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

Making Code Voting Secure against Insider Threats using Unconditionally Secure MIX Schemes and Human PSMT Protocols

Code voting was introduced by Chaum as a solution for using a possibly infected-by-malware device to cast a vote in an electronic voting application. Chaum's work on code voting assumed voting codes are physically delivered to voters using the mail system, implicitly requiring to trust the mail system. This is not necessarily a valid assumption to make - especially if the mail system cannot be trusted. When conspiring with the recipient of the cast ballots, privacy is broken. It is clear to the public that when it comes to privacy, computers and "secure" communication over the Internet cannot fully be trusted. This emphasizes the importance of using: (1) Unconditional security for secure network communication. (2) Reduce reliance on untrusted computers. In this paper we explore how to remove the mail system trust assumption in code voting. We use PSMT protocols (SCN 2012) where with the help of visual aids, humans can carry out $\mod 10$ addition correctly with a 99\% degree of accuracy. We introduce an unconditionally secure MIX based on the combinatorics of set systems. Given that end users of our proposed voting scheme construction are humans we \emph{cannot use} classical Secure Multi Party Computation protocols. Our solutions are for both single and multi-seat elections achieving: \begin{enumerate}[i)] \item An anonymous and perfectly secure communication network secure against a $t$-bounded passive adversary used to deliver voting, \item The end step of the protocol can be handled by a human to evade the threat of malware. \end{enumerate} We do not focus on active adversaries

Transient Calcium and Dopamine Increase PKA Activity and DARPP-32 Phosphorylation

Reinforcement learning theorizes that strengthening of synaptic connections in medium spiny neurons of the striatum occurs when glutamatergic input (from cortex) and dopaminergic input (from substantia nigra) are received simultaneously. Subsequent to learning, medium spiny neurons with strengthened synapses are more likely to fire in response to cortical input alone. This synaptic plasticity is produced by phosphorylation of AMPA receptors, caused by phosphorylation of various signalling molecules. A key signalling molecule is the phosphoprotein DARPP-32, highly expressed in striatal medium spiny neurons. DARPP-32 is regulated by several neurotransmitters through a complex network of intracellular signalling pathways involving cAMP (increased through dopamine stimulation) and calcium (increased through glutamate stimulation). Since DARPP-32 controls several kinases and phosphatases involved in striatal synaptic plasticity, understanding the interactions between cAMP and calcium, in particular the effect of transient stimuli on DARPP-32 phosphorylation, has major implications for understanding reinforcement learning. We developed a computer model of the biochemical reaction pathways involved in the phosphorylation of DARPP-32 on Thr34 and Thr75. Ordinary differential equations describing the biochemical reactions were implemented in a single compartment model using the software XPPAUT. Reaction rate constants were obtained from the biochemical literature. The first set of simulations using sustained elevations of dopamine and calcium produced phosphorylation levels of DARPP-32 similar to that measured experimentally, thereby validating the model. The second set of simulations, using the validated model, showed that transient dopamine elevations increased the phosphorylation of Thr34 as expected, but transient calcium elevations also increased the phosphorylation of Thr34, contrary to what is believed. When transient calcium and dopamine stimuli were paired, PKA activation and Thr34 phosphorylation increased compared with dopamine alone. This result, which is robust to variation in model parameters, supports reinforcement learning theories in which activity-dependent long-term synaptic plasticity requires paired glutamate and dopamine inputs

Development and validation of two self-reported tools for insulin resistance and hypertension risk assessment in a European cohort : the Feel4Diabetes-study

Early identification of type 2 diabetes mellitus (T2DM) and hypertension (HTN) risk may improve prevention and promote public health. Implementation of self-reported scores for risk assessment provides an alternative cost-effective tool. The study aimed to develop and validate two easy-to-apply screening tools identifying high-risk individuals for insulin resistance (IR) and HTN in a European cohort. Sociodemographic, lifestyle, anthropometric and clinical data obtained from 1581 and 1350 adults (baseline data from the Feel4Diabetes-study) were used for the European IR and the European HTN risk assessment index respectively. Body mass index, waist circumference, sex, age, breakfast consumption, alcohol, legumes and sugary drinks intake, physical activity and sedentary behavior were significantly correlated with Homeostatic Model Assessment of IR (HOMA-IR) and/or HTN and incorporated in the two models. For the IR index, the Area Under the Curve (AUC), sensitivity and specificity for identifying individuals above the 75th and 95th of HOMA-IR percentiles were 0.768 (95%CI: 0.721–0.815), 0.720 and 0.691 and 0.828 (95%CI: 0.766–0.890), 0.696 and 0.778 respectively. For the HTN index, the AUC, sensitivity and specificity were 0.778 (95%CI: 0.680–0.876), 0.667 and 0.797. The developed risk assessment tools are easy-to-apply, valid, and low-cost, identifying European adults at high risk for developing T2DM or having HTN

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

Oxygen Activation and Energy Conservation by Cytochrome c Oxidase

This review focuses on the type A cytochrome c oxidases (C cO), which are found in all mitochondria and also in several aerobic bacteria. C cO catalyzes the respiratory reduction of dioxygen (O2) to water by an intriguing mechanism, the details of which are fairly well understood today as a result of research for over four decades. Perhaps even more intriguingly, the membrane-bound C cO couples the O2 reduction chemistry to translocation of protons across the membrane, thus contributing to generation of the electrochemical proton gradient that is used to drive the synthesis of ATP as catalyzed by the rotary ATP synthase in the same membrane. After reviewing the structure of the core subunits of C cO, the active site, and the transfer paths of electrons, protons, oxygen, and water, we describe the states of the catalytic cycle and point out the few remaining uncertainties. Finally, we discuss the mechanism of proton translocation and the controversies in that area that still prevail.Peer reviewe

Bi-directional modulation of AMPA receptor unitary conductance by synaptic activity

BACKGROUND: Knowledge of how synapses alter their efficiency of communication is central to the understanding of learning and memory. The most extensively studied forms of synaptic plasticity are long-term potentiation (LTP) and its counterpart long-term depression (LTD) of AMPA receptor-mediated synaptic transmission. In the CA1 region of the hippocampus, it has been shown that LTP often involves a rapid increase in the unitary conductance of AMPA receptor channels. However, LTP can also occur in the absence of any alteration in AMPA receptor unitary conductance. In the present study we have used whole-cell dendritic recording, failures analysis and non-stationary fluctuation analysis to investigate the mechanism of depotentiation of LTP. RESULTS: We find that when LTP involves an increase in unitary conductance, subsequent depotentiation invariably involves the return of unitary conductance to pre-LTP values. In contrast, when LTP does not involve a change in unitary conductance then depotentiation also occurs in the absence of any change in unitary conductance, indicating a reduction in the number of activated receptors as the most likely mechanism. CONCLUSIONS: These data show that unitary conductance can be bi-directionally modified by synaptic activity. Furthermore, there are at least two distinct mechanisms to restore synaptic strength from a potentiated state, which depend upon the mechanism of the previous potentiation