Quantitative analysis of small pharmaceutical drugs using a high repetition rate laser matrix-assisted laser/desorption ionization source

In this work, a high repetition rate laser matrix-assisted laser desorption/ionization (MALDI) source is studied on a quadrupole-time-of-flight (QqTOF) and a triple quadrupole (QqQ) mass spectrometer for rapid quantification of small pharmaceutical drugs. The high repetition rate laser allows an up to 100-fold higher pulse frequency as compared with regular MALDI lasers, resulting in much larger sample throughput and number of accumulated spectra. This increases the reproducibility of signal intensities considerably, with average values being around 5% relative standard deviation after taking into account the area ratio of the analyte to an internal standard. Experiments were conducted in MS/MS mode to circumvent the large chemical background due to MALDI matrix ions in the low mass range. The dynamic range of calibration curves on the QqTOF mass spectrometer extended over at least two orders of magnitude, whereas on the QqQ it extended over at least three orders of magnitude. Detection limits ranged from 60-400 pg/microL on the QqTOF and from 6-70 pg/microL on the QqQ for a series of benzodiazepines. The benzodiazepine content of commercial pill formulations was quantified, and less than 5% error was obtained between the present method and the manufacturer's certified values. Furthermore, a high sample throughput was achieved with this method, so that a single MALDI spot could be quantitatively scanned in as little as 15 s, and an entire 96-well MALDI plate in 24 min.     

Global optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming

When the follower's optimality conditions are both necessary and sufficient, the nonlinear bilevel program can be solved as a global optimization problem. The complementary slackness condition is usually the complicating constraint in such problems. We show how this constraint can be replaced by an equivalent system of convex and separable quadratic constraints. In this paper, we propose different methods for finding the global minimum of a concave function subject to quadratic separable constraints. The first method is of the branch and bound type, and is based on rectangular partitions to obtain upper and lower bounds. Convergence of the proposed algorithm is also proved. For computational purposes, different procedures that accelerate the convergence of the proposed algorithm are analysed. The second method is based on piecewise linear approximations of the constraint functions. When the constraints are convex, the problem is reduced to global concave minimization subject to linear constraints. In the case of non-convex constraints, we use zero-one integer variables to linearize the constraints. The number of integer variables depends only on the concave parts of the constraint functions.Parts of the present paper were prepared while the second author was visiting Georgia Tech and the University of Florida.     

Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented.     

SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Algorithms with high order convergence speed for blind source extraction

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p>3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p?1.     

Hybrid pricing in a coupled European power market with more wind power

In the European electricity market, the promotion of wind power leads to more network congestion. Zonal pricing (market coupling), which does not take the physical characteristics of transmission into account, is the most commonly used method to relieve network congestion in Europe. However, zonal pricing fails to provide adequate locational price signals regarding scarcity of energy and thus creates a large amount of unscheduled cross-border flows originating from wind-generated power. In this paper, we investigate the effects of applying a hybrid congestion management model, i.e., a nodal pricing model for one country embedded in a zonal pricing system for the rest of the market. We find that, compared to full nodal pricing, hybrid pricing fails to fully utilize all the resources in the network and some wrong price signals might be given. However, hybrid pricing still outperforms zonal pricing. The results from the study cases show that, within the area applying nodal pricing, better price signals are given; the need for re-dispatching is reduced; more congestion rent is collected domestically and the unit cost of power is reduced.     

High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.