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

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

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

Victimization, crime propensity and deviance: a multinational test of general strain theory

General Strain Theory (GST) identifies victimization as one of the strains most strongly related to crime which, like other sources of strain, is moderated by individual and social factors. Recently, Agnew (2013) extended the theorization of coping strategies by proposing that the effects of strain on deviance are conditioned by individual and social factors in combination, rather than singly, which he labelled crime propensity. Tests of the propensity hypothesis have so far yielded mixed results, highlighting the value of additional studies. Whereas previous tests have focused on single countries, either in North America or Asia, we test the propensity hypothesis using data on adolescents in 25 countries collected through the International Self-Report Delinquency Study (ISRD3; n= 57,760). A series of OLS regressions show that the relationship between victimization and delinquency/substance use is conditioned by the effects of individuals’ crime propensity, thereby supporting the recent extension to GST

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

Developing and validating an experience sampling measure of aggression:The Aggression-ES Scale

Experience sampling methodologies are likely to play an important role in advancing our understanding of momentary influences on aggression, including short-term antecedent psychological states and situations. In this study, we evaluate whether a newly developed experiencing sampling measure of aggression, the Aggression Experience Sampler (Aggression-ES), provides a valid and reliable measure of aggression in experience sampling contexts. Participants were a convenience sample of 23 young adults recruited from the local University community. Data were collected using an experience sampling smartphone application over 8 days. They were analyzed using multilevel structural equation modeling. Our results support the within- and between-person reliability and the criterion validity of the Aggression-ES. The Aggression-ES represents a good choice of measure for use in experience sampling studies of aggression. Further work in other samples will help to provide further validity evidence for the measure

The extent of neuroradiological findings in COVID-19 shows correlation with blood biomarkers, Glasgow coma scale score and days in intensive care

Background and purpose: A wide range of neuroradiological findings has been reported in patients with coronavirus disease 2019 (COVID-19), ranging from subcortical white matter changes to infarcts, haemorrhages and focal contrast media enhancement. These have been descriptively but inconsistently reported and correlations with clinical findings and biomarkers have been difficult to extract from the literature. The purpose of this study was to quantify the extents of neuroradiological findings in a cohort of patients with COVID-19 and neurological symptoms, and to investigate correlations with clinical findings, duration of intensive care and biomarkers in blood. Material and methods: Patients with positive SARS-CoV-2 and at least one new-onset neurological symptom were included from April until July 2020. Nineteen patients were examined regarding clinical symptoms, biomarkers in blood and MRI of the brain. In order to quantify the MRI findings, a semi-quantitative neuroradiological severity scale was constructed a priori, and applied to the MR images by two specialists in neuroradiology. Results and conclusions: The score from the severity scale correlated significantly with blood biomarkers of CNS injury (glial fibrillary acidic protein, total-tau, ubiquitin carboxyl-terminal hydrolase L1) and inflammation (C-reactive protein), Glasgow Coma Scale score, and the number of days spent in intensive care. The underlying radiological assessments had inter-rater agreements of 90.5%/86% (for assessments with 2/3 alternatives). Total intraclass correlation was 0.80. Previously reported neuroradiological findings in COVID-19 have been diverse and heterogenous. In this study, the extent of findings in MRI examination of the brain, quantified using a structured report, shows correlation with relevant biomarkers

Making Sigma-Protocols Non-interactive Without Random Oracles

Damg˚ard, Fazio and Nicolosi (TCC 2006) gave a transformation of Sigma-protocols, 3-move honest verifier zero-knowledge proofs, into efficient non-interactive zero-knowledge arguments for a designated verifier. Their transformation uses additively homomorphic encryption to encrypt the verifier’s challenge, which the prover uses to compute an encrypted answer. The transformation does not rely on the random oracle model but proving soundness requires a complexity leveraging assumption. We propose an alternative instantiation of their transformation and show that it achieves culpable soundness without complexity leveraging. This improves upon an earlier result by Ventre and Visconti (Africacrypt 2009), who used a different construction which achieved weak culpable soundness. We demonstrate how our construction can be used to prove validity of encrypted votes in a referendum. This yields a voting system with homomorphic tallying that does not rely on the Fiat-Shamir heuristic

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