We define a diffeomorphism invariant of smooth 4–manifolds which we can estimate for many smoothings of R and other smooth 4–manifolds. Using this invariant we can show that uncountably many smoothings of R support no Stein structure. Gompf [11] constructed uncountably many smoothings of R which do support Stein structures. Other applications of this invariant are given. AMS Classification numb...

An estimator in the extended class of Stein estimators has two undesirable properties. For a small value of prior guess, it ignores the data. Moreover, for some cases its risk is not uniformly smaller than that of Stein estimator. We show that there exists a lower bound on T(S) to guarantee a smaller risk, and the resulting estimator does not ignore the data.

154 Compact Vibration Measuring System for in-vehicle Applications G. J. Stein, R. Chmúrny, V. Rosík 1 Institute of Materials and Machine Mechanics, Slovak Academy of Sciences, Račianska 75, SK 831 02 Bratislava, Slovakia, e-mail: [email protected], [email protected] 2 Institute of Measurement, Slovak Academy of Sciences, Dúbravská cesta 9, SK 841 04 Bratislava, Slovakia, e-mail: [email protected]

In this paper the problem of estimating the scale matrix in a complex elliptically contoured distribution(complex ECD) is addressed. An extended Haff-Stein identity for this model is derived. It is shown that the minimax estimators of the covariance matrix obtained under the complex normal model remain robust under the complex ECD model when the Stein loss function is employed.

We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.

Abstract: This survey article discusses the main concepts and techniques of Stein’s method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration of measure inequalities. The material is presented at a level accessible to beginning graduate students studying probability with the main emphasis on the themes that a...

Posttraumatic stress disorder is characterized by the failure of the acute fear response to diminish after exposure to a lifethreatening traumatic event. Risk factors for PTSD include sex (female), education (less), and familial and genetic factors, as well as factors pertaining to the type and severity of trauma(s) experienced by the individual over time (including childhood maltreatment). The...

Prologue —R. Martorell, J. R. Behrman, R. Grajeda, and J. Hoddinott ......................................................... S3 Rationale for a follow-up study focusing on economic productivity —R. Martorell, J. R. Behrman, R. Flores, and A. D. Stein ...................................................................................................................................... S5 The Hum...