The correlation structure of spatial autoregressions

This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.

Optimisation of the aqueous extraction conditions of phenols from meadowsweet (Filipendula ulmaria L.) for incorporation into beverages

Meadowsweet was extracted in water at a range of temperatures (60–100 °C), and the total phenols, tannins, quercetin, salicylic acid content and colour were analysed. The extraction of total phenols followed pseudo first-order kinetics, the rate constant (k) increased from 0.09 ± 0.02 min−1 to 0.44 ± 0.09 min−1, as the temperature increased from 60 to 100 °C. An increase in temperature from 60 to 100 °C increased the concentration of total phenols extracted from 39 ± 2 to 63 ± 3 mg g−1 gallic acid equivalents, although it did not significantly affect the proportion of tannin and non-tannin fractions. The extraction of quercetin and salicyclic acid from meadowsweet also followed pseudo first-order kinetics, the rate constant of both compounds increasing with an increase in temperature up until 90 °C. Therefore, the aqueous extraction of meadowsweet at temperatures at or above 90 °C for 15 min yields extracts high in phenols, which may be added to beverages.

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 last glacial cycle: transient simulations with an AOGCM

A number of transient climate runs simulating the last 120kyr have been carried out using FAMOUS, a fast atmosphere-ocean general circulation model (AOGCM). This is the first time such experiments have been done with a full AOGCM, providing a three-dimensional simulation of both atmosphere and ocean over this period. Our simulation thus includes internally generated temporal variability over periods from days to millennia, and physical, detailed representations of important processes such as clouds and precipitation. Although the model is fast, computational restrictions mean that the rate of change of the forcings has been increased by a factor of 10, making each experiment 12kyr long. Atmospheric greenhouse gases (GHGs), northern hemisphere ice sheets and variations in solar radiation arising from changes in the Earth's orbit are treated as forcing factors, and are applied either separately or combined in different experiments. The long-term temperature changes on Antarctica match well with reconstructions derived from ice-core data, as does variability on timescales longer than 10 kyr. Last Glacial Maximum (LGM) cooling on Greenland is reasonably well simulated, although our simulations, which lack ice-sheet meltwater forcing, do not reproduce the abrupt, millennial scale climate shifts seen in northern hemisphere climate proxies or their slower southern hemisphere counterparts. The spatial pattern of sea surface cooling at the LGM matches proxy reconstructions reasonably well. There is significant anti-correlated variability in the strengths of the Atlantic Meridional Overturning Circulation (AMOC) and the Antarctic Circumpolar Current (ACC) on timescales greater than 10kyr in our experiments. We find that GHG forcing weakens the AMOC and strengthens the ACC, whilst the presence of northern hemisphere ice-sheets strengthens the AMOC and weakens the ACC. The structure of the AMOC at the LGM is found to be sensitive to the details of the ice-sheet reconstruction used. The precessional component of the orbital forcing induces ~20kyr oscillations in the AMOC and ACC, whose amplitude is mediated by changes in the eccentricity of the Earth's orbit. These forcing influences combine, to first order, in a linear fashion to produce the mean climate and ocean variability seen in the run with all forcings.

Thermal and high hydrostatic pressure inactivation of myrosinase from green cabbage: a kinetic study

Myrosinase, a family of enzymes which coexist with glucosinolates in all Brassica vegetables, catalyses the hydrolysis of glucosinolates to yield compounds that can have beneficial effects on human health. In this study, the thermal and pressure inactivation of myrosinase from green cabbage was kinetically investigated. Thermal inactivation started at 35 C and inactivation kinetics was studied in the temperature range 35–55 C. Thermal inactivation of green cabbage myrosinase followed the well known consecutive step model. Pressure inactivation started at 300 MPa, even at 10 C, and the consecutive step model effectively described pressure inactivation in the range 300–450 MPa at 10 C. The combined effects of applying various pressures and temperatures on myrosinase inactivation kinetics were studied in the ranges 35–50 C and, 100–400 MPa. The inactivation followed first-order kinetics at all of the applied combinations. This study demonstrates that myrosinase from green cabbage is highly susceptible to both thermal and high pressure processing. Furthermore, it is also noted that myrosinase stability during processing appears to vary widely between different Brassica species.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

On the numerical integration of a class of singular perturbation problems

A three-point difference scheme recently proposed in Ref. 1 for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to a one-sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.

Large is fast, small is tight: determinants of speed and affinity in subunit capture by a periplasmic chaperone

The chaperone/usher pathway assembles surface virulence organelles of Gram-negative bacteria, consisting of fibers of linearly polymerized protein subunits. Fiber subunits are connected through 'donor strand complementation': each subunit completes the immunoglobulin (Ig)-like fold of the neighboring subunit by donating the seventh β-strand in trans. Whereas the folding of Ig domains is a fast first-order process, folding of Ig modules into the fiber conformation is a slow second-order process. Periplasmic chaperones separate this process in two parts by forming transient complexes with subunits. Interactions between chaperones and subunits are also based on the principle of donor strand complementation. In this study, we have performed mutagenesis of the binding motifs of the Caf1M chaperone and Caf1 capsular subunit from Yersinia pestis and analyzed the effect of the mutations on the structure, stability, and kinetics of Caf1M-Caf1 and Caf1-Caf1 interactions. The results suggest that a large hydrophobic effect combined with extensive main-chain hydrogen bonding enables Caf1M to rapidly bind an early folding intermediate of Caf1 and direct its partial folding. The switch from the Caf1M-Caf1 contact to the less hydrophobic, but considerably tighter and less dynamic Caf1-Caf1 contact occurs via the zip-out-zip-in donor strand exchange pathway with pocket 5 acting as the initiation site. Based on these findings, Caf1M was engineered to bind Caf1 faster, tighter, or both faster and tighter. To our knowledge, this is the first successful attempt to rationally design an assembly chaperone with improved chaperone function.

Statistical decadal predictions for sea surface temperatures: a benchmark for dynamical GCM predictions

Accurate decadal climate predictions could be used to inform adaptation actions to a changing climate. The skill of such predictions from initialised dynamical global climate models (GCMs) may be assessed by comparing with predictions from statistical models which are based solely on historical observations. This paper presents two benchmark statistical models for predicting both the radiatively forced trend and internal variability of annual mean sea surface temperatures (SSTs) on a decadal timescale based on the gridded observation data set HadISST. For both statistical models, the trend related to radiative forcing is modelled using a linear regression of SST time series at each grid box on the time series of equivalent global mean atmospheric CO2 concentration. The residual internal variability is then modelled by (1) a first-order autoregressive model (AR1) and (2) a constructed analogue model (CA). From the verification of 46 retrospective forecasts with start years from 1960 to 2005, the correlation coefficient for anomaly forecasts using trend with AR1 is greater than 0.7 over parts of extra-tropical North Atlantic, the Indian Ocean and western Pacific. This is primarily related to the prediction of the forced trend. More importantly, both CA and AR1 give skillful predictions of the internal variability of SSTs in the subpolar gyre region over the far North Atlantic for lead time of 2 to 5 years, with correlation coefficients greater than 0.5. For the subpolar gyre and parts of the South Atlantic, CA is superior to AR1 for lead time of 6 to 9 years. These statistical forecasts are also compared with ensemble mean retrospective forecasts by DePreSys, an initialised GCM. DePreSys is found to outperform the statistical models over large parts of North Atlantic for lead times of 2 to 5 years and 6 to 9 years, however trend with AR1 is generally superior to DePreSys in the North Atlantic Current region, while trend with CA is superior to DePreSys in parts of South Atlantic for lead time of 6 to 9 years. These findings encourage further development of benchmark statistical decadal prediction models, and methods to combine different predictions.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

On the entrainment assumption in Schatzmann's integral plume model

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumption developed by Schatzmann and adjusted to a set of experimental results requires four constants and an ad hoc hypothesis to eliminate undesirable terms. With this assumption, Schatzmann’s model exhibits numerical instability for certain cases of plumes with small velocity excesses, due to very fast radius growth. The purpose of this paper is to present an alternative entrainment assumption based on a first-order turbulence closure, which only requires two adjustable constants and seems to solve this problem. The asymptotic behaviour of the new formulation is studied and compared to previous ones. The validation tests presented by Schatzmann are repeated and it is found that the new formulation not only eliminates numerical instability but also predicts more plausible growth rates for jets in co-flowing streams.

Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis

Subfossil pollen and plant macrofossil data derived from 14C-dated sediment profiles can provide quantitative information on glacial and interglacial climates. The data allow climate variables related to growing season warmth, winter cold, and plant-available moisture to be reconstructed. Continental-scale reconstructions have been made for the mid-Holocene (MH, around 6 ka) and Last Glacial Maximum (LGM, around 21 ka), allowing comparison with palaeoclimate simulations currently being carried out as part of the fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change. The synthesis of the available MH and LGM climate reconstructions and their uncertainties, obtained using modern analogue, regression and model-inversion techniques, is presented for four temperature variables and two moisture variables. Reconstructions of the same variables based on surface-pollen assemblages are shown to be accurate and unbiased. Reconstructed LGM and MH climate anomaly patterns are coherent, consistent between variables, and robust with respect to the choice of technique. They support a conceptual model of the controls of Late Quaternary climate change whereby the first-order effects of orbital variations and greenhouse forcing on the seasonal cycle of temperature are predictably modified by responses of the atmospheric circulation and surface energy balance.

Functional model for catecholase-like activity: A mechanistic approach with manganese(III) complexes of salen type Schiff base ligands

Three new Mn(III) complexes [MnL1(OOCH)(OH2)] (1), [MnL2(OH2)(2)][Mn2L22(NO2)(3)] (2) and [Mn2L21(NO2)(2)] (3) (where H2L1 = H(2)Me(2)Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene and H2L2 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta-1,6-diene) have been synthesized. X-ray crystal structure analysis reveals that 1 is a mononuclear species whereas 2 contains a mononuclear cationic and a dinuclear nitrite bridged (mu-1 kappa O:2 kappa O') anionic unit. Complex 3 is a phenoxido bridged dimer containing terminally coordinated nitrite. Complexes 1-3 show excellent catecholase-like activity with 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. Kinetic measurements suggest that the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first order kinetics with respect to the catalyst. Formation of bis(mu-oxo)dimanganese(III,III) as an intermediate during the course of reaction is identified from ESI-MS spectra. The characteristic six line EPR spectra of complex 2 in the presence of 3,5-DTBC supports the formation of manganese(II)-semiquinonate as an intermediate species during the catalytic oxidation of 3,5-DTBC.

Synthesis, crystal structure, and catecholase activity of three trinuclear heterometallic NiII2-MnII complexes derived from a salen-type Schiff base ligand

Three new trinuclear heterometallic nickel(II)manganese(II) complexes, [(NiL)2Mn(NCS)2] (1), [(NiL)2Mn(NCO)2] (2), and [{NiL(EtOH)}2Mn(NO2)2]center dot 2EtOH (3), have been synthesized by using [NiL] as the so-called ligand complex [where H2L = N,N'-bis(salicylidene)-1,3-propanediamine] and have been structurally characterized. Crystal structure analyses revealed that complexes 1 and 2 are angular trinuclear species, in which two terminal four-coordinate square planar [NiL] moieties are coordinated to a central MnII through double phenoxido bridges. The MnII is in a six-coordinate distorted octahedral environment that is bonded additionally to two mutually cis nitrogen atoms of terminal thiocyanate (in 1) and cyanate (in 2). In complex 3, in addition to the double phenoxo bridge, the two terminal NiII ions are linked to the central MnII by means of a nitrite bridge (1?N:2?O) that, together with a coordinated ethanol molecule, gives rise to an octahedral environment around the NiII ions and consequently the structure becomes linear. Catecholase activity of these three complexes was examined by using 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. All three complexes mimic catecholase activity and the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first-order kinetics with respect to the catalyst. The EPR spectra of the complexes exhibit characteristic six line spectra, which indicate the presence of high-spin octahedral MnII species in solution state. The ESI-MS positive spectrum of 1 in the presence of 3,5-DTBC has been recorded to investigate possible complexsubstrate intermediates.

On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range.