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

A structured model based diagnosis method for discrate dynamic process using event sequences

A novel model-based fault detection and diagnosis method is proposed that is based on following event sequences measured in a discrete dynamic process. The model of the nominal and faulty operation modes is given in the form of event sequences, that are decomposed according to the components and sub-components present in the process system. The faulty event sequences are defined using extended procedure HAZID tables. A diagnostic algorithm is also presented that uses a component- wise decomposed form of the event sequences. The operation of the algorithm is illustrated on a simple example of a process system consisting of three similar tanks

Immediate event-aware model and algortithm of a general scheduler

A stochastic scheduling problem is investigated in this work that considers workpieces to be manufactured according to individual recipes containing manufacturing steps performed by workstations as resources. Unexpected stochastic breakdown of a workstation or the faulty termination of a recipe, when a manufacturing failure renders the workpiece out of specifications, forms the set of immediate events. A model and an algorithm are proposed as the basis of a scheduler, which takes into account the possible immediate events, estimates their probability and suggests resource allocations which provide the best overall work-flow even when an immediate event happens. This model includes the possibility of handling alternative resources that can substitute each other in case of an immediate event, like sudden technical failure of a resource. Immediate events are not exactly predictable; however, based on previous experiences, their probabilities can be estimated. Our model uses the properties of the resources (including how they can substitute other types of resources) and the required sequence of them during the workflow (i.e. the recipes). The proposed scheduling algorithm constructs a solution workflow that reacts in the best way (in average) even for an unexpected event. The proposed model and scheduling algorithm is illustrated on two industrial case studies