper is to give theoretical support to this procedure.…”