Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Assessing bee species richness in two Mediterranean communities: importance of habitat type and sampling techniques

The decline of bees has raised concerns regarding their conservation and the maintenance of ecosystem services they provide to bee-pollinated wild flowers and crops. Although the Mediterranean region is a hotspot for bee species richness, their status remains poorly studied. There is an urgent need for cost-effective, reliable, and unbiased sampling methods that give good bee species richness estimates. This study aims: (a) to assess bee species richness in two common Mediterranean habitat types: semi-natural scrub (phrygana) and managed olive groves; (b) to compare species richness in those systems to that of other biogeographic regions, and (c) to assess whether six different sampling methods (pan traps, variable and standardized transect walks, observation plots and trap nests), previously tested in other European biogeographic regions, are suitable in Mediterranean communities. Eight study sites, four per habitat type, were selected on the island of Lesvos, Greece. The species richness observed was high compared to other habitat types worldwide for which comparable data exist. Pan traps collected the highest proportion of the total bee species richness across all methods at the scale of a study site. Variable and standardized transect walks detected the highest total richness over all eight study sites. Trap nests and observation plots detected only a limited fraction of the bee species richness. To assess the total bee species richness in bee diversity hotspots, such as the studied habitats, we suggest a combination of transect walks conducted by trained bee collectors and pan trap sampling

Optimisation of the extraction and processing conditions of chamomile (Matricaria chamomilla L.) for incorporation into a beverage

The total phenols, apigenin 7-glucoside, turbidity and colour of extracts from dried chamomile flowers were studied with a view to develop chamomile extracts with potential anti-inflammatory properties for incorporation into beverages. The extraction of all constituents followed pseudo first-order kinetics. In general, the rate constant (k) increased as the temperature increased from 57 to 100 °C. The turbidity only increased significantly between 90 and 100 °C. Therefore, aqueous chamomile extracts had maximum total phenol concentration and minimum turbidity when extracted at 90 °C for 20 min. The effect of drying conditions on chamomile extracted using these conditions was determined. A significant reduction in phenol concentration, from 19.7 ± 0.5 mg/g GAE in fresh chamomile to 13 ± 1 mg/g GAE, was found only in the plant material oven-dried at 80 °C (p ⩽ 0.05). The biggest colour change was between fresh chamomile and that oven-dried at 80 °C, followed by samples air-dried. There was no significant difference in colour of material freeze-dried and oven-dried at 40 °C.

The study of chiral adsorption systems using synchrotron- based structural and spectroscopic techniques: stereospecific adsorption of serine on Au-modified chiral Cu{531} surfaces

We apply modern synchrotron-based structural techniques to the study of serine adsorbed on the pure andAumodified intrinsically chiral Cu{531} surface. XPS and NEXAFS data in combination with DFT show that on the pure surface both enantiomers adsorb in l4 geometries (with de-protonated b-OH groups) at low coverage and in l3 geometries at saturation coverage. Significantly larger enantiomeric differences are seen for the l4 geometries, which involve substrate bonds of three side groups of the chiral center, i.e. a three-point interaction. The l3 adsorption geometry, where only the carboxylate and amino groups form substrate bonds, leads to smaller but still significant enantiomeric differences, both in geometry and the decomposition behavior. When Cu{531} is modified by the deposition of 1 and 2ML Au the orientations of serine at saturation coverage are significantly different from those on the clean surface. In all cases, however, a l3 bond coordination is found at saturation involving different numbers of Au atoms, which leads to relatively small enantiomeric differences.

Complexation of lanthanides, actinides and transition metal cations with a 6-(1,2,4-triazin-3-yl)-2,2′:6′,2′′-terpyridine ligand: implications for actinide(III)/lanthanide(III) partitioning

The quadridentate N-heterocyclic ligand 6-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin- 3-yl)-2,2′ : 6′,2′′-terpyridine (CyMe4-hemi-BTBP) has been synthesized and its interactions with Am(III),U(VI), Ln(III) and some transition metal cations have been evaluated by X-ray crystallographic analysis, Am(III)/Eu(III) solvent extraction experiments, UVabsorption spectrophotometry, NMR studies and ESI-MS. Structures of 1 : 1 complexes with Eu(III), Ce(III) and the linear uranyl (UO2 2+) ion were obtained by X-ray crystallographic analysis, and they showed similar coordination behavior to related BTBP complexes. In methanol, the stability constants of the Ln(III) complexes are slightly lower than those of the analogous quadridentate bis-triazine BTBP ligands, while the stability constant for the Yb(III)complex is higher. 1H NMR titrations and ESI-MS with lanthanide nitrates showed that the ligand forms only 1 : 1 complexes with Eu(III), Ce(III) and Yb(III), while both 1 : 1 and 1 : 2 complexes were formed with La(III) and Y(III) in acetonitrile. A mixture of isomeric chiral 2 : 2 helical complexes was formed with Cu(I), with a slight preference (1.4 : 1) for a single directional isomer. In contrast, a 1 : 1 complex was observed with the larger Ag(I) ion. The ligand was unable to extract Am(III) or Eu(III) from nitric acid solutions into 1-octanol, except in the presence of a synergist at low acidity. The results show that the presence of two outer 1,2,4-triazine rings is required for the efficient extraction and separation of An(III)from Ln(III) by quadridentate N-donor ligands.

Urban retrofitting: identifying disruptive and sustaining technologies using performative and foresight techniques

Cities, which are now inhabited by a majority of the world's population, are not only an important source of global environmental and resource depletion problems, but can also act as important centres of technological innovation and social learning in the continuing quest for a low carbon future. Planning and managing large-scale transitions in cities to deal with these pressures require an understanding of urban retrofitting at city scale. In this context performative techniques (such as backcasting and roadmapping) can provide valuable tools for helping cities develop a strategic view of the future. However, it is also important to identify ‘disruptive’ and ‘sustaining’ technologies which may contribute to city-based sustainability transitions. This paper presents research findings from the EPSRC Retrofit 2050 project, and explores the relationship between technology roadmaps and transition theory literature, highlighting the research gaps at urban/city level. The paper develops a research methodology to describe the development of three guiding visions for city-regional retrofit futures, and identifies key sustaining and disruptive technologies at city scale within these visions using foresight (horizon scanning) techniques. The implications of the research for city-based transition studies and related methodologies are discussed.

Towards pain-free diagnosis of skin diseases through multiplexed microneedles: biomarker extraction and detection using a highly sensitive blotting method

Immunodiagnostic microneedles provide a novel way to extract protein biomarkers from the skin in a minimally invasive manner for analysis in vitro. The technology could overcome challenges in biomarker analysis specifically in solid tissue, which currently often involves invasive biopsies. This study describes the development of a multiplex immunodiagnostic device incorporating mechanisms to detect multiple antigens simultaneously, as well as internal assay controls for result validation. A novel detection method is also proposed. It enables signal detection specifically at microneedle tips and therefore may aid the construction of depth profiles of skin biomarkers. The detection method can be coupled with computerised densitometry for signal quantitation. The antigen specificity, sensitivity and functional stability of the device were assessed against a number of model biomarkers. Detection and analysis of endogenous antigens (interleukins 1α and 6) from the skin using the device was demonstrated. The results were verified using conventional enzyme-linked immunosorbent assays. The detection limit of the microneedle device, at ≤10 pg/mL, was at least comparable to conventional plate-based solid-phase enzyme immunoassays.

Extraction behavior of the synergistic system 2,6-bis-(benzoxazolyl)-4-dodecyloxylpyridine and 2-bromodecanoic acid using Am and Eu as radioactive tracers

In this study, the extraction properties of a synergistic system consisting of 2,6-bis-(benzoxazolyl)-4-dodecyloxylpyridine (BODO) and 2-bromodecanoic acid (HA) in tert-butyl benzene (TBB) have been investigated as a function of ionic strength by varying the nitrate ion and perchlorate ion concentrations. The influence of the hydrogen ion concentration has also been investigated. Distribution ratios between 0.03-12 and 0.003-0.8 have been found for Am(III) and Eu(HI), respectively, but there were no attempts to maximize these values. It has been shown that the distribution ratios decrease with increasing amounts of ClO4-, NO3-, and H+. The mechanisms, however, by which the decrease occurs, are different. In the case of increasing perchlorate ion concentration, the decrease in extraction is linear in a log-log plot of the distribution ratio vs. the ionic strength, while in the nitrate case the complexation between nitrate and Am or Eu increases at high nitrate ion concentrations and thereby decreases the distribution ratio in a non-linearway. The decrease in extraction could be caused by changes in activity coefficients that can be explained with specific ion interaction theory (SIT); shielding of the metal ions, and by nitrate complexation with Am and Eu as competing mechanism at high ionic strengths. The separation factor between Am and Eu reaches a maximum at similar to1 M nitrate ion concentration. Thereafter the values decrease with increasing nitrate ion concentrations.

QSAR studies of multidentate nitrogen ligands used in lanthanide and actinide extraction processes

Quantitative structure activity relationships (QSARs) have been developed to optimise the choice of nitrogen heterocyclic molecules that can be used to separate the minor actinides such as americium(III) from europium(III) in the aqueous PUREX raffinate of nuclear waste. Experimental data on distribution coefficients and separation factors (SFs) for 47 such ligands have been obtained and show SF values ranging from 0.61 to 100. The ligands were divided into a training set of 36 molecules to develop the QSAR and a test set of 11 molecules to validate the QSAR. Over 1500 molecular descriptors were calculated for each heterocycle and the Genetic Algorithm was used to select the most appropriate for use in multiple regression equations. Equations were developed fitting the separation factors to 6-8 molecular descriptors which gave r(2) values of >0.8 for the training set and values of >0.7 for the test set, thus showing good predictive quality. The descriptors used in the equations were primarily electronic and steric. These equations can be used to predict the separation factors of nitrogen heterocycles not yet synthesised and/or tested and hence obtain the most efficient ligands for lanthanide and actinide separation. (C) 2003 Elsevier B.V. All rights reserved.

An investigation into the extraction of americium(III), lanthanides and D-block metals by 6,6 '-bis-(5,6-dipentyl-[1,2,4]triazin-3-yl)-[2,2 ']bipyridinyl(C-5-BTBP)

The tetradentate ligand (C-5-BTBP) was able to extract americium(III) selectively from nitric acid. In octanol/kerosene the distribution ratios suggest that stripping will be possible. C-5-BTBP has unusual properties and potentially offers a means of separating metals, which otherwise are difficult to separate. For example C-5-BTBP has the potential to separate paliadium(II) from a mixture containing rhodium(III) and ruthenium(H) nitrosyl. In addition, C-5-BTBP has the potential to remove traces of cadmium from effluent or from solutions of other metals contaminated with cadmium. C-5-BTBP has potential as a reagent for the separation of americium(III) from solutions contaminated with iron(III) and nickel(II), hence offering a means of concentrating americium(III) for analytical purposes from nitric acid solutions containing high concentrations of iron(III) or nickel(II).

6,6 '-bis (5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-benzo[1,2,4]triazin-3-yl) [2,2 ']bipyridine, an effective extracting agent for the separation of americium(III) and curium(III) from the lanthanides

The extraction of americium(III), curium(III), and the lanthanides(III) from nitric acid by 6,6'- bis (5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-benzo[1,2,4]triazin-3-yl)-[2,2'] bipyridine (CyMe4-BTBP) has been studied. Since the extraction kinetics were slow, N,N'-dimethyl-N,N'-dioctyl-2-(2-hexyloxy-ethyl)malonamide (DMDOHEMA) was added as a phase transfer reagent. With a mixture of 0.01 M CyMe4-BTBP + 0.25 M DMDOHEMA in n -octanol, extraction equilibrium was reached within 5 min of mixing. At a nitric acid concentration of 1 M, an americium(III) distribution ratio of approx. 10 was achieved. Americium(III)/lanthanide(III) separation factors between 50 (dysprosium) and 1500 (lanthanum) were obtained. Whereas americium(III) and curium(III) were extracted as disolvates, the stoichiometries of the lanthanide(III) complexes were not identified unambiguously, owing to the presence of DMDOHEMA. In the absence of DMDOHEMA, both americium(III) and europium(III) were extracted as disolvates. Back-extraction with 0.1 M nitric acid was thermodynamically possible but rather slow. Using a buffered glycolate solution of pH=4, an americium(III) distribution ratio of 0.01 was obtained within 5 min of mixing. There was no evidence of degradation of the extractant, for example, the extraction performance of CyMe4-BTBP during hydrolylsis with 1 M nitric acid did not change over a two month contact.

Studies on the parallel synthesis and evaluation of new heterocyclic extractants for the partitioning of minor actinides

Multiple parallel synthesis and evaluation have been combined in order to identify new nitrogen heterocycles for the partitioning of minor actinides(III) such as americium(III) from lanthanides such as europium(Ill). An array of triazine-containing molecules was made using multiple parallel syntheses from diketones and amide hydrazides. An excess of each of the resulting purified reagents was dissolved in 1,1,2,2-tetrachloroethane containing 2-bromodecanoic acid, and equilibrated with an aqueous solution containing the radiotracers Eu-152 and Am-241 in nitric acid ([Eu] + [Am] < 400 nanomol dm(-3)). Gamma counting of the organic and aqueous phases led to the identification of several new reagents for the selective extraction of americium(III). In particular, 6-(2-pyridyl)-2-(5,6-dialkyl-1,2,4-triazaphenyl)pyridines were found to be effective reagents for the separation of americium(III) from europium(III), (SFAm/Eu was ca. 30 in [HNO3] = 0.013 mol/L).

Chromatographic alignment of LC-MS and LC-MS/MS datasets by genetic algorithm feature extraction

Liquid chromatography-mass spectrometry (LC-MS) datasets can be compared or combined following chromatographic alignment. Here we describe a simple solution to the specific problem of aligning one LC-MS dataset and one LC-MS/MS dataset, acquired on separate instruments from an enzymatic digest of a protein mixture, using feature extraction and a genetic algorithm. First, the LC-MS dataset is searched within a few ppm of the calculated theoretical masses of peptides confidently identified by LC-MS/MS. A piecewise linear function is then fitted to these matched peptides using a genetic algorithm with a fitness function that is insensitive to incorrect matches but sufficiently flexible to adapt to the discrete shifts common when comparing LC datasets. We demonstrate the utility of this method by aligning ion trap LC-MS/MS data with accurate LC-MS data from an FTICR mass spectrometer and show how hybrid datasets can improve peptide and protein identification by combining the speed of the ion trap with the mass accuracy of the FTICR, similar to using a hybrid ion trap-FTICR instrument. We also show that the high resolving power of FTICR can improve precision and linear dynamic range in quantitative proteomics. The alignment software, msalign, is freely available as open source.

Volatile flavour profile of goat meat extracted by three widely used techniques

Three procedures for the isolation of volatiles from grilled goat meat were compared: dynamic headspace entrainment on Tenax TA, simultaneous steam distillation-extraction, and solid-phase microextraction. Headspace entrainment on Tenax TA extracted the highest number of Maillard-derived volatile compounds. Two hundred and three volatile components were identified: 159 are reported for the first time in goat meat. Most of the volatiles detected (155) were lipid oxidation products, such as hydrocarbons, aldehydes, alcohols, ketones, carboxylic acids and esters. Forty-eight Maillard-derived compounds were identified. comprising pyrazines, pyrroles, thiophenes, furanthiol derivatives, alkyl and alicyclic sulphides, pyridines, and thiazoles. Some reported character impact compounds of cooked meat, e.g., 12-methyltridecanal, (EE)-2,4-decadienal, methional, and dimethyl trisulphide were identified in the volatile profile of goat meat, together with a series of C-2 to C-5 alkylformylcyclopentenes, which have been reported in cooked chicken, pork, beef and lamb, as being important for the characteristic flavour impression of different animal species. (C) 2009 Published by Elsevier Ltd.