Generalized nuclearity conditions and the split property in quantum field theory

Generalized nuclearity conditions that are applicable in arbitrary superselection sectors of a quantum field theory and to theories with a maximal temperature are discussed. They are shown to imply the (distal) split property and to impose specific restrictions on the spectral properties of modular operators associated with local algebras and vectors of compact energy support.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

Bounded perturbations of dynamics

If and are one-parameter automorphism groups of a von Neumann algebraM is said to be a bounded perturbation of if _t – _t 0 ast0. We give a complete characterization of the bounded perturbations of . In particular, we show that if can be implemented by a strongly continuous one-parameter group with self-adjoint generator (Hamiltonian)H, then can be implemented in the same way and the corresponding HamiltonianH can be chosen to be of the formH=VHV ^–1+h, whereV is a unitary ofM andh=h*M.On leave of absence from II. Institut für Theoretische Physik, Universität Hamburg, D-2000 Hamburg 50, Federal Republic of Germany     

Lifetimes of charged and neutralD mesons

We have measured the lifetimes of hadronically produced charged and neutralD mesons using silicon microstrip detectors and an active silicon target in the NA32 spectrometer at the CERN SPS. We obtainτ _D± = (10.9± _1.5 ^1.9 )·10^?13s andτ _D ^(?)10 = (4.2±0.5)·10^?13s based on 59 and 90 fully reconstructed decays respectively, giving a ratioτ _D±/τ _D ^(?)10 of 2.6 ±0.5.     

Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

Metal–Polymer Hybrid Nanoparticles for Correlative High‐Resolution Light and Electron Microscopy

The combination of fluorescence microscopy and electron microscopy promises a deeper insight into the ultrastructural features of cell organelles, e.g., after drug administration. Both methods complement each other and provide, as a correlative approach, a keen insight into the fate of nanoparticles within the cell. Moreover, it represents a promising tool to determine alterations of the cellular environment as a response to particle uptake. However, the availability of suitable correlative markers is mandatory for such correlative approaches. In this contribution, the utilization of poly(ethylene imine) based metal–polymer hybrid particles labeled with small gold nanoparticles and Rhodamine B facilitating the observation of the particles by means of fluorescence as well as by transmission electron microscopy is suggested. Correlative light and electron microscopy is used to study uptake and intracellular fusion processes of endosomal/lysosomal structures.