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Wheat bran and pectin (100 g/kg) were added to a basal diet and fed to rats. An in vifvo dialysis technique was used to measure the distribution of caecal and faecal water between the bound, i.e. that held by bacteria and undigested macromolecules, and free water. Bran increased wet (67 %) and dry (74 %) faecal weight. Pectin increased wet faecal weight (59 %), but did not influence dry weight. In faeces both bran and pectin increased the amount of total and bound water, but only pectin increased total and bound water when expressed on a dry weight basis. Caecal wet (90 %) and dry (67 %) weights increased with pectin but not with bran. Bran did not change total water but increased bound water whereas pectin increased both. This suggests that water contributed more to the increase in stool bulk in the pectinsupplemented animals due to free and bound water associated with both increased numbers of bacteria and residual pectin. Pectin altered the distribution of water in faeces. Bran has no effect on water distribution and is only partly fermented. The residual water-holding capacity leads to an increased wet and dry stool output.

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In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.