The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Interaction of plant growth regulators and reactive oxygen species to regulate petal senescence in wallflowers (Erysimum linifolium)

Background In many species floral senescence is coordinated by ethylene. Endogenous levels rise, and exogenous application accelerates senescence. Furthermore, floral senescence is often associated with increased reactive oxygen species, and is delayed by exogenously applied cytokinin. However, how these processes are linked remains largely unresolved. Erysimum linifolium (wallflower) provides an excellent model for understanding these interactions due to its easily staged flowers and close taxonomic relationship to Arabidopsis. This has facilitated microarray analysis of gene expression during petal senescence and provided gene markers for following the effects of treatments on different regulatory pathways. Results In detached Erysimum linifolium (wallflower) flowers ethylene production peaks in open flowers. Furthermore senescence is delayed by treatments with the ethylene signalling inhibitor silver thiosulphate, and accelerated with ethylene released by 2-chloroethylphosphonic acid. Both treatments with exogenous cytokinin, or 6-methyl purine (which is an inhibitor of cytokinin oxidase), delay petal senescence. However, treatment with cytokinin also increases ethylene biosynthesis. Despite the similar effects on senescence, transcript abundance of gene markers is affected differentially by the treatments. A significant rise in transcript abundance of WLS73 (a putative aminocyclopropanecarboxylate oxidase) was abolished by cytokinin or 6-methyl purine treatments. In contrast, WFSAG12 transcript (a senescence marker) continued to accumulate significantly, albeit at a reduced rate. Silver thiosulphate suppressed the increase in transcript abundance both of WFSAG12 and WLS73. Activity of reactive oxygen species scavenging enzymes changed during senescence. Treatments that increased cytokinin levels, or inhibited ethylene action, reduced accumulation of hydrogen peroxide. Furthermore, although auxin levels rose with senescence, treatments that delayed early senescence did not affect transcript abundance of WPS46, an auxin-induced gene. Conclusions A model for the interaction between cytokinins, ethylene, reactive oxygen species and auxin in the regulation of floral senescence in wallflowers is proposed. The combined increase in ethylene and reduction in cytokinin triggers the initiation of senescence and these two plant growth regulators directly or indirectly result in increased reactive oxygen species levels. A fall in conjugated auxin and/or the total auxin pool eventually triggers abscission.

Effect of growth time on the surface and adhesion properties of Lactobacillus rhamnosus GG

Aims: To investigate the changes in the surface properties of Lactobacillus rhamnosus GG during growth, and relate them with the ability of the Lactobacillus cells to adhere to Caco-2 cells. Methods and Results: Lactobacillus rhamnosus GG was grown in complex medium, and cell samples taken at four time points and freeze dried. Untreated and trypsin treated freeze dried samples were analysed for their composition using SDS-PAGE analysis and Fourier transform infrared spectroscopy (FTIR), hydrophobicity and zeta potential, and for their ability to adhere to Caco-2 cells. The results suggested that in the case of early exponential phase samples (4 and 8 h), the net surface properties, i.e. hydrophobicity and charge, were determined to a large extent by anionic hydrophilic components, whereas in the case of stationary phase samples (13 and 26 h), hydrophobic proteins seemed to play the biggest role. Considerable differences were also observed between the ability of the different samples to adhere to Caco-2 cells; maximum adhesion was observed for the early stationary phase sample (13 h). The results suggested that the adhesion to Caco-2 cells was influenced by both proteins and non-proteinaceous compounds present on the surface of the Lactobacillus cells. Conclusion: The surface properties of Lact. rhamnosus GG changed during growth, which in return affected the ability of the Lactobacillus cells to adhere to Caco-2 cells. Significance and Impact of the Study: The levels of adhesion of Lactobacillus cells to Caco-2 cells were influenced by the growth time and reflected changes on the bacterial surface. This study provides critical information on the physicochemical factors that influence bacterial adhesion to intestinal cells.

High temperature stress and spikelet fertility in rice (Oryza sativa L.)

In future climates, greater heat tolerance at anthesis will be required in rice. The effect of high temperature at anthesis on spikelet fertility was studied on IR64 (lowland indica) and Azucena (upland Japonica) at 29.6 degrees C (control), 33.7 degrees C, and 36.2 degrees C tissue temperatures. The objectives of the study were to: (i) determine the effect of temperature on flowering pattern; (ii) examine the effect of time of day of spikelet anthesis relative to a high temperature episode on spikelet fertility; and (iii) study the interactions between duration of exposure and temperature on spikelet fertility. Plants were grown at 30/24 degrees C day/night temperature in a greenhouse and transferred to growth cabinets for the temperature treatments. Individual spikelets were marked with paint to relate fertility to the time of exposure to different temperatures and durations. In both genotypes the pattern of flowering was similar, and peak anthesis occurred between 10.30 h and 11.30 h at 29.2 degrees C, and about 45 min earlier at 36.2 degrees C. In IR64, high temperature increased the number of spikelets reaching anthesis, whereas in Azucena numbers were reduced. In both genotypes :511 h exposure to >= 33.7 degrees C at anthesis caused sterility. In IR64, there was no interaction between temperature and duration of exposure, and spikelet fertility was reduced by about 7% per degrees C > 29.6 degrees C. In Azucena there was a significant interaction and spikelet fertility was reduced by 2.4% degrees Cd-1 above a threshold of 33 degrees C. Marking individual spikelets is an effective method to phenotype genotypes and lines for heat tolerance that removes any apparent tolerance due to temporal escape.

Permanent changes in growth and physiology of Bacillus subtilis ToC46 after loss of a recombinant plasmid

The physiology and growth of plasmid-bearing Bacillus subtilis carrying plasmid pPFF1, the non-transformed host, and cells after loss of the plasmid (so-called plasmid-cured cells) were investigated. It was found that, following plasmid loss, cells exhibited phenotypic characteristics different from those of the non-transformed host strains. Compared to plasmid-bearing cells and non-transformed host cells, an approximate 25% increase in the maximum specific growth rate and a more rapid increase in total RNA per unit cell mass were observed in plasmid-cured cells. The total enthalpy associated with irreversible denaturation events was determined in whole cells by differential scanning calorimetry. This showed higher enthalpies for plasmid-cured cells compared with the non-transformed host, which suggests increased ribosome numbers. The result from cellular DNA hybridisation suggests that there was no direct evidence of plasmid integration into the host chromosome. (C) 2004 Elsevier Inc. All rights reserved.

Growth and public infrastructure

The paper analyzes a multicountry extension of the Barro model of productive public expenditure. In the presence of positive infrastructural externalities between countries, the provision of infrastructure will be inefficiently low if countries do not coordinate. This provides a role for a supranational body, such as the European Union, to coordinate the policies of the individual governments. It is shown how intervention by a supranational body can raise welfare by internalizing the infrastructural externality. Infrastructural externalities increase the importance of tax policy in the growth process and distribute the benefits of taxation across countries.

Biomass partitioning and growth efficiency in four naturally regenerated forest tree species

Current forest growth models and yield tables are almost exclusively based on data from mature trees, reducing their applicability to young and developing stands. To address this gap, young European beech, sessile oak, Scots pine and Norway spruce trees approximately 0 to 10 years old were destructively sampled in a range of naturally regenerated forest stands in Central Europe. Diameter at base and height were first measured in situ for up to 175 individuals per species. Subsequently, the trees were excavated and dry biomass of foliage, branches, stems and roots was measured. Allometric relations were then used to calculate biomass allocation coefficients (BAC) and growth efficiency (GE) patterns in young trees. We found large differences in BAC and GE between broadleaves and conifers, but also between species within these categories. Both BAC and GE are strongly age-specific in young trees, their rapidly changing values reflecting different growth strategies in the earliest stages of growth. We show that linear relationships describing biomass allocation in older trees are not applicable in young trees. To accurately predict forest biomass and carbon stocks, forest growth models need to include species and age specific parameters of biomass allocation patterns.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

Hypersensitivity and growth adaptation of oestrogen-deprived MCF-7 human breast cancer cells

Background: Efficacy of endocrine therapy is compromised when human breast cancer cells circumvent imposed growth inhibition. The model of long-term oestrogen-deprived MCF-7 human breast cancer cells has suggested the mechanism results from hypersensitivity to low levels of residual oestrogen. Materials and methods: MCF-7 cells were maintained for up to 30 weeks in phenol-red-free medium and charcoal-stripped serum with 10-8 M 17-oestradiol and 10 g/ml insulin (stock 1), 10-8 M 17-oestradiol (stock 2), 10 g/ml insulin (stock 3) or no addition (stock 4). Results: Loss of growth response to oestrogen was observed only in stock 4 cells. Long-term maintenance with insulin in the absence of oestradiol (stock 3) resulted in raised oestrogen receptor alpha (ERlevels (measured by western immunoblotting) and development of hypersensitivity (assayed by oestrogen-responsive reporter gene induction and dose response to oestradiol for proliferation under serum-free conditions), but with no loss of growth response to oestrogen. Conclusion: Hypersensitivity can develop without any growth adaptation and therefore is not a prerequisite for loss of growth response in MCF-7 cells.

Age and firm growth: evidence from three European countries

This article provides new insights into the dependence of firm growth on age along the entire distribution of growth rates, and conditional on survival. Using data from the European firms in a global economy survey, and adopting a quantile regression approach, we uncover evidence for a sample of French, Italian and Spanish manufacturing firms with more than ten employees in the period from 2001 to 2008. We find that: (1) young firms grow faster than old firms, especially in the highest growth quantiles; (2) young firms face the same probability of declining as their older counterparts; (3) results are robust to the inclusion of other firms’ characteristics such as labor productivity, capital intensity and the financial structure; (4) high growth is associated with younger chief executive officers and other attributes that capture the attitude of the firm toward growth and change. The effect of age on firm growth is rather similar across countries.

Statistical characterisation of the growth and spatial scales of the substorm onset arc

We present the first multi-event study of the spatial and temporal structuring of the aurora to provide statistical evidence of the near-Earth plasma instability which causes the substorm onset arc. Using data from ground-based auroral imagers, we study repeatable signatures of along-arc auroral beads, which are thought to represent the ionospheric projection of magnetospheric instability in the near-Earth plasma sheet. We show that the growth and spatial scales of these wave-like fluctuations are similar across multiple events, indicating that each sudden auroral brightening has a common explanation. We find statistically that growth rates for auroral beads peak at low wavenumber with the most unstable spatial scales mapping to an azimuthal wavelength λ≈1700 − 2500 km in the equatorial magnetosphere at around 9-12 RE. We compare growth rates and spatial scales with a range of theoretical predictions of magnetotail instabilities, including the cross-field current instability and the shear-flow ballooning instability. We conclude that, although the cross-field current instability can generate similar magnitude of growth rates, the range of unstable wavenumbers indicates that the shear-flow ballooning instability is the most likely explanation for our observations.

The effect of simulated flooding post-anthesis on pre-harvest sprouting and subsequent seed longevity in contrasting rice cultivars

Unpredictable flooding is a major constraint to rice production. It can occur at any growth stage. The effect of simulated flooding post-anthesis on yield and subsequent seed quality of pot-grown rice (Oryza sativa L.) plants was investigated in glasshouses and controlled-environment growth cabinets. Submergence post-anthesis (9-40 DAA) for 3 or 5 days reduced seed weight of japonica rice cv. Gleva, with considerable pre-harvest sprouting (up to 53%). The latter was greater the later in seed development and maturation that flooding occurred. Sprouted seed had poor ability to survive desiccation or germinate normally upon rehydration, whereas the effects of flooding on the subsequent air-dry seed storage longevity (p50) of the non-sprouted seed fraction was negligible. The indica rice cvs IR64 and IR64Sub1 (introgression of submergence tolerance gene Submergence1A-1) were both far more tolerant to flooding post-anthesis than cv. Gleva: four days’ submergence of these two near-isogenic cultivars at 10-40 DAA resulted less than 1% sprouted seeds. The presence of the Sub1A-1 allele in cv. IR64Sub1 was verified by gel electrophoresis and DNA sequencing. It had no harmful effect on loss in seed viability during storage compared with IR64 in both control and flooded environments. Moreover, the germinability and changes in dormancy during seed development and maturation were very similar to IR64. The efficiency of using chemical spray to increase seed dormancy was investigated in the pre-harvest sprouting susceptible rice cv. Gleva. Foliar application of molybdenum at 100 mg L-1 reduced sprouted seeds by 15-21% following 4 days’ submergence at 20-30 DAA. Analyses confirmed that the treatment did result in molybdenum uptake by the plants, and also tended to increase seed abscisic acid concentration. The latter was reduced by submergence and declined exponentially during grain ripening. The selection of submergence-tolerant varieties was more successful than application of molybdenum in reducing pre-harvest sprouting.

African easterly wave variability and its relationship to Atlantic tropical cyclone activity

Automatic tracking of vorticity centers in European Centre for Medium-Range Weather Forecasts analyses has been used to develop a 20-yr climatology of African easterly wave activity. The tracking statistics at 600 and 850 mb confirm the complicated easterly wave structures present over the African continent. The rainy zone equatorward of 15 degreesN is dominated by 600-mb activity, and the much drier Saharan region poleward of 15 degreesN is more dominated by 850-mb activity. Over the Atlantic Ocean there is just one storm track with the 600- and 850-mb wave activity collocated. Based on growth/decay and genesis statistics, it appears that the 850-mb waves poleward of 15 degreesN over land generally do not get involved with the equatorward storm track over the ocean. Instead, there appears to be significant development of 850-mb activity at the West African coast in the rainy zone around (10 degreesN, 10 degreesW), which, it is proposed, is associated with latent heat release. Based on the tracking statistics, it has been shown that there is marked interannual variability in African easterly wave (AEW) activity. It is especially marked at the 850-mb level at the West African coast between about 10 degrees and 15 degreesN, where the coefficient of variation is 0.29. For the period between 1985 and 1998, a notable positive correlation is seen between this AEW activity and Atlantic tropical cyclone activity. This correlation is particularly strong for the postreanalysis period between 1994 and 1998. This result suggests that Atlantic tropical cyclone activity may be influenced by the number of AEWs leaving the West African coast, which have significant low-level amplitudes, and not simply by the total number of AEWs.

Record of natural and anthropogenic changes in reef environments (Barbados West Indies) using laser ablation ICP-MS and sclerochronology on coral cores

Coral growth rate can be affected by environmental parameters such as seawater temperature, depth, and light intensity. The natural reef environment is also disturbed by human influences such as anthropogenic pollutants, which in Barbados are released close to the reefs. Here we describe a relatively new method of assessing the history of pollution and explain how these effects have influenced the coral communities off the west coast of Barbados. We evaluate the relative impact of both anthropogenic pollutants and natural stresses. Sclerochronology documents framework and skeletal growth rate and records pollution history (recorded as reduced growth) for a suite of sampled Montastraea annularis coral cores. X-radiography shows annual growth band patterns of the corals extending back over several decades and indicates significantly lower growth rate in polluted sites. Results using laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) on the whole sample (aragonite, organic matter, trapped particulate matter, etc.), have shown contrasting concentrations of the trace elements (Cu, Sn, Zn, and Pb) between corals at different locations and within a single coral. Deepwater corals 7 km apart, record different levels of Pb and Sn, suggesting that a current transported the metal pollution in the water. In addition, the 1995 hurricanes are associated with anomalous values for Sn and Cu from most sites. These are believed to result from dispersion of nearshore polluted water. We compared the concentrations of trace elements in the coral growth of particular years to those in the relevant contemporaneous seawater. Mean values for the concentration factor in the coral, relative to the water, ranged from 10 for Cu and Ni to 2.4 and 0.7 for Cd and Zn, respectively. Although the uncertainties are large (60-80%), the coral record enabled us to demonstrate the possibility of calculating a history of seawater pollution for these elements from the 1940s to 1997. Our values were much higher than those obtained from analysis of carefully cleaned coral aragonite; they demonstrate the incorporation of more contamination including that from particulate material as well as dissolved metals.