X. P. Tang, A. Becker, W. Liu, M. Sharifi, O. Kosareva, V. P. Kandidov, P. Agostini, and S. L. Chin Centre d’Optique, Photonique et Laser (COPL) and Département de Physique de Génie Physique et d’Optique, Université Laval, Québec, Québec, Canada G1K 7P4 Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany International Laser Center, Department of Phy...

We prove that a pseudoholomorphic diffeomorphism between two almost complex manifolds with boundaries satisfying some pseudoconvexity type conditions cannot map a pseudoholomorphic disc in the boundary to a single point. This can be viewed as an almost complex analogue of a well known theorem of J.E.Fornaess.

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such a" that of James and Stein, but instead will likely incur a greater error th...

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f . We show, for instance, that if an X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurfac...

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of the...

We continued the study of the contact homology of subcritical Stein manifolds initiated by Mei-Lin Yau. With the technical assumption that the first Chern class of the Stein domain vanishes, we determined the full contact homology of the boundary of a subcritical Stein domain. Moreover we calculated the genus 0 correlators and descendants of one marked point for the Stein domain. As an applicat...

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We establish existence of Stein kernels for probability measures on R satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W2 with optimal rate and dependence on the dimension. As a byproduct, we obtain a stable version of an estimate of the Po...

Charles Stein [10] discovered that, under quadratic loss, the usual unbiased estimator for the mean vector of a multivariate normal distribution is inadmissible if the dimension n of the mean vector exceeds two. On the way, he constructed shrinkage estimators that dominate the usual estimator asymptotically in n. It has since been claimed that Stein’s results and the subsequent James–Stein esti...

*Corresponding author: Dr. Amir Sabet, Department of Nuclear Medicine, University of Bonn, Sigmund-Freud, Strasse 25, 53127 Bonn, Germany. Fax: +49 228 287 9