Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and Theorem 5.3 are adde

Hyperholomorpic connections on coherent sheaves and stability

Let $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on 2-forms. If the curvature is square-integrable, then $F$ is stable and its singularities are hyperkaehler subvarieties in $M$. Such sheaves (called hyperholomorphic sheaves) are well understood. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessarily square-integrable. This situation arises often, for instance, when one deals with higher direct images of holomorphic bundles. We show that such sheaves are stable.Comment: 37 pages, version 11, reference updated, corrected many minor errors and typos found by the refere

Invariant elliptic curves as attractors in the projective plane

Let f be a rational self-map of P^2 which leaves invariant an elliptic curve C with strictly negative transverse Lyapunov exponent. We show that C is an attractor, i.e. it possesses a dense orbit and its basin is of strictly positive measure

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Multirater Validation of Peripapillary Hyperreflective Ovoid Mass-like Structures (PHOMS)

Peripapillary hyperreflective ovoid mass-like structures (PHOMS) are a new retinal optical coherence tomography (OCT) finding. The Optic Disc Drusen Studies Consortium had made recommendations to distinguish PHOMS from true optic disc drusen (ODD) in 2018. While publications on PHOMS have increased since then, the accuracy of the definition of PHOMS and reliability of detection is unknown. In this multi-rater study, we demonstrate that the 2018 definition of PHOMS resulted in a poor multi-rater kappa of 0.356. We performed a Delphi consensus process to develop a consistent and refined definition of PHOMS with clear principles around the nature of PHOMS and how they differ from normal anatomy. Fifty explanatory teaching slides, provided as supplementary material, allowed our expert group of raters to achieve a good level of agreement (kappa 0.701, 50 OCT scans, 21 raters). We recommend adopting the refined definition for PHOMS

Oka's inequality for currents and applications

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46241/1/208_2005_Article_BF01446636.pd

Angiotensin-converting enzyme and male fertility

The angiotensin-converting enzyme (ACE; EC 3.4.15.1) gene (Ace) encodes both a somatic isozyme found in blood and several other tissues, including the epididymis, and a testis-specific isozyme (testis ACE) found only in developing spermatids and mature sperm. We recently used gene targeting to disrupt the gene coding for both ACE isozymes in mice and reported that male homozygous mutants mate normally but have reduced fertility; the mutant females are fertile. Here we explore the male fertility defect. We demonstrate that ACE is important for achieving in vivo fertilization and that sperm from mice lacking both ACE isozymes show defects in transport within the oviducts and in binding to zonae pellucidae. Males generated by gene targeting that lack somatic ACE but retain testis ACE are normally fertile, establishing that somatic ACE in males is not essential for their fertility. Furthermore, male and female mice lacking angiotensinogen have normal fertility, indicating that angiotensin I is not a necessary substrate for testis ACE. Males heterozygous for the mutation inactivating both ACE isozymes sire wild-type and heterozygous offspring at an indistinguishable frequency, indicating no selection against sperm carrying the mutation

Grids of stellar models with rotation VII : models from 0.8 to 300 M⊙ at supersolar metallicity (Z = 0.020)

We present a grid of stellar models at supersolar metallicity (Z = 0.020) extending the previous grids of Geneva models at solar and sub-solar metallicities. A metallicity of Z = 0.020 was chosen to match that of the inner Galactic disc. A modest increase of 43 per cent (= 0.02/0.014) in metallicity compared to solar models means that the models evolve similarly to solar models but with slightly larger mass-loss. Mass-loss limits the final total masses of the supersolar models to 35 M⊙ even for stars with initial masses much larger than 100 M⊙. Mass-loss is strong enough in stars above 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) to remove the entire hydrogen-rich envelope. Our models thus predict SNII below 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) and SNIb (possibly SNIc) above that. We computed both isochrones and synthetic clusters to compare our supersolar models to the Westerlund 1 (Wd1) massive young cluster. A synthetic cluster combining rotating and non-rotating models with an age spread between log10(age/yr) = 6.7 and 7.0 is able to reproduce qualitatively the observed populations of WR, RSG, and YSG stars in Wd1, in particular their simultaneous presence at log10(L/L⊙) = 5–5.5. The quantitative agreement is imperfect and we discuss the likely causes: synthetic cluster parameters, binary interactions, mass-loss and their related uncertainties. In particular, mass-loss in the cool part of the HRD plays a key role

The legal framework for financial advertising:curbing behavioural exploitation

Policy makers and behavioural finance scholars express growing concern that marketing practices by financial institutions exploit retail investors’ behavioural biases. Investor protection regulation should thus address these marketing practices and include mechanisms curbing behavioural exploitation. That raises the question whether the marketing communications regime of the new Markets in Financial Instruments Directive can live up to this demand. This article develops a regulatory model that integrates behavioural finance insights into the new marketing communications regime. It then determines how regulatory authorities can apply this model when they interpret and apply specific regulatory requirements. It demonstrates how a regulatory authority or a court can translate empirical behavioural finance research findings into legal arguments when assessing whether marketing practices can significantly distort a model investor’s decision-making process. The article further establishes that the detailed requirements imposed on investment firms by the new Markets in Financial Instruments Directive are necessary in order to protect investors from behavioural exploitation. Finally, the article submits policy proposals that aim to protect investors more effectively from behavioural exploitation