Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che

Finding weakly reversible realizations of chemical reaction networks using optimization

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph theory and important former results on the dense realizations of CRNs. The proposed method is also capable of determining if no dynamically equivalent weakly reversible structure exists for a given reaction network with a previously fixed complex set.Comment: 18 pages, 9 figure

Decision-theoretical formulation of the calibration problem

The choice of calibration policy is of basic importance in analytical chemistry. A prototype of the practical calibration problem is formulated as a mathematical task and a Bayesian solution of the resulting decision problem is presented. The optimum feedback calibration policy can then be found by dynamic programming. The underlying parameter estimation and filtering are solved by updating relevant conditional distributions. In this way: the necessary information is specified (for instance, the need for knowledge of the probability distribution of unknown samples is clearly recognized as the conceptually unavoidable informational source); the relationship of the information gained from a calibration experiment to the ultimate goal of calibration, i.e., to the estimation of unknown samples, is explained; an ideal solution is given which can serve for comparing various ways of calibration; and a consistent and conceptually simple guideline is given for using decision theory when solving problems of analytical chemistry containing uncertain data. The abstract formulation is systematically illustrated by an example taken from gas chromatography

Towards properly controlled analytical measurement methods

It is of great practical importance to develop simple methods for the automatic detection ofthe controlled state of the analytical method being applied. The key point is to find quantities that greatly affect the quality of the analytical results and that can be easily estimated during the measurement process from the measured data. The signal-to-noise ratio has proved to be such a quantity in gas chromatographic methods. The statistical properties of the estimation of the signal-to-noise ratio from gas chromatographic data have been investigated. The suggested practical method for estimating the signal-to-noise ratio proved to be biased from a mathematical statistical point of view, but the bias is usually not greater than 10%. It has been shown by practical examples that the signal-to-noise ratio affects the quality of the analytical results and it is easy to estimate its value from practical data