\alpha_S from LEP

Recent results on measurements of the strong coupling $\alpha_S$ from LEP are reported. These include analyses of the 4-jet rate using the Durham or Cambridge algorithm, of hadronic $Z^0$ decays with hard final state photon radiation, of scaling violations of the fragmentation function, of the longitudinal cross section, of the $Z^0$ lineshape and of hadronic $\tau$ lepton decays.Comment: 3 pages, 2 figures, invited parallel talk at EPS HEP 2007 Manchester, added comment on estimation of theory error in section 5 and new ref [10

Power Corrections in Electron-Positron Annihilation: Experimental Review

Experimental studies of power corrections with e+e- data are reviewed. An overview of the available data for jet and event shape observables is given and recent analyses based on the Dokshitzer-Marchesini-Webber (DMW) model of power corrections are summarised. The studies involve both distributions of the observables and their mean values. The agreement between perturbative QCD combined with DMW power corrections and the data is generally good, and the few exceptions are discussed. The use of low energy data sets highlights deficiencies in the existing calculations for some observables. A study of the finiteness of the physical strong coupling at low energies using hadronic $\tau$ decays is shown.Comment: 10 pages, 6 figures, 2 tables, contribution to FRIF workshop on first principles non-perturbative QCD of hadron jets (Jan 2006

Review of alpha_s Measurements

We present a review of measurements of alpha_S. The individual measurements are discussed and intermediate averages for classes of related measurements are found. The final average is built using the intermediate values. Correlations are treated consistently. The ICHEP 2006 world average is alpha_S(M_Z) = 0.1175 +/- 0.0011 dominated by the recent result from lattice QCD.Comment: 4 pages, 1 figure, 1 table, contribution to ICHEP 2006 (Moscow) proceeding

On the Degree of Ill-Posedness of Multi-Dimensional Magnetic Particle Imaging

Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has received much interest in the literature. In this work, we study one prototypical mathematical model in multi-dimension, i.e., the equilibrium model, which formulates the problem as a linear Fredholm integral equation of the first kind. We analyze the degree of ill-posedness of the associated linear integral operator by means of the singular value decay estimate for Sobolev smooth bivariate functions, and discuss the influence of various experimental parameters. In particular, applied magnetic fields with a field free point and a field free line are distinguished. The study is complemented with extensive numerical experiments.Comment: 20 pages, 6 figure