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

Change in electron and spin density upon electron transfer to haem

AbstractHaems are the cofactors of cytochromes and important catalysts of biological electron transfer. They are composed of a planar porphyrin structure with iron coordinated at the centre. It is known from spectroscopy that ferric low-spin haem has one unpaired electron at the iron, and that this spin is paired as the haem receives an electron upon reduction (I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin/Cummins Publ. Co., Menlo Park, CA, 1986, pp. 165–170; H.M. Goff, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part I, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 237–281; G. Palmer, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part II, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 43–88). Here we show by quantum chemical calculations on a haem a model that upon reduction the spin pairing at the iron is accompanied by effective delocalisation of electrons from the iron towards the periphery of the porphyrin ring, including its substituents. The change of charge of the iron atom is only approx. 0.1 electrons, despite the unit difference in formal oxidation state. Extensive charge delocalisation on reduction is important in order for the haem to be accommodated in the low dielectric of a protein, and may have impact on the distance dependence of the rates of electron transfer. The lost individuality of the electron added to the haem on reduction is another example of the importance of quantum mechanical effects in biological systems

Time-resolved generation of membrane potential by ba3 cytochrome c oxidase from Thermus thermophilus coupled to single electron injection into the O and OH states

peer-reviewedTwo electrogenic phases with characteristic times of ~ 14 μs and ~ 290 μs are resolved in the kinetics of membrane potential generation coupled to single-electron reduction of the oxidized “relaxed” O state of ba3 oxidase from T. thermophilus (O → E transition). The rapid phase reflects electron redistribution between CuA and heme b. The slow phase includes electron redistribution from both CuA and heme b to heme a3, and electrogenic proton transfer coupled to reduction of heme a3. The distance of proton translocation corresponds to uptake of a proton from the inner water phase into the binuclear center where heme a3 is reduced, but there is no proton pumping and no reduction of CuB. Single-electron reduction of the oxidized “unrelaxed” state (OH → EH transition) is accompanied by electrogenic reduction of the heme b/heme a3 pair by CuA in a “fast” phase (~ 22 μs) and transfer of protons in “middle” and “slow” electrogenic phases (~ 0.185 ms and ~ 0.78 ms) coupled to electron redistribution from the heme b/heme a3 pair to the CuB site. The “middle” and “slow” electrogenic phases seem to be associated with transfer of protons to the proton-loading site (PLS) of the proton pump, but when all injected electrons reach CuB the electronic charge appears to be compensated by back-leakage of the protons from the PLS into the binuclear site. Thus proton pumping occurs only to the extent of ~ 0.1 H+/e−, probably due to the formed membrane potential in the experiment.ACCEPTEDpeer-reviewe

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

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

Re-thinking the “ecological envelope” of Eastern Baltic cod (Gadus morhua): conditions for productivity, reproduction, and feeding over time

Hypoxia is presently seen as the principal driver behind the decline of the former dominating Eastern Baltic cod stock (EBC; Gadus morhua). It has been proposed that both worsening conditions for reproduction and lower individual growth, condition, and survival are linked to hypoxia. Here, we elucidate the ecological envelope of EBC in terms of salinity stratification, oxygen content, and benthic animal biomasses, and how it has affected EBC productivity over time. The spawning conditions started deteriorating in the Gotland Deep in the 1950s due to oxygen depletion. In contrast, in the Bornholm Basin, hydrographic conditions have remained unchanged over the last 60 years. Indeed, the current extent of both well-oxygenated areas and the frequency of hypoxia events do not differ substantially from periods with high EBC productivity in the 1970s–1980s. Furthermore, oxygenated and therefore potentially suitable feeding areas are abundant in all parts of the Baltic Sea, and our novel analysis provides no evidence of a reduction in benthic food sources for EBC over the last 30 years. We find that while reproduction failure is intricately linked to hydrographic dynamics, a relationship between the spread of hypoxia and the decline in EBC productivity during the last decades cannot be substantiated.Peer reviewe

The Combined Roles of Moral Emotion and Moral Rules in Explaining Acts of Violence Using a Situational Action Theory Perspective

The roles of shame and guilt, and their relationships to empathy, have not been modeled adequately as key factors in moral decision-making in the study of violence. The role of moral emotion has been neglected in existing criminological research and this study seeks to develop current explanations of the comprehensive myriad of factors that play a role in moral crime decision-making. This research will test the different roles of empathy, shame, and guilt in violence decision-making using a situational action theory (SAT) perspective. Data taken from the Peterborough Adolescent and Young Adult Development Study (PADS+), a longitudinal study with a large representative sample, provide quantitative questionnaire indices to enable comparison of a persistent and frequent violent offender subsample (N = 48) with the remaining PADS+ study sample (N = 607). A striking majority of violent offenders report that they do not think it is wrong to commit violence, and do not care about it, that is, they lack shame and guilt, and report that violence comes as a morally acceptable and natural action alternative. Furthermore, violent offenders do not register the predicament of their victims; there is a distinct lack of empathy. This article demonstrates a key finding which has rarely been explored to date; regression analyses reveal an interaction effect whereby individuals with weak shame and guilt, combined specifically with weak moral rules, are more likely to commit acts of violence. The study findings provide strong support for the SAT of the role of weak morality in violence decision-making. To reduce the possibility of crime being seen as an action alternative, moral development programs should be developed and administered in childhood