Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

Platelet protein disulfide isomerase is required for thrombus formation but not essential for hemostasis in mice

Protein disulfide isomerase (PDI) derived from intravascular cells is required for thrombus formation. However, it remains unclear whether platelet PDI contributes to the process. Using platelet-specific PDI-deficient mice, we demonstrate that PDI-null platelets have defects in aggregation and ATP secretion induced by thrombin, collagen, and ADP. Such defects were rescued by exogenously-added wild-type but not mutant PDI, indicating that the isomerase activity of platelet surface PDI is critical for the regulatory effect. PDI-deficient platelets expressed increased levels of intracellular ERp57 and ERp72. Platelet PDI regulated αIIbβ3 integrin activation but not P-selectin exposure, Ca2+ mobilization, β3-talin interaction, and platelet spreading on immobilized fibrinogen. Inhibition of ERp57 further diminished αIIbβ3 integrin activation, aggregation and ATP secretion of activated PDI-deficient platelets, suggesting distinct roles of PDI and ERp57 in platelet functions. We found that platelet PDI is important for thrombus formation on collagen-coated surfaces under arteriolar shear. Intravital microscopy demonstrates that platelet PDI is important for platelet accumulation but not initial adhesion and fibrin generation following laser-induced arteriolar injury. Tail bleeding time and blood loss in platelet-specific PDI-deficient mice were not significantly increased. Our results provide important evidence that platelet PDI is essential for thrombus formation but not for hemostasis in mice.

Connexin40 regulates platelet function

The presence of multiple connexins was recently demonstrated in platelets, with notable expression of Cx37. Studies with Cx37-deficient mice and connexin inhibitors established roles for hemichannels and gap junctions in platelet function. It was uncertain, however, whether Cx37 functions alone or in collaboration with other family members through heteromeric interactions in regulation of platelet function. Here we report the presence and functions of an additional platelet connexin, Cx40. Inhibition of Cx40 in human platelets or its deletion in mice reduces platelet aggregation, fibrinogen binding, granule secretion and clot retraction. The effects of the Cx37 inhibitor 37,43Gap27 on Cx40-/- mouse platelets and of the Cx40 inhibitor 40Gap27 on Cx37-/- mouse platelets revealed that each connexin is able to function independently. Inhibition or deletion of Cx40 reduces haemostatic responses in mice, indicating the physiological importance of this protein in platelets. We conclude that multiple connexins are involved in regulating platelet function, thereby contributing to haemostasis and thrombosis.

The role of plasma membrane STIM1 and Ca(2+)entry in platelet aggregation. STIM1 binds to novel proteins in human platelets.

Ca(2+) elevation is essential to platelet activation. STIM1 senses Ca(2+) in the endoplasmic reticulum and activates Orai channels allowing store-operated Ca(2+) entry (SOCE). STIM1 has also been reported to be present in the plasma membrane (PM) with its N-terminal region exposed to the outside medium but its role is not fully understood. We have examined the effects of the antibody GOK/STIM1, which recognises the N-terminal region of STIM1, on SOCE, agonist-stimulated Ca(2+) entry, surface exposure, in vitro thrombus formation and aggregation in human platelets. We also determined novel binding partners of STIM1 using proteomics. The dialysed GOK/STIM1 antibody failed to reduced thapsigargin- and agonist-mediated Ca(2+) entry in Fura2-labelled cells. Using flow cytometry we detect a portion of STIM1 to be surface-exposed. The dialysed GOK/STIM1 antibody reduced thrombus formation by whole blood on collagen-coated capillaries under flow and platelet aggregation induced by collagen. In immunoprecipitation experiments followed by proteomic analysis, STIM1 was found to extract a number of proteins including myosin, DOCK10, thrombospondin-1 and actin. These studies suggest that PM STIM1 may facilitate platelet activation by collagen through novel interactions at the plasma membrane while the essential Ca(2+)-sensing role of STIM1 is served by the protein in the ER.

Probability functions to build composite indicators: a methodology to measure environmental impacts of genetically modified crops

There is an on-going debate on the environmental effects of genetically modified crops to which this paper aims to contribute. First, data on environmental impacts of genetically modified (GM) and conventional crops are collected from peer-reviewed journals, and secondly an analysis is conducted in order to examine which crop type is less harmful for the environment. Published data on environmental impacts are measured using an array of indicators, and their analysis requires their normalisation and aggregation. Taking advantage of composite indicators literature, this paper builds composite indicators to measure the impact of GM and conventional crops in three dimensions: (1) non-target key species richness, (2) pesticide use, and (3) aggregated environmental impact. The comparison between the three composite indicators for both crop types allows us to establish not only a ranking to elucidate which crop is more convenient for the environment but the probability that one crop type outperforms the other from an environmental perspective. Results show that GM crops tend to cause lower environmental impacts than conventional crops for the analysed indicators.

Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.

Biodiversity and resilience of ecosystem functions

Accelerating rates of environmental change and the continued loss of global biodiversity threaten functions and services delivered by ecosystems. Much ecosystem monitoring and management is focused on the provision of ecosystem functions and services under current environmental conditions, yet this could lead to inappropriate management guidance and undervaluation of the importance of biodiversity. The maintenance of ecosystem functions and services under substantial predicted future environmental change (i.e., their ‘resilience’) is crucial. Here we identify a range of mechanisms underpinning the resilience of ecosystem functions across three ecological scales. Although potentially less important in the short term, biodiversity, encompassing variation from within species to across landscapes, may be crucial for the longer-term resilience of ecosystem functions and the services that they underpin.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.