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

Consanguineous marriage, prepregnancy maternal characteristics and stillbirth risk: A population-based case-control study

Introduction. Consanguineous marriage is associated with increased risks for congenital anomalies, low birthweight, and other adverse perinatal outcomes. In this population-based, case-control study we investigated the association between consanguineous marriage (first-cousin marriage) and stillbirth risk, using prospectively collected information from prepregnancy visits. Material and methods. From 2007 to 2009, we identified 283 stillbirths (cases) and 2088 randomly selected live control births through prepregnancy visits in rural Golestan, Iran. The associations between consanguinity and prepregnancy maternal characteristics and stillbirth risk were examined using multivariate logistic regression. Results. The rate of consanguineous marriage was 19.4% among cases and 13.6% among controls. Consanguinity was associated with increased stillbirth risk [odds ratio (OR) 1.53; 95% CI 1.10-2.14]. The association was significantly increased for preterm stillbirth (< 37 gestational weeks) (OR 2.43; 95% CI 1.46-4.04) but not for term stillbirth (≥ 37 weeks) (OR 1.14; 95% CI 0.75-1.74). Low and high maternal age, underweight, obesity, nulliparity, a history of infertility or miscarriage, previous obstetric complications (preeclampsia, preterm delivery, and stillbirth in previous pregnancies) were also associated with increased stillbirth risks. Conclusions. Consanguineous marriage is associated with increased risk of stillbirth, particularly preterm stillbirth. Findings for other maternal risk factors for stillbirth in rural Iran are consistent with previously reported findings from high-income countries. © 2015 Nordic Federation of Societies of Obstetrics and Gynecology

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

Electric fields control water-gated proton transfer in cytochrome c oxidase

Funding Information: ACKNOWLEDGMENTS. This work was funded by the Knut and Alice Wallenberg Foundation (2019.0251 and 2019.0043 to V.R.I.K.). V.R.I.K. also acknowledges support from the German Research Foundation (DFG) via the Collaborative Research Centre (SFB1078) as Mercator Fellow. Computational resources were provided by Funding Information: the Swedish National Infrastructure for Computing (SNIC 2021/1-40, SNIC 2022/1-29) at the Center of High-Performance Computing (PDC), and by the Leibniz-Rechenzentrum. M.W. was supported by the Institute of Biotechnology, University of Helsinki. Funding Information: This work was funded by the Knut and Alice Wallenberg Foundation (2019.0251 and 2019.0043 to V.R.I.K.). V.R.I.K. also acknowledges support from the German Research Foundation (DFG) via the Collaborative Research Centre (SFB1078) as Mercator Fellow. Computational resources were provided by the Swedish National Infrastructure for Computing (SNIC 2021/1-40, SNIC 2022/1-29) at the Center of High-Performance Computing (PDC), and by the Leibniz-Rechenzentrum. M.W. was supported by the Institute of Biotechnology, University of Helsinki. Publisher Copyright: Copyright © 2022 the Author(s). Published by PNAS.Aerobic life is powered by membrane-bound enzymes that catalyze the transfer of electrons to oxygen and protons across a biological membrane. Cytochrome c oxidase (CcO) functions as a terminal electron acceptor in mitochondrial and bacterial respiratory chains, driving cellular respiration and transducing the free energy from O2 reduction into proton pumping. Here we show that CcO creates orientated electric fields around a nonpolar cavity next to the active site, establishing a molecular switch that directs the protons along distinct pathways. By combining large-scale quantum chemical density functional theory (DFT) calculations with hybrid quantum mechanics/ molecular mechanics (QM/MM) simulations and atomistic molecular dynamics (MD) explorations, we find that reduction of the electron donor, heme a, leads to dissociation of an arginine (Arg438)-heme a3 D-propionate ion-pair. This ion-pair dissociation creates a strong electric field of up to 1 V A21 along a water-mediated proton array leading to a transient proton loading site (PLS) near the active site. Protonation of the PLS triggers the reduction of the active site, which in turn aligns the electric field vectors along a second, "chemical," proton pathway. We find a linear energy relationship of the proton transfer barrier with the electric field strength that explains the effectivity of the gating process. Our mechanism shows distinct similarities to principles also found in other energy-converting enzymes, suggesting that orientated electric fields generally control enzyme catalysis.Peer reviewe

Fibrinolytic and coagulative activities of Yersinia pestis

Peer reviewe

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

Superweakly interacting dark matter from the Minimal Walking Technicolor

We study a superweakly interacting dark matter particle motivated by minimal walking technicolor theories. Our WIMP is a mixture of a sterile state and a state with the charges of a standard model fourth family neutrino. We show that the model can give the right amount of dark matter over a range of the WIMP mass and mixing angle. We compute bounds on the model parameters from the current accelerator data including the oblique corrections to the precision electroweak parameters, as well as from cryogenic experiments, Super-Kamiokande and from the IceCube experiment. We show that consistent dark matter solutions exist which satisfy all current constraints. However, almost the entire parameter range of the model lies within the the combined reach of the next generation experiments.Comment: 29 pages, 6 figure