In vitro fermentation of a red wine extract by human gut microbiota: changes in microbial groups and formation of phenolic metabolites

An in vitro batch culture fermentation experiment was conducted with fecal inocula from three healthy volunteers in the presence and absence of a red wine extract. Changes in main bacterial groups were determined by FISH during a 48 h fermentation period. The catabolism of main flavonoids (i.e., flavan-3-ols and anthocyanins) and the formation of a wide a range of phenolic microbial metabolites were determined by a targeted UPLC-PAD-ESI-TQ MS method. Statistical analysis revealed that catechol/pyrocatechol, as well as 4-hydroxy-5-(phenyl)-valeric, 3- and 4-hydroxyphenylacetic, phenylacetic, phenylpropionic, and benzoic acids, showed the greatest increases in concentration during fermentation, whereas 5-(3′-hydroxyphenyl)-γ-valerolactone, its open form 4-hydroxy-5-(3′-hydroxyphenyl)-valeric acid, and 3,4-dihydroxyphenylacetic acid represented the largest interindividual variations in the catabolism of red wine polyphenols. Despite these changes, microbial catabolism did not produce significant changes in the main bacterial groups detected, although a slight inhibition of the Clostridium histolyticum group was observed.

Interactions between shallow and deep convection under a finite departure from convective quasi–equilibrium

The present paper presents a simple theory for the transformation of non-precipitating, shallow convection into precipitating, deep convective clouds. In order to make the pertinent point a much idealized system is considered, consisting only of shallow and deep convection without large–scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms, leading to destabilization and stabilization respectively. Consequently, in their own stand–alone modes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling the modes together is the only way to reconcile these undesirable separate tendencies so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy–cycle description as originally formulated by Arakawa and Schubert, and presented herein is suitable for direct implementation into models using a mass–flux parameterization, and would alleviate the current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large–eddy simulations and cloud–resolving modelling.

On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

The potential for community groups to promote sustainable living

In recent times there has been a growing recognition amongst policy-makers of the role for community-based action in contributing to the broader aims of energy policy and climate change. In this paper, we will examine the potential for existing community groups to use their influence and elements of internal cohesion to encourage more widespread understanding and adoption of sustainable lifestyle habits; both amongst their members and within the broader communities of which they are a part. Findings are presented from recent empirical work with a range of well-established community groups for whom environmental issues are not their main priority. A central aspect of the research was to explore both the current status and potential role of groups that may have the capacity to reach and influence a broader sphere of the public than energy/environment specific initiatives of recent times have been able to achieve. Representing a diversity of interests, age groups and functionality, the results suggest that the potential for more effective ‘bottom-up’ engagement on climate change and sustainable living might be given fresh impetus by these types of established community groups and their networks. An assessment of what motivates participation and membership in the groups highlights a series of factors common to all groups and a smaller number that are significant for particular groups individually. It is argued that an appreciation of motivating factors can be useful in understanding more clearly how such groups are able to survive and maintain cohesion over time. The findings also suggest that climate change action means different things for different groups, with the diversity of the groups bringing with it the challenge of making sustainable living relevant to a range of interests and different shared values.

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.

Evidence for insertional codemixing: mixed compounds and French nominal groups in Brussels Dutch

In this paper we analyse mixed compounds, such as legume+winkel ‘vegetable shop, greengrocery’ and winter+paletot ‘winter coat’ which contain a French and a Dutch element, and French nominal groups, such as carte d’identité ‘identity card’, and journal parlé ‘radio news’, which bilingual speakers from Brussels frequently insert into Brussels Dutch utterances. Using Muysken’s (2000) typology of bilingual speech, we claim that the mixed compounds and the nominal groups display the characteristics of insertional code-mixing. In addition, some evidence for the existence of a continuum between borrowing and code-switching can be obtained from these examples. As the multimorphemic units that are inserted into Dutch are neither single words, nor full constituents, their status in the lexicon raises interesting issues for researchers interested in the interface between syntax and the lexicon (see also Backus 2003). We try to argue that nominal groups such as carte d’identité and journal parlé are probably best seen as lexical templates or constructional idioms (Booij, 2002b). The insertion of French constructional idioms in Brussels Dutch represents an innovation in the lexical patterns that are available to speakers of this language, which is highly relevant for theories of language change.

Mutual binding of polymer end-groups by complementary π–π-stacking: a molecular “Roman Handshake”

Self-complementary tweezer-molecules based on a naphthalenediimide core self-assemble into supramolecular dimers through mutual π–π-stacking and hydrogen bonding. The resulting motif is extremely stable in solution (Ka = 105 M−1), and its attachment to one terminal position of a poly(ethylene glycol) chain leads to a doubling of the polymer's apparent molecular weight.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev