A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

Solutions of special asymptotics to the Einstein constraint equations

We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.Comment: 13 pages; the error in Lemma 3.5 fixed and typos corrected; to appear in Class. Quantum Gra

Attention modulates psychophysical and electrophysiological response to visual texture segmentation in humans

none5noTo investigate whether processing underlying texture segmentation is limited when texture is not attended, we measured orientation discrimination accuracy and visual evoked potentials (VEPs) while a texture bar was cyclically alternated with a uniform texture, either attended or not. Orientation discrimination was maximum when the bar was explicitly attended, above threshold when implicitly attended, and fell to just chance when unattended, suggesting that orientation discrimination based on grouping of elements along texture boundary requires explicit attention. We analyzed tsVEPs (variations in VEP amplitude obtained by algebraic of uniform-texture from segmented-texture VEPs) elicited by the texture boundary orientation discrimination task. When texture was unattended, tsVEPs still reflected local texture segregation. We found larger amplitudes of early tsVEP components (N75, P100, N150, N200) when texture boundary was parallel to texture elements, indicating a saliency effect, perhaps at V1 level. This effect was modulated by attention, disappearing when the texture was not attended, a result indicating that attention facilitates grouping by collinearity in the direction of the texture boundary.openCasco, C; Grieco, A; Campana, G; CORVINO M., P; Caputo, GIOVANNI BATTISTACasco, C; Grieco, A; Campana, G; CORVINO M., P; Caputo, GIOVANNI BATTIST

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic