A Novel Multi-Scale Strategy for Multi-Parametric Optimization
The motion of a sailing yacht is the result of an equilibrium between the aerodynamic forces, generated by the sails, and the hydrodynamic forces, generated by the hull(s) and the appendages (such as the keels, the rudders, the foils, etc.), which may be fixed or movable and not only compensate the aero-forces, but are also used to drive the boat. In most of the design, the 3D shape of an appendage is the combination of a plan form (2D side shape) and a planar section(s) perpendicular to it, whose design depends on the function of the appendage. We often need a section which generates a certain quantity of lift to fulfill its function, but the lift comes with a penalty which is the drag. Th…
An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision
Abstract Exponential polynomials are essential in subdivision for the reconstruction of specific families of curves and surfaces, such as conic sections and quadric surfaces. It is well known that if a linear subdivision scheme is able to reproduce a certain space of exponential polynomials, then it must be level-dependent, with rules depending on the frequencies (and eventual multiplicities) defining the considered space. This work discusses a general strategy that exploits annihilating operators to locally detect those frequencies directly from the given data and therefore to choose the correct subdivision rule to be applied. This is intended as a first step towards the construction of se…
Annihilation Operators for Exponential Spaces in Subdivision
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
Overlapped moving windows followed by principal component analysis to extract information from chromatograms and application to classification analysis
Variable generation from chromatograms is conveniently accomplished using unsupervised rather than manual techniques. With unsupervised techniques, there is no need for selecting a few peaks for manual integration and valuable information is quickly and efficiently collected. The generation of variables can be performed by using either peak searching or moving window (MW) strategies. With a MW approach, the peaks are ignored and many variables, only part of them carrying information, are generated. Thus, variable generation by MWs should be followed by data compression to generate the variables to be further used for classification or quantitation purposes. In this work, unsupervised proces…
Enhancement in the computation of gradient retention times in liquid chromatography using root-finding methods.
Abstract Gradient elution may provide adequate separations within acceptably short times in a single run, by gradually increasing the elution speed. Similarly to isocratic elution, chromatograms can be predicted under any experimental condition, through strategies based on retention models. The most usual approach implies solving an integral equation (i.e., the fundamental equation of gradient elution), which has an analytical solution only for certain combinations of retention model and gradient programme. This limitation can be overcome by using numerical integration, which is a universal approach although at the cost of longer computation times. In this work, several alternatives to impr…
Assisted baseline subtraction in complex chromatograms using the BEADS algorithm.
The data processing step of complex signals in high-performance liquid chromatography may constitute a bottleneck to obtain significant information from chromatograms. Data pre-processing should be preferably done with little (or no) user supervision, for a maximal benefit and highest speed. In this work, a tool for the configuration of a state-of-the-art baseline subtraction algorithm, called BEADS (Baseline Estimation And Denoising using Sparsity) is developed and verified. A quality criterion based on the measurement of the autocorrelation level was designed to select the most suitable working parameters to obtain the best baseline. The use of a log transformation of the signal attenuate…
Gradient design for liquid chromatography using multi-scale optimization.
Abstract In reversed phase-liquid chromatography, the usual solution to the “general elution problem” is the application of gradient elution with programmed changes of organic solvent (or other properties). A correct quantification of chromatographic peaks in liquid chromatography requires well resolved signals in a proper analysis time. When the complexity of the sample is high, the gradient program should be accommodated to the local resolution needs of each analyte. This makes the optimization of such situations rather troublesome, since enhancing the resolution for a given analyte may imply a collateral worsening of the resolution of other analytes. The aim of this work is to design mul…
Multi-scale optimisation vs. genetic algorithms in the gradient separation of diuretics by reversed-phase liquid chromatography
Abstract Multi-linear gradients are a convenient solution to get separation of complex samples by modulating carefully the gradient slope, in order to accomplish the local selectivity needs for each particular solute cluster. These gradients can be designed by trial-and-error according to the chromatographer experience, but this strategy becomes quickly inappropriate for complex separations. More evolved solutions imply the sequential construction of multi-segmented gradients. However, this strategy discards part of the search space in each step of the construction and, again, cannot deal properly with very complex samples. When the complexity is too large, the only valid alternative for fi…
High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach
Abstract In the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case. We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a hig…