Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Evaluating raw ensembles with the continuous ranked probability score

The continuous ranked probability score (CRPS) is a frequently used scoring rule. In contrast with many other scoring rules, the CRPS evaluates cumulative distribution functions. An ensemble of forecasts can easily be converted into a piecewise constant cumulative distribution function with steps at the ensemble members. This renders the CRPS a convenient scoring rule for the evaluation of ‘raw’ ensembles, obviating the need for sophisticated ensemble model output statistics or dressing methods prior to evaluation. In this article, a relation between the CRPS score and the quantile score is established. The evaluation of ‘raw’ ensembles using the CRPS is discussed in this light. It is shown that latent in this evaluation is an interpretation of the ensemble as quantiles but with non-uniform levels. This needs to be taken into account if the ensemble is evaluated further, for example with rank histograms.

In vitro fermentation of grape seed flavan-3-ol fractions by human faecal microbiota: changes in microbial groups and phenolic metabolites

With the aim of investigating the potential of flavan-3-ols to influence the growth of intestinal bacterial groups, we have carried out the in vitro fermentation, with human faecal microbiota, of two purified fractions from grape seed extract (GSE): GSE-M (70% monomers and 28% procyanidins) and GSE-O (21% monomers and 78 % procyanidins). Samples were collected at 0, 5, 10, 24, 30 and 48 h of fermentation for bacterial enumeration by fluorescent in situ hybridization and for analysis of phenolic metabolites. Both GSE-M and GSE-O fractions promoted growth of Lactobacillus/Enterococcus and decrease in the Clostridium histolyticum group during fermentation, although the effects were only statistically significant with GSE-M for Lactobacillus/Enterococcus (at 5 and 10 h of fermentation) and GSE-O for C. histolyticum (at 10 h of fermentation). Main changes in polyphenol catabolism also occurred during the first 10 h of fermentation, however no significant correlation coefficients (P>0.05) were found between changes in microbial populations and precursor flavan-3-ols or microbial metabolites. Together these data suggest that the flavan-3-ol profile of a particular food source could affect the microbiota composition and its catabolic activity, inducing changes that could in turn affect the bioavailability and potential bioactivity of these compounds.

Synergistic effects of mixing cocksfoot and sainfoin on in vitro rumen fermentation: role of condensed tannins

Some bioactive secondary metabolites in forage legumes can cause digestive interactions, so that the rumen fermentation pattern of a mixture of forages can differ from the average values of its components. The objective of this study was to investigate the potential role of condensed tannins (CT) on the synergistic effects between one grass species, cocksfoot, and one CT-containing legume species, sainfoin, on in vitro rumen fermentation characteristics. Cocksfoot and sainfoin in different proportions (in g/kg, 1000:0, 750:250, 500:500, 250:750 and 0:1000) were incubated under anaerobic conditions in culture bottles containing buffered rumen fluid from sheep. Incubations were carried out using artificial saliva with and without polyethylene glycol (PEG), which binds and thus inactivates CT. Rumen fermentation parameters describing the degradation and the fate of the energetic and nitrogenous substrates were measured at 3.5 and 24 h. At the early fermentation stage, when the sainfoin level increased from 0 to 1000 g/kg, the ammonia concentration in the medium quadratically decreased from 3.20 to 0.53 mmol/l in absence of PEG (P<0.01) but not in its presence. This result demonstrates that sainfoin CT decreased the rumen degradation of the proteins in the whole mixture, including the proteins in cocksfoot, rather than just the proteins in sainfoin. Interestingly, the total gas and methane productions were lower in mixtures incubated in absence of PEG than in presence of PEG (P<0.001) while no significant PEG effect was observed on digestibility. At the late fermentation stage, a positive quadratic effect on dry matter digestibility was detected without PEG (P<0.05), indicating a synergistic action of cocksfoot plus sainfoin on plant substrate degradation due to CT. The presence of PEG increased gas production (P<0.001) and NH3-N concentration in the medium (P<0.001). Our results suggest that CT could allow a better utilization of plant substrates in mixtures by the rumen ecosystem by improving the partitioning of degraded substrates toward lower gas losses, and decreasing the protein degradation.

Persistence of anticancer activity in berry extracts after simulated gastrointestinal digestion and colonic fermentation.

Fruit and vegetable consumption is associated at the population level with a protective effect against colorectal cancer. Phenolic compounds, especially abundant in berries, are of interest due to their putative anticancer activity. After consumption, however, phenolic compounds are subject to digestive conditions within the gastrointestinal tract that alter their structures and potentially their function. However, the majority of phenolic compounds are not efficiently absorbed in the small intestine and a substantial portion pass into the colon. We characterized berry extracts (raspberries, strawberries, blackcurrants) produced by in vitro-simulated upper intestinal tract digestion and subsequent fecal fermentation. These extracts and selected individual colonic metabolites were then evaluated for their putative anticancer activities using in vitro models of colorectal cancer, representing the key stages of initiation, promotion and invasion. Over a physiologically-relevant dose range (0-50 µg/ml gallic acid equivalents), the digested and fermented extracts demonstrated significant anti-genotoxic, anti-mutagenic and anti-invasive activity on colonocytes. This work indicates that phenolic compounds from berries undergo considerable structural modifications during their passage through the gastrointestinal tract but their breakdown products and metabolites retain biological activity and can modulate cellular processes associated with colon cancer.

In vitro fermentation of commercial α-gluco-oligosaccharide by faecal microbiota from lean and obese human subjects

The fermentation selectivity of a commercial source of α-gluco-oligosaccharides (BioEcolians; Solabia) was investigated in vitro. Fermentation by faecal bacteria from four lean and four obese healthy adults was determined in anaerobic, pH-controlled faecal batch cultures. Inulin was used as a positive prebiotic control. Samples were obtained at 0, 10, 24 and 36 h for bacterial enumeration by fluorescent in situ hybridisation and SCFA analyses. Gas production during fermentation was investigated in non-pH-controlled batch cultures. α-Gluco-oligosaccharides significantly increased the Bifidobacterium sp. population compared with the control. Other bacterial groups enumerated were unaffected with the exception of an increase in the Bacteroides–Prevotella group and a decrease in Faecalibacterium prausnitzii on both α-gluco-oligosaccharides and inulin compared with baseline. An increase in acetate and propionate was seen on both substrates. The fermentation of α-gluco-oligosaccharides produced less total gas at a more gradual rate of production than inulin. Generally, substrates fermented with the obese microbiota produced similar results to the lean fermentation regarding bacteriology and metabolic activity. No significant difference at baseline (0 h) was detected between the lean and obese individuals in any of the faecal bacterial groups studied.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.