Strong invariance principles for sequential Bahadur--Kiefer and Vervaat error processes of long-range dependent sequences

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur--Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, that is, the integrated sequential Bahadur--Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur--Kiefer and the Vervaat error processes cannot converge weakly in the i.i.d. case. In contrast to this, we conclude that the Bahadur--Kiefer and Vervaat error processes, as well as their sequential versions, do converge weakly to a Dehling--Taqqu type limit process for certain long-range dependent sequences.Comment: Published at http://dx.doi.org/10.1214/009053606000000164 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

In vivo super-resolution photoacoustic computed tomography by localization of single dyed droplets

The spatial resolution of photoacoustic (PA) computed tomography (PACT) is limited by acoustic diffraction. Here, we report in vivo superresolution PACT, which breaks the acoustic diffraction limit by localizing the centers of single dyed droplets. The dyed droplets generate much stronger PA signals than blood and can flow smoothly in blood vessels; thus, they are excellent tracers for localization-based superresolution imaging. The flowing droplets were first localized, and then their center positions were used to construct a superresolution image that exhibits sharper features and more finely resolved vascular details. A 6-fold improvement in spatial resolution has been realized in vivo