In-event background and signal reconstruction for two-photon invariant-mass analyses

A method is presented for the reconstruction of both the background and signal in invariant-mass analyses for two-photon decays. The procedure does not make use of event mixing techniques and as such is based exclusively on an event-by-event analysis. Consequently, topological correlations of the event (e.g. jet structures) are automatically taken into account. By means of the decay process $\pi^{0} \to \gamma \gamma$ it will be demonstrated how the procedure allows for determination of the $\pi^{0}$ yield from the observed decay photons

State and trait characteristics of early course major depressive disorder

Contains fulltext : 109595.pdf (Publisher’s version ) (Open Access)Radboud Universiteit Nijmegen, 21 december 2012Promotores : Buitelaar, J.K., Fernandez, G.S.E. Co-promotor : Tendolkar, I

A construction of generalized eigenprojections based on geometric measure theory

Let M denote a $\sigma$-compact locally compact metric space which satisfies certain geometrical conditions. Then for each $\sigma$-additive projection valued measure P on M there can be constructed a canonical Radon-Nikodym derivative $\Pi: \alpha \mapsto \pi_\alpha$, $\alpha \in M$, with respect to a suitable basic measure $\rho$on M. The family $(\Pi_\alpha)_{\alpha \in M}$ consists of generalized eigenprojections related to the commutative von Neumann algebra generated by the projections $P(\Delta)$, $\Delta$ a Borel set of M