Lower dimensional Yang-Mills theory as a laboratory to study the infrared regime

Lattice studies of the infrared regime of gauge theories are complicated by the required extensive limits, the performed gauge fixing and the demand for high statistics. Using a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions we show that the infrared behavior of Greens functions is both qualitatively and quantitatively similar in two, three and four spacetime dimensions. Therefore, lower dimensional lattice simulations can serve as a simplified laboratory to analyze the presently applied approximations and to obtain first results for higher correlation functions.Comment: 7 pages, 6 figures; talk presented at Lattice 200

Online privacy: towards informational self-determination on the internet : report from Dagstuhl Perspectives Workshop 11061

The Dagstuhl Perspectives Workshop "Online Privacy: Towards Informational Self-Determination on the Internet" (11061) has been held in February 6-11, 2011 at Schloss Dagstuhl. 30 participants from academia, public sector, and industry have identified the current status-of-the-art of and challenges for online privacy as well as derived recommendations for improving online privacy. Whereas the Dagstuhl Manifesto of this workshop concludes the results of the working groups and panel discussions, this article presents the talks of this workshop by their abstracts

Uncrossed cortico-muscular projections in humans are abundant to facial muscles of the upper and lower face, but may differ between sexes

Abstract : It is a popular concept in clinical neurology that muscles of the lower face receive predominantly crossed cortico-bulbar motor input, whereas muscles of the upper face receive additional ipsilateral, uncrossed input. To test this notion, we used focal transcranial magnetic brain stimulation to quantify crossed and uncrossed cortico-muscular projections to 6 different facial muscles (right and left Mm. frontalis, nasalis, and orbicularis oris) in 36 healthy right-handed volunteers (15 men, 21 women, mean age 25 years). Uncrossed input was present in 78% to 92% of the 6 examined muscles. The mean uncrossed: crossed response amplitude ratios were 0.74/0.65 in right/left frontalis, 0.73/0.59 in nasalis, and 0.54/0.71 in orbicularis oris; ANOVA p>0.05). Judged by the sizes of motor evoked potentials, the cortical representation of the 3 muscles was similar. The amount of uncrossed projections was different between men and women, since men had stronger left-to-left projections and women stronger right-to-right projections. We conclude that the amount of uncrossed pyramidal projections is not different for muscles of the upper from those of the lower face. The clinical observation that frontal muscles are often spared in central facial palsies must, therefore, be explained differently. Moreover, gender specific lateralization phenomena may not only be present for higher level behavioural functions, but may also affect simple systems on a lower level of motor hierarch

On the convergence of the Metropolis algorithm with fixed-order updates for multivariate binary probability distributions

The Metropolis algorithm is arguably the most fundamental Markov chain Monte Carlo (MCMC) method. But the algorithm is not guaranteed to converge to the desired distribution in the case of multivariate binary distributions (e.g., Ising models or stochastic neural networks such as Boltzmann machines) if the variables (sites or neurons) are updated in a fixed order, a setting commonly used in practice. The reason is that the corresponding Markov chain may not be irreducible. We propose a modified Metropolis transition operator that behaves almost always identically to the standard Metropolis operator and prove that it ensures irreducibility and convergence to the limiting distribution in the multivariate binary case with fixed-order updates. The result provides an explanation for the behaviour of Metropolis MCMC in that setting and closes a long-standing theoretical gap. We experimentally studied the standard and modified Metropolis operator for models were they actually behave differently. If the standard algorithm also converges, the modified operator exhibits similar (if not better) performance in terms of convergence speed