In this article we address the question of how, given information about the reaction fluxes of a system, flux values can be assigned to the elementary modes of that system. Having described a method by which this may be accomplished, we first illustrate its application to a hypothetical, in silico system, and then apply it to fermentation data from Lactobacillus rhamnosus. This reveals substantial changes in the flux values assigned to elementary modes, and thus to the internal metabolism, as the fermentation progresses. This is information that could not, to our knowledge, be obtained by existing methods. The relationship between our technique and the well-known method of Metabolic Flux Analysis is also discussed.

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Abstract. In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation of our algorithm more computationally demanding.Mathematics Subject Classification. 35R30, 31A25.

We have studied the problem of determining part of the boundary of a domain where a potential satisfies the Laplace equation. The potential and its normal derivative have prescribed values on the known part of the boundary that encloses while its normal derivative must vanish on the remaining part. We establish a sufficient condition for the potential to be monotonic along the unknown boundary. This allows us to use the potential to parametrize the boundary. Two methods are presented that solve the problem under this assumption. The first one solves the problem in a closed form and it can be used to define a parameter that will describe the ill-posedness of the problem. The effect of this parameter on the second method presented has been determined for a particular numerical example.