Newer developments on self-modeling curve resolution implementing equality and unimodality constraints
Newer developments on self-modeling curve resolution implementing equality and unimodality constraints
复制标题
DOI：
10.1016/j.aca.2014.03.019
复制
发表时间：
2014-05-27
影响因子：
6.2
通讯作者：
Rajko, Robert
中科院分区：
文献类型：
--
作者：
Beyramysoltan, Samira;Abdollahi, Hamid;Rajko, Robert
解析性自建模曲线解析（SMCR）方法仅使用非负约束将数据集解析为一系列可行解。Lawton-Sylvestre方法是第一个分析双组分系统的直接方法。将其推广为确定三组分系统可行区域的Borgen图。考虑曲线分解方法似乎需要一个几何的观点，因为复杂的（仅仅是代数的）概念导致对博尔根工作的一般研究停滞了20年。Rajko和Istvan修订并阐明了SMCR方法中现有理论的原理，随后引入了计算几何工具，用于开发在三组分系统中绘制Borgen图的算法。这些发展是理论上的发明，公式并不总是能够以接近的形式或正则的形式给出，特别是对于几何描述，这就是为什么应该开发出一些算法，甚至为理论推导和确定提供算法。在本研究中，分析SMCR方法进行了修订，并使用简单的概念进行了描述。给出了一种发育型Borgen图的绘制算法。此外，在文献中首次成功地在Lawton-Sylvestre方法中实现了等式和单模约束。为此，提出了一种新的最先进的程序来对Borgen地块施加平等约束。采用新的分析曲线解析方法对两组分和三组分HPLC-DAD数据集进行了模拟和分析。根据得到的抽象空间给出了详细的描述和解释。(C) 2014 Elsevier B.V.版权所有
Analytical self-modeling curve resolution (SMCR) methods resolve data sets to a range of feasible solutions using only non-negative constraints. The Lawton-Sylvestre method was the first direct method to analyze a two-component system. It was generalized as a Borgen plot for determining the feasible regions in three-component systems. It seems that a geometrical view is required for considering curve resolution methods, because the complicated (only algebraic) conceptions caused a stop in the general study of Borgen's work for 20 years. Rajko and Istvan revised and elucidated the principles of existing theory in SMCR methods and subsequently introduced computational geometry tools for developing an algorithm to draw Borgen plots in three-component systems. These developments are theoretical inventions and the formulations are not always able to be given in close form or regularized formalism, especially for geometric descriptions, that is why several algorithms should have been developed and provided for even the theoretical deductions and determinations. In this study, analytical SMCR methods are revised and described using simple concepts. The details of a drawing algorithm for a developmental type of Borgen plot are given. Additionally, for the first time in the literature, equality and unimodality constraints are successfully implemented in the Lawton-Sylvestre method. To this end, a new state-of-the-art procedure is proposed to impose equality constraint in Borgen plots. Two- and three-component HPLC-DAD data set were simulated and analyzed by the new analytical curve resolution methods with and without additional constraints. Detailed descriptions and explanations are given based on the obtained abstract spaces. (C) 2014 Elsevier B.V. All rights reserved.