Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

STOVE: Seed treatments for organic vegetable production

The aim of the EU-financed research project „STOVE“ (Seed Treatments for Organic Vegetable Production) is to evaluate different methods potentially suited for seed treatment of vegetables in organic farming regarding their efficacy, to optimise these methods, and where feasible to combine them with each other. Scientists from seven European research institutions and a producer of organic vegetable seeds carry out the project

Cerebral Biomarkers and Blood-Brain Barrier Integrity in Preeclampsia

Cerebral complications in preeclampsia contribute substantially to maternal mortality and morbidity. There is a lack of reliable and accessible predictors for preeclampsia-related cerebral complications. In this study, plasma from women with preeclampsia (n = 28), women with normal pregnancies (n = 28) and non-pregnant women (n = 16) was analyzed for concentrations of the cerebral biomarkers neurofilament light (NfL), tau, neuron-specific enolase (NSE) and S100B. Then, an in vitro blood–brain barrier (BBB) model, based on the human cerebral microvascular endothelial cell line (hCMEC/D3), was employed to assess the effect of plasma from the three study groups. Transendothelial electrical resistance (TEER) was used as an estimation of BBB integrity. NfL and tau are proteins expressed in axons, NSE in neurons and S100B in glial cells and are used as biomarkers for neurological injury in other diseases such as dementia, traumatic brain injury and hypoxic brain injury. Plasma concentrations of NfL, tau, NSE and S100B were all higher in women with preeclampsia compared with women with normal pregnancies (8.85 vs. 5.25 ng/L, p < 0.001; 2.90 vs. 2.40 ng/L, p < 0.05; 3.50 vs. 2.37 µg/L, p < 0.001 and 0.08 vs. 0.05 µg/L, p < 0.01, respectively). Plasma concentrations of NfL were also higher in women with preeclampsia compared with non-pregnant women (p < 0.001). Higher plasma concentrations of the cerebral biomarker NfL were associated with decreased TEER (p = 0.002) in an in vitro model of the BBB, a finding which indicates that NfL could be a promising biomarker for BBB alterations in preeclampsia

Repetitive levosimendan infusions for patients with advanced chronic heart failure in the vulnerable post-discharge period

Hospitalization for acute heart failure (HF) is associated with a substantial morbidity burden and with associated healthcare costs and an increased mortality risk. However, few if any major medical innovations have been witnessed in this area in recent times. Levosimendan is a first-in-class calcium sensitizer and potassium channel opener indicated for the management of acute HF. Experience in several clinical studies has indicated that administration of intravenous levosimendan in intermittent cycles may reduce hospitalization and mortality rates in patients with advanced HF; however, none of those trials were designed or powered to give conclusive insights into that possibility. This paper describes the rationale and protocol of LeoDOR (levosimendan infusions for patients with advanced chronic heart failure), a randomized, double-blind, placebo-controlled, international, multicentre trial that will explore the efficacy and safety of intermittent levosimendan therapy, in addition to optimized standard therapy, in patients following hospitalization for acute HF. Salient features of LeoDOR include the use of two treatment regimens, in order to evaluate the effects of different schedules and doses of levosimendan during a 12 week treatment phase, and the use of a global rank primary endpoint, in which all patients are ranked across three hierarchical groups ranging from time to death or urgent heart transplantation or implantation of a ventricular assist device to time to rehospitalization and, lastly, time-averaged proportional change in N-terminal pro-brain natriuretic peptide. Secondary endpoints include changes in HF symptoms and functional status at 14 weeks

Common carotid intima media thickness and ankle-brachial pressure index correlate with local but not global atheroma burden:a cross sectional study using whole body magnetic resonance angiography

Common carotid intima media thickness (CIMT) and ankle brachial pressure index (ABPI) are used as surrogate marker of atherosclerosis, and have been shown to correlate with arterial stiffness, however their correlation with global atherosclerotic burden has not been previously assessed. We compare CIMT and ABPI with atheroma burden as measured by whole body magnetic resonance angiography (WB-MRA).50 patients with symptomatic peripheral arterial disease were recruited. CIMT was measured using ultrasound while rest and exercise ABPI were performed. WB-MRA was performed in a 1.5T MRI scanner using 4 volume acquisitions with a divided dose of intravenous gadolinium gadoterate meglumine (Dotarem, Guerbet, FR). The WB-MRA data was divided into 31 anatomical arterial segments with each scored according to degree of luminal narrowing: 0 = normal, 1 = <50%, 2 = 50-70%, 3 = 70-99%, 4 = vessel occlusion. The segment scores were summed and from this a standardized atheroma score was calculated.The atherosclerotic burden was high with a standardised atheroma score of 39.5±11. Common CIMT showed a positive correlation with the whole body atheroma score (β 0.32, p = 0.045), however this was due to its strong correlation with the neck and thoracic segments (β 0.42 p = 0.01) with no correlation with the rest of the body. ABPI correlated with the whole body atheroma score (β -0.39, p = 0.012), which was due to a strong correlation with the ilio-femoral vessels with no correlation with the thoracic or neck vessels. On multiple linear regression, no correlation between CIMT and global atheroma burden was present (β 0.13 p = 0.45), while the correlation between ABPI and atheroma burden persisted (β -0.45 p = 0.005).ABPI but not CIMT correlates with global atheroma burden as measured by whole body contrast enhanced magnetic resonance angiography in a population with symptomatic peripheral arterial disease. However this is primarily due to a strong correlation with ilio-femoral atheroma burden

Repetitive use of levosimendan for treatment of chronic advanced heart failure: Clinical evidence, practical considerations, and perspectives: An expert panel consensus

Background The intravenous inodilator levosimendan was developed for the treatment of patients with acutely decompensated heart failure. In the last decade scientific and clinical interest has arisen for its repetitive or intermittent use in patients with advanced chronic, but not necessarily acutely decompensated, heart failure. Recent studies have suggested long-lasting favourable effects of levosimendan when administered repetitively, in terms of haemodynamic parameters, neurohormonal and inflammatory markers, and clinical outcomes. The existing data, however, requires further exploration to allow for definitive conclusions on the safety and clinical efficacy of repetitive use of levosimendan. Methods and results A panel of 30 experts from 15 countries convened to review and discuss the existing data, and agreed on the patient groups that can be considered to potentially benefit from intermittent treatment with levosimendan. The panel gave recommendations regarding patient dosing and monitoring, derived from the available evidence and from clinical experience. Conclusions The current data suggest that in selected patients and support out-of-hospital care, intermittent/repetitive levosimendan can be used in advanced heart failure to maintain patient stability. Further studies are needed to focus on morbidity and mortality outcomes, dosing intervals, and patient monitoring. Recommendations for the design of further clinical studies are made

An Evaluation Model For Web-based 3D Mass Customization Toolkit Design

The development of geometric modelling technologies and web technologies provides the ability to present a virtual 3D product in a mass customization (MC) toolkit. Compared with 2D graphic toolkits, 3D toolkit design requires better consideration of individual customer needs, consumer and toolkit interaction, and also a means of integrating with the underlying technical infrastructure. However, there is currently no widely accepted model or criteria to regulate and evaluate 3D MC toolkit design. Given these considerations, in this paper we provide an evaluation model for web-based 3D toolkits and a heuristic evaluation of two representative commercial web-based 3D toolkits. The evaluation results indicate the usefulness and effectiveness of the model as a scale for evaluating 3D toolkits. It also reveals that despite a fair amount of effort that has been devoted to theoretical research, current 3D toolkits are still at an early development stage. We therefore conclude this paper by identifying and encouraging further topics and questions as directions for future research

Nanoparticle–membrane interactions

Engineered nanomaterials have a wide range of applications and as a result, are increasingly present in the environment. While they offer new technological opportunities, there is also the potential for adverse impact, in particular through possible toxicity. In this review, we discuss the current state of the art in the experimental characterisation of nanoparticle-membrane interactions relevant to the prediction of toxicity arising from disruption of biological systems. One key point of discussion is the urgent need for more quantitative studies of nano-bio interactions in experimental models of lipid system that mimic in vivo membranes