'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

A multidimensional comparison of discourse organization in English and Chinese university students' argumentative writing

Three methodological limitations in English-Chinese contrastive rhetoric research have been identified in previous research, namely: the failure to control for the quality of L1 data; an inference approach to interpreting the relationship between L1 and L2 writing; and a focus on national cultural factors in interpreting rhetorical differences. Addressing these limitations, the current study examined the presence or absence and placement of thesis statement and topic sentences in four sets of argumentative texts produced by three groups of university students. We found that Chinese students tended to favour a direct/deductive approach in their English and Chinese writing, while native English writers typically adopted an indirect/inductive approach. This study argues for a dynamic and ecological interpretation of rhetorical practices in different languages and cultures.

Platelet endothelial cell adhesion molecule-1 inhibits platelet response to thrombin and von Willebrand factor by regulating the internalization of glycoprotein Ib via AKT/glycogen synthase kinase-3/dynamin and integrin αIIbβ3

OBJECTIVE: Platelet endothelial cell adhesion molecule-1 (PECAM-1) regulates platelet response to multiple agonists. How this immunoreceptor tyrosine-based inhibitory motif-containing receptor inhibits G protein-coupled receptor-mediated thrombin-induced activation of platelets is unknown. APPROACH AND RESULTS: Here, we show that the activation of PECAM-1 inhibits fibrinogen binding to integrin αIIbβ3 and P-selectin surface expression in response to thrombin (0.1-3 U/mL) but not thrombin receptor-activating peptides SFLLRN (3×10(-7)-1×10(-5) mol/L) and GYPGQV (3×10(-6)-1×10(-4) mol/L). We hypothesized a role for PECAM-1 in reducing the tethering of thrombin to glycoprotein Ibα (GPIbα) on the platelet surface. We show that PECAM-1 signaling regulates the binding of fluorescein isothiocyanate-labeled thrombin to the platelet surface and reduces the levels of cell surface GPIbα by promoting its internalization, while concomitantly reducing the binding of platelets to von Willebrand factor under flow in vitro. PECAM-1-mediated internalization of GPIbα was reduced in the presence of both EGTA and cytochalasin D or latrunculin, but not either individually, and was reduced in mice in which tyrosines 747 and 759 of the cytoplasmic tail of β3 integrin were mutated to phenylalanine. Furthermore, PECAM-1 cross-linking led to a significant reduction in the phosphorylation of glycogen synthase kinase-3β Ser(9), but interestingly an increase in glycogen synthase kinase-3α pSer(21). PECAM-1-mediated internalization of GPIbα was reduced by inhibitors of dynamin (Dynasore) and glycogen synthase kinase-3 (CHIR99021), an effect that was enhanced in the presence of EGTA. CONCLUSIONS: PECAM-1 mediates internalization of GPIbα in platelets through dual AKT/protein kinase B/glycogen synthase kinase-3/dynamin-dependent and αIIbβ3-dependent mechanisms. These findings expand our understanding of how PECAM-1 regulates nonimmunoreceptor signaling pathways and helps to explains how PECAM-1 regulates thrombosis.

e-Leadership through strategic alignment: an empirical study of small and medium sized enterprises in the digital age

Small and medium sized enterprises (SMEs) play an important role in the European economy. A critical challenge faced by SME leaders, as a consequence of the continuing digital technology revolution, is how to optimally align business strategy with digital technology to fully leverage the potential offered by these technologies in pursuit of longevity and growth. There is a paucity of empirical research examining how e-leadership in SMEs drives successful alignment between business strategy and digital technology fostering longevity and growth. To address this gap, in this paper we develop an empirically derived e-leadership model. Initially we develop a theoretical model of e-leadership drawing on strategic alignment theory. This provides a theoretical foundation on how SMEs can harness digital technology in support of their business strategy enabling sustainable growth. An in-depth empirical study was undertaken interviewing 42 successful European SME leaders to validate, advance and substantiate our theoretically driven model. The outcome of the two stage process – inductive development of a theoretically driven e-leadership model and deductive advancement to develop a complete model through in-depth interviews with successful European SME leaders – is an e-leadership model with specific constructs fostering effective strategic alignment. The resulting diagnostic model enables SME decision makers to exercise effective e-leadership by creating productive alignment between business strategy and digital technology improving longevity and growth prospects.

Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.

Naturally occurring radioactive material (NORM) from a former phosphoric acid processing plant

In recent years there has been an increasing awareness of the radiological impact of non-nuclear industries that extract and/or process ores and minerals containing naturally occurring radioactive material (NORM). These industrial activities may result in significant radioactive contamination of (by-) products, wastes and plant installations. In this study, scale samples were collected from a decommissioned phosphoric acid processing plant. To determine the nature and concentration of NORM retained in pipe-work and associated process plant, four main areas of the site were investigated: (1) the 'Green Acid Plant', where crude acid was concentrated; (2) the green acid storage tanks; (3) the Purified White Acid (PWA) plant, where inorganic impurities were removed; and (4) the solid waste, disposed of on-site as landfill. The scale samples predominantly comprise the following: fluorides (e.g. ralstonite); calcium sulphate (e.g. gypsum); and an assemblage of mixed fluorides and phosphates (e.g. iron fluoride hydrate, calcium phosphate), respectively. The radioactive inventory is dominated by U-238 and its decay chain products, and significant fractionation along the series occurs. Compared to the feedstock ore, elevated concentrations (<= 8.8 Bq/g) of U-238 Were found to be retained in installations where the process stream was rich in fluorides and phosphates. In addition, enriched levels (<= 11 Bq/g) of Ra-226 were found in association with precipitates of calcium sulphate. Water extraction tests indicate that many of the scales and waste contain significantly soluble materials and readily release radioactivity into solution. (c) 2005 Elsevier Ltd. All rights reserved.

Moist singular vectors and the predictability of some high impact European cyclones

The ECMWF full-physics and dry singular vector (SV) packages, using a dry energy norm and a 1-day optimization time, are applied to four high impact European cyclones of recent years that were almost universally badly forecast in the short range. It is shown that these full-physics SVs are much more relevant to severe cyclonic development than those based on dry dynamics plus boundary layer alone. The crucial extra ingredient is the representation of large-scale latent heat release. The severe winter storms all have a long, nearly straight region of high baroclinicity stretching across the Atlantic towards Europe, with a tongue of very high moisture content on its equatorward flank. In each case some of the final-time top SV structures pick out the region of the actual storm. The initial structures were generally located in the mid- to low troposphere. Forecasts based on initial conditions perturbed by moist SVs with opposite signs and various amplitudes show the range of possible 1-day outcomes for reasonable magnitudes of forecast error. In each case one of the perturbation structures gave a forecast very much closer to the actual storm than the control forecast. Deductions are made about the predictability of high-impact extratropical cyclone events. Implications are drawn for the short-range forecast problem and suggestions made for one practicable way to approach short-range ensemble forecasting. Copyright © 2005 Royal Meteorological Society.

Infant feeding choices: experience, self-identity and lifestyle

In England 78% of mothers initiate breastfeeding and in the UK less than 1% exclusively breastfeed until 6 months, despite WHO recommendations to do so. This study investigated women’s infant feeding choices using in-depth interviews with 12 mothers of infants aged 7-18 weeks. Using content analysis, four themes emerged: (1) Information, Knowledge and Decision Making, (2) Physical Capability, (3) Family and Social Influences, (4) Lifestyle, Independence and Self-Identity. Whilst women were aware of the ‘Breast is Best’ message, some expressed distrust in this information if they had not been breastfed themselves. Women felt their own infant feeding choice was influenced by the perceived norm amongst family and friends. Women described how breastfeeding hindered their ability to retain their self-identities beyond motherhood as it limited their independence. Several second-time mothers felt they lacked support from health professionals when breastfeeding their second baby, even if they had previously encountered breastfeeding difficulties. The study indicates that experience of breastfeeding, and belief in the health benefits associated with it are important factors for initiation of breastfeeding, whilst decreased independence and self-identity may influence duration of breastfeeding. Intervention and support schemes should tackle all mothers, not just first-time mothers.

Agonist-dependent internalization of D2 receptors: imaging quantification by confocal microscopy

In positron emission tomography and single photon emission computed tomography studies using D2 dopamine (DA) receptor radiotracers, a decrease in radiotracer binding potential (BP) is usually interpreted in terms of increased competition with synaptic DA. However, some data suggest that this signal may also reflect agonist (DA)-induced increases in D2 receptor (D2R) internalization, a process which would presumably also decrease the population of receptors available for binding to hydrophilic radioligands. To advance interpretation of alterations in D2 radiotracer BP, direct methods of assessment of D2R internalization are required. Here, we describe a confocal microscopy-based approach for the quantification of agonist-dependent receptor internalization. The method relies upon double-labeling of the receptors with antibodies directed against intracellular as well as extracellular epitopes. Following agonist stimulation, DA D2R internalization was quantified by differentiating, in optical cell sections, the signal due to the staining of the extracellular from intracellular epitopes of D2Rs. Receptor internalization was increased in the presence of the D2 agonists DA and bromocriptine, but not the D1 agonist SKF38393. Pretreatment with either the D2 antagonist sulpiride, or inhibitors of internalization (phenylarsine oxide and high molarity sucrose), blocked D2-agonist induced receptor internalization, thus validating this method in vitro. This approach therefore provides a direct and streamlined methodology for investigating the pharmacological and mechanistic aspects of D2R internalization, and should inform the interpretation of results from in vivo receptor imaging studies.

Joint effects of density and a growth inhibitor on the life history and population growth rate of the midge Chironomus riparius

Results of previous laboratory studies suggest that high population density often buffers the effects of chemical stressors that predominately increase mortality. Mortality stressors act to release more resources for the survivors and, therefore, produce less-than-additive effects. By contrast, growth stressors are expected to have opposite results or more-than-additive effects. We investigated the effects of a growth inhibitor (lufenuron) on larval growth and survival of Chironomus riparius and examined its joint effects with density on population growth rate (PGR). Exposure to 60 mu g/kg sediment or greater inhibited larval growth, and exposure to 88 mu g/kg or greater often resulted in mortality before reaching emergence. The effects of lufenuron, however, differed with population density. At 88 mu g/kg, mortalities and, to a lesser extent, reduced fecundity resulted in a reduction in PGR at low density. Conversely, when populations were initiated at high density, PGR was similar to that of controls, because the few survivors reached maturity sooner and started producing offspring earlier. The effect of density as a growth stressor therefore was stronger than the effect of lufenuron, which had effects similar to those of a mortality stressor and produced less-than-additive effects. Longterm studies under field conditions, however, are needed before less-than-additive effects are considered to be the norm.

Mechanisms and function of flower and inflorescence reversion

Flower and inflorescence reversion involve a switch from floral development back to vegetative development, thus rendering flowering a phase in an ongoing growth pattern rather than a terminal act of the meristem. Although it can be considered an unusual event, reversion raises questions about the nature and function of flowering. It is linked to environmental conditions and is most often a response to conditions opposite to those that induce flowering. Research on molecular genetic mechanisms underlying plant development over the last 15 years has pinpointed some of the key genes involved in the transition to flowering and flower development. Such investigations have also uncovered mutations which reduce floral maintenance or alter the balance between vegetative and floral features of the plant. How this information contributes to an understanding of floral reversion is assessed here. One issue that arises is whether floral commitment (defined as the ability to continue flowering when inductive conditions no longer exist) is a developmental switch affecting the whole plant or is a mechanism which assigns autonomy to individual meristems. A related question is whether floral or vegetative development is the underlying default pathway of the plant. This review begins by considering how studies of flowering in Arabidopsis thaliana have aided understanding of mechanisms of floral maintenance. Arabidopsis has not been found to revert to leaf production in any of the conditions or genetic backgrounds analysed to date. A clear-cut reversion to leaf production has, however, been described in Impatiens balsamina. It is proposed that a single gene controls whether Impatiens reverts or can maintain flowering when inductive conditions are removed, and it is inferred that this gene functions to control the synthesis or transport of a leaf-generated signal. But it is also argued that the susceptibility of Impatiens to reversion is a consequence of the meristem-based mechanisms controlling development of the flower in this species. Thus, in Impatiens, a leaf-derived signal is critical for completion of flowering and can be considered to be the basis of a plant-wide floral commitment that is achieved without accompanying meristem autonomy. The evidence, derived from in vitro and other studies, that similar mechanisms operate in other species is assessed. It is concluded that most species (including Arabidopsis) are less prone to reversion because signals from the leaf are less ephemeral, and the pathways driving flower development have a high level of redundancy that generates meristem autonomy even when leaf-derived signals are weak. This gives stability to the flowering process, even where its initiation is dependent on environmental cues. On this interpretation, Impatiens reversion appears as an anomaly resulting from an unusual combination of leaf signalling and meristem regulation. Nevertheless, it is shown that the ability to revert can serve a function in the life history strategy (perenniality) or reproductive habit (pseudovivipary) of many plants. In these instances reversion has been assimilated into regular plant development and plays a crucial role there.

Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor-lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins' constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.

beta-arrestin binding to the beta(2)-adrenergic receptor requires both receptor phosphorylation and receptor activation

Homologous desensitization of beta(2)-adrenergic receptors has been shown to be mediated by phosphorylation of the agonist-stimulated receptor by G-protein-coupled receptor kinase 2 (GRK2) followed by binding of beta-arrestins to the phosphorylated receptor. Binding of beta-arrestin to the receptor is a prerequisite for subsequent receptor desensitization, internalization via clathrin-coated pits, and the initiation of alternative signaling pathways. In this study we have investigated the interactions between receptors and beta-arrestin2 in living cells using fluorescence resonance energy transfer. We show that (a) the initial kinetics of beta-arrestin2 binding to the receptor is limited by the kinetics of GRK2-mediated receptor phosphorylation; (b) repeated stimulation leads to the accumulation of GRK2-phosphorylated receptor, which can bind beta-arrestin2 very rapidly; and (c) the interaction of beta-arrestin2 with the receptor depends on the activation of the receptor by agonist because agonist withdrawal leads to swift dissociation of the receptor-beta-arrestin2 complex. This fast agonist-controlled association and dissociation of beta-arrestins from prephosphorylated receptors should permit rapid control of receptor sensitivity in repeatedly stimulated cells such as neurons.

Agonist-selective, receptor-specific interaction of human P-2Y receptors with beta-arrestin-1 and-2

Interaction of G-protein-coupled receptors with beta-arrestins is an important step in receptor desensitization and in triggering "alternative" signals. By means of confocal microscopy and fluorescence resonance energy transfer, we have investigated the internalization of the human P2Y receptors 1, 2, 4, 6, 11, and 12 and their interaction with beta-arrestin-1 and -2. Co-transfection of each individual P2Y receptor with beta-arrestin-1-GFP or beta-arrestin-2-YFP into HEK-293 cells and stimulation with the corresponding agonists resulted in a receptor-specific interaction pattern. The P2Y(1) receptor stimulated with ADP strongly translocated beta-arrestin-2-YFP, whereas only a slight translocation was observed for beta-arrestin-1-GFP. The P2Y(4) receptor exhibited equally strong translocation for beta-arrestin-1-GFP and beta-arrestin-2YFP when stimulated with UTP. The P2Y(6), P2Y(11), and P2Y(12) receptor internalized only when GRK2 was additionally cotransfected, but beta-arrestin translocation was only visible for the P2Y(6) and P2Y(11) receptor. The P2Y(2) receptor showed a beta-arrestin translocation pattern that was dependent on the agonist used for stimulation. UTP translocated beta-arrestin-1-GFP and beta-arrestin-2-YFP equally well, whereas ATP translocated beta-arrestin-1-GFP to a much lower extent than beta-arrestin2- YFP. The same agonist-dependent pattern was seen in fluorescence resonance energy transfer experiments between the fluorescently labeled P2Y(2) receptor and beta-arrestins. Thus, the P2Y(2) receptor would be classified as a class A receptor when stimulated with ATP or as a class B receptor when stimulated with UTP. The ligand-specific recruitment of beta-arrestins by ATP and UTP stimulation of P2Y(2) receptors was further found to result in differential stimulation of ERK phosphorylation. This suggests that the two different agonists induce distinct active states of this receptor that show differential interactions with beta-arrestins.