Duality methods for a class of quasilinear systems

Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

The new frozen spin target at MAMI

The new frozen spin polarized target for experiments at the polarized beam of the real photon facility A2 of the MAMI accelerator is described. The A2-collaboration at the Mainz Microtron MAMI is measuring photon absorption cross section using circularly and linearly polarized photons up to the energy of 1.5 GeV. The photons are produced in the’ Bremsstrahlungs’ process. In the years 2005/2006 the Crystal Ball detector with its unique capability to cope with multi photon final states was set up in Mainz. Since 2010 the experimental apparatus has been completed by a polarized target. The horizontal dilution refrigerator of the Frozen-Spin Target has been constructed and is operated in close cooperation with the Joint Institute for Nuclear Research in Dubna, Russia. The system offers the opportunity to provide longitudinally and transversely polarized protons and deuteron. In this paper the operation experience of this new Frozen-Spin Target and first results from the runs in 2010 and 2011 are presented.     

Electronic transport in graphene nanostructures on SiO2

We report two experiments on graphene nanostructures. The first was performed on a graphene nanoribbon, where the nature of electronic transport was investigated in detail. Electrons or holes are found to localize in pockets of the potential along the ribbon. Transport is governed by the joint action of localization and Coulomb interaction. The temperature-dependence of the conductance shows activated behavior at temperatures above a few Kelvin. The activation energy retraces the edges of Coulomb blockade diamonds found in nonlinear transport. In the second experiment the metallic tip of a low-temperature scanning force microscope was scanned above a graphene quantum dot. In addition to the familiar Coulomb blockade fringes, localized states are detected forming in the constrictions connecting the dot to source and drain.     

What’s New with the Neutron and Proton

The existence and importance of the proton radius puzzle, observed via a Lamb shift measurement in muonic atoms, is discussed. Possible resolutions of the puzzle are discussed. Then the broader question of the meaning of the proton radius is addressed and examples of correctly defined charge densities are presented.