55 research outputs found
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
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