Active set algorithms for isotonic regression; A unifying framework

In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order where eachw _i is strictly positive and eachy _i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n ²). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship.     

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Dynamics and lithium binding energies of polyelectrolytes based on functionalized poly(para-phenylene terephthalamide)

Polyelectrolyte materials are an interesting class of electrolytes for use in fuel cell and battery applications. Poly(para-phenylene terephthalamide) (PPTA, Kevlar) is a liquid crystalline polymer that, when sulfonated, is a polyelectrolyte that exhibits moderate ion conductivity at elevated temperatures. In this work, quasi-elastic neutron scattering (QENS) experiments were performed to gain insight into the effect of the presence of lithium counterions on the chain dynamics in the material. It was found that the addition of lithium ions decreases the dynamics of the chains. Additionally, the binding of lithium ions to the sulfonic acids groups was investigated by density functional theory (DFT) calculations. It was found that the local surroundings of the sulfonic acid group have very little effect on the lithium-ion binding energy. Binding energies for a variety of different systems were all calculated to be around 150 kcal/mol. The DFT calculations also show the existence of a structure in which a single lithium ion interacts with two sulfonic acid moieties on different chains. The formation of such "electrostatic cross-links" is believed to be the source of the increased tendency to aggregate and the reduced dynamics in the presence of lithium ions.     

High-performance liquid chromatography with on-line coupled UV, mass spectrometric and biochemical detection for identification of acetylcholinesterase inhibitors from natural products

A high-performance liquid chromatography (HPLC) method with on-line coupled ultraviolet (UV), mass spectrometry (MS) and biochemical detection for acetylcholinesterase (AChE) inhibitory activity has been developed. By combining the separation power of HPLC, the high selectivity of biochemical detection, and the ability to provide molecular mass and structural information of MS, AChE inhibitors can be rapidly identified. The biochemical detection was based on a colorimetric method using Ellman's reagent. The detection limit of galanthamine, an AChE inhibitor, in the HPLC-biochemical detection is 0.3 nmol. The three detector lines used, i.e., UV, MS and Vis for the biochemical detection were recorded simultaneously and the delay times of the peaks obtained were found to be consistent. This on-line post-column detection technique can be used for the identification of AChE inhibitors in plant extracts and other complex mixtures such as combinatorial libraries.