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

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

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

On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes

The sensitivity of a search for sources of TeV neutrinos can be improved by grouping potential sources together into generic classes in a procedure that is known as source stacking. In this paper, we define catalogs of Active Galactic Nuclei (AGN) and use them to perform a source stacking analysis. The grouping of AGN into classes is done in two steps: first, AGN classes are defined, then, sources to be stacked are selected assuming that a potential neutrino flux is linearly correlated with the photon luminosity in a certain energy band (radio, IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino production in AGN, this correlation is motivated by hadronic AGN models, as briefly reviewed in this paper. The source stacking search for neutrinos from generic AGN classes is illustrated using the data collected by the AMANDA-II high energy neutrino detector during the year 2000. No significant excess for any of the suggested groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic

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

Unpacking the relationships between impulsivity, neighborhood disadvantage, and adolescent violence : an application of a neighborhood-based group decomposition

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement no. 615159 (ERC Consolidator Grant DEPRIVEDHOODS, Socio-spatial inequality, deprived neighbourhoods, and neighbourhood effects); and from the Marie Curie programme under the European Union’s Seventh Framework Programme (FP/2007–2013)/Career Integration Grant no. PCIG10-GA-2011-303728 (CIG Grant NBHCHOICE, Neighbourhood choice, neighbourhood sorting, and neighbourhood effects).Scholars have become increasingly interested in how social environments condition the relationships between individual risk-factors and adolescent behavior. An appreciable portion of this literature is concerned with the relationship between impulsivity and delinquency across neighborhood settings. The present article builds upon this growing body of research by considering the more nuanced pathways through which neighborhood disadvantage shapes the development of impulsivity and provides a situational context for impulsive tendencies to manifest in violent and aggressive behaviors. Using a sample of 12,935 adolescent from the National Longitudinal Study of Adolescent to Adult Health (Add Health) (mean age = 15.3, 51% female; 20% Black, 17% Hispanic), we demonstrate the extent to which variation in the association between impulsivity and delinquency across neighborhoods can be attributed to (1) differences in mean-levels of impulsivity and violence and (2) differences in coefficients across neighborhoods. The results of a series of multivariate regression models indicate that impulsivity is positively associated with self-reported violence, and that this relationship is strongest among youth living in disadvantaged neighborhoods. The moderating effect of neighborhood disadvantage can be attributed primarily to the stronger effect of impulsivity on violence in these areas, while differences in average levels of violence and impulsivity account for a smaller, yet nontrivial portion of the observed relationship. These results indicate that the differential effect of impulsivity on violence can be attributed to both developmental processes that lead to the greater concentration of violent and impulsive adolescents in economically deprived neighborhoods as well as the greater likelihood of impulsive adolescents engaging in violence when they reside in economically disadvantaged communities.Publisher PDFPeer reviewe