Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Topical delivery of a naproxen-dithranol co-drug: in vitro skin penetration, permeation, and staining

Purpose This work probed the topical delivery and skin-staining properties of a novel co-drug, naproxyl-dithranol (Nap-DTH), which comprises anti-inflammatory (naproxen) and anti-proliferative (dithranol) moieties. Method Freshly excised, full-thickness porcine ear skin was dosed with saturated solutions of the compounds. After 24 h, the skin was recovered and used to prepare comparative depth profiles by the tape-stripping technique and to examine the extent of skin staining. Results Depth profiles showed that Nap-DTH led to a 5-fold increase in drug retention in the skin compared to dithranol. The application of Nap-DTH also demonstrated improved stability, resulting in lower levels of dithranol degradation products in the skin. Furthermore, significantly less naproxen from hydrolysed Nap-DTH permeated into the receptor phase compared to naproxen when applied alone (0.08 ± 0.03 nmol cm-² and 180 ± 60 nmol cm-², respectively). Moreover, the reduced staining of the skin was very apparent for Nap-DTH compared to dithranol. Conclusions Topical delivery of Nap-DTH not only improves the delivery of naproxen and dithranol, but also reduces unwanted effects of the parent moieties, in particular the skin staining, which is a major issue concerning the use of dithranol.

Heat-shock response in Arabidopsis thaliana explored by multiplexed quantitative proteomics using differential metabolic labeling

We have developed a general method for multiplexed quantitative proteomics using differential metabolic stable isotope labeling and mass spectrometry. The method was successfully used to study the dynamics of heat-shock response in Arabidopsis thaliana. A number of known heat-shock proteins were confirmed, and some proteins not previously associated with heat shock were discovered. The method is applicable in stable isotope labeling and allows for high degrees of multiplexing.

An optimized reverse-phase high performance liquid chromatographic method for evaluating percutaneous absorption of glucosamine hydrochloride

A relatively simple, selective, precise and accurate high performance liquid chromatography (HPLC) method based on a reaction of phenylisothiocyanate (PITC) with glucosamine (GL) in alkaline media was developed and validated to determine glucosamine hydrochloride permeating through human skin in vitro. It is usually problematic to develop an accurate assay for chemicals traversing skin because the excellent barrier properties of the tissue ensure that only low amounts of the material pass through the membrane and skin components may leach out of the tissue to interfere with the analysis. In addition, in the case of glucosamine hydrochloride, chemical instability adds further complexity to assay development. The assay, utilising the PITC-GL reaction was refined by optimizing the reaction temperature, reaction time and PITC concentration. The reaction produces a phenylthiocarbarnyl-glucosamine (PTC-GL) adduct which was separated on a reverse-phase (RP) column packed with 5 mu m ODS (C-18) Hypersil particles using a diode array detector (DAD) at 245 nm. The mobile phase was methanol-water-glacial acetic acid (10:89.96:0.04 v/v/v, pH 3.5) delivered to the column at 1 ml min(-1) and the column temperature was maintained at 30 degrees C Using a saturated aqueous solution of glucosamine hydrochloride, in vitro permeation studies were performed at 32 +/- 1 degrees C over 48 h using human epidermal membranes prepared by a heat separation method and mounted in Franz-type diffusion cells with a diffusional area 2.15 +/- 0.1 cm(2). The optimum derivatisation reaction conditions for reaction temperature, reaction time and PITC concentration were found to be 80 degrees C, 30 min and 1 % v/v, respectively. PTC-Gal and GL adducts eluted at 8.9 and 9.7 min, respectively. The detector response was found to be linear in the concentration range 0-1000 mu g ml(-1). The assay was robust with intra- and inter-day precisions (described as a percentage of relative standard deviation, %R.S.D.) < 12. Intra- and inter-day accuracy (as a percentage of the relative error, %RE) was <=-5.60 and <=-8.00, respectively. Using this assay, it was found that GL-HCI permeates through human skin with a flux 1.497 +/- 0.42 mu g cm(-2) h(-1), a permeability coefficient of 5.66 +/- 1.6 x 10(-6) cm h(-1) and with a lag time of 10.9 +/- 4.6 h. (c) 2005 Elsevier B.V. All rights reserved.

Permeation of bioactive constituents from Arnica montana preparations through human skin in-vitro

This study investigated and characterised transdermal permeation of bioactive agents from a topically applied Arnica montana tincture. Permeation experiments conducted over 48 h used polyclimethylsiloxane (silastic) and human epidermal membranes mounted in Franz-type diffusion cells with a methanol-water (50:50 v/v) receptor fluid. A commercially available tincture of A. montana L. derived from dried Spanish flower heads was a donor solution. Further donor solutions prepared from this stock tincture concentrated the tincture constituents 1, 2 and 10 fold and its sesquiterpene lactones 10 fold. Permeants were assayed using a high-performance liquid chromatography method. Five components permeated through silastic membranes providing peaks with relative retention factors to an internal standard (santonin) of 0.28, 1.18, 1.45, 1.98 and 2.76, respectively. No permeant was detected within 12 h of applying the Arnica tincture onto human epidermal membranes. However, after 12 h, the first two of these components were detected. These were,shown by Zimmermann reagent reaction to be sesquiterpene lactones and liquid chromatography/diode array detection/mass spectrometry indicated that these two permeants were 11,13-dihydrohelenalin (DH) analogues (methacrylate and tiglate esters). The same two components were also detected within 3 h of topical application of the 10-fold concentrated tincture and the concentrated sesquiterpene lactone extract.

Multiplexed quantitative proteomics using differential metabolic 15N-labeling

There are several advantages of using metabolic labeling in quantitative proteomics. The early pooling of samples compared to post-labeling methods eliminates errors from different sample processing, protein extraction and enzymatic digestion. Metabolic labeling is also highly efficient and relatively inexpensive compared to commercial labeling reagents. However, methods for multiplexed quantitation in the MS-domain (or ‘non-isobaric’ methods), suffer from signal dilution at higher degrees of multiplexing, as the MS/MS signal for peptide identification is lower given the same amount of peptide loaded onto the column or injected into the mass spectrometer. This may partly be overcome by mixing the samples at non-uniform ratios, for instance by increasing the fraction of unlabeled proteins. We have developed an algorithm for arbitrary degrees of nonisobaric multiplexing for relative protein abundance measurements. We have used metabolic labeling with different levels of 15N, but the algorithm is in principle applicable to any isotope or combination of isotopes. Ion trap mass spectrometers are fast and suitable for LC-MS/MS and peptide identification. However, they cannot resolve overlapping isotopic envelopes from different peptides, which makes them less suitable for MS-based quantitation. Fourier-transform ion cyclotron resonance (FTICR) mass spectrometry is less suitable for LC-MS/MS, but provides the resolving power required to resolve overlapping isotopic envelopes. We therefore combined ion trap LC-MS/MS for peptide identification with FTICR LC-MS for quantitation using chromatographic alignment. We applied the method in a heat shock study in a plant model system (A. thaliana) and compared the results with gene expression data from similar experiments in literature.

Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Simple solution for a complex problem: Proanthocyanidins, galloyl glucoses and ellagitannins fit on a single calibration curve in high performance-gel permeation chromatography

This study was undertaken to explore gel permeation chromatography (GPC) for estimating molecular weights of proanthocyanidin fractions isolated from sainfoin (Onobrychis viciifolia). The results were compared with data obtained by thiolytic degradation of the same fractions. Polystyrene, polyethylene glycol and polymethyl methacrylate standards were not suitable for estimating the molecular weights of underivatized proanthocyanidins. Therefore, a novel HPLC-GPC method was developed based on two serially connected PolarGel-L columns using DMF that contained 5% water, 1% acetic acid and 0.15 M LiBr at 0.7 ml/min and 50 degrees C. This yielded a single calibration curve for galloyl glucoses (trigalloyl glucose, pentagalloyl glucose), ellagitannins (pedunculagin, vescalagin, punicalagin, oenothein B, gemin A), proanthocyanidins (procyanidin B2, cinnamtannin B1), and several other polyphenols (catechin, epicatechin gallate, epicallocatechin gallate, amentoflavone). These GPC predicted molecular weights represented a considerable advance over previously reported HPLC-GPC methods for underivatized proanthocyanidins. (C) 2011 Elsevier B.V. All rights reserved.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

A genome-wide test of the differential susceptibility hypothesis reveals a genetic predictor of differential response to psychological treatments for child anxiety disorders

Background: The differential susceptibly hypothesis suggests that certain genetic variants moderate the effects of both negative and positive environments on mental health and may therefore be important predictors of response to psychological treatments. Nevertheless, the identification of such variants has so far been limited to preselected candidate genes. In this study we extended the differential susceptibility hypothesis from a candidate gene to a genome-wide approach to test whether a polygenic score of environmental sensitivity predicted response to Cognitive Behavioural Therapy (CBT) in children with anxiety disorders. Methods: We identified variants associated with environmental sensitivity using a novel method in which within-pair variability in emotional problems in 1026 monozygotic (MZ) twin pairs was examined as a function of the pairs’ genotype. We created a polygenic score of environmental sensitivity based on the whole-genome findings and tested the score as a moderator of parenting on emotional problems in 1,406 children and response to individual, group and brief parent-led CBT in 973 children with anxiety disorders. Results: The polygenic score significantly moderated the effects of parenting on emotional problems and the effects of treatment. Individuals with a high score responded significantly better to individual CBT than group CBT or brief parent-led CBT (remission rates: 70.9%, 55.5% and 41.6% respectively). Conclusions: Pending successful replication, our results should be considered exploratory. Nevertheless, if replicated, they suggest that individuals with the greatest environmental sensitivity may be more likely to develop emotional problems in adverse environments, but also benefit more from the most intensive types of treatment.