Hamiltonian Study of Improved U(1U(1 Lattice Gauge Theory in Three Dimensions

A comprehensive analysis of the Symanzik improved anisotropic three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made. Monte Carlo techniques are used to obtain numerical results for the static potential, ratio of the renormalized and bare anisotropies, the string tension, lowest glueball masses and the mass ratio. Evidence that rotational symmetry is established more accurately for the Symanzik improved anisotropic action is presented. The discretization errors in the static potential and the renormalization of the bare anisotropy are found to be only a few percent compared to errors of about 20-25% for the unimproved gauge action. Evidence of scaling in the string tension, antisymmetric mass gap and the mass ratio is observed in the weak coupling region and the behaviour is tested against analytic and numerical results obtained in various other Hamiltonian studies of the theory. We find that more accurate determination of the scaling coefficients of the string tension and the antisymmetric mass gap has been achieved, and the agreement with various other Hamiltonian studies of the theory is excellent. The improved action is found to give faster convergence to the continuum limit. Very clear evidence is obtained that in the continuum limit the glueball ratio $M_{S}/M_{A}$ approaches exactly 2, as expected in a theory of free, massive bosons.Comment: 13 pages, 15 figures, submitted to Phys. Rev.

Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions

Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static quark potential, the string tension and the low-lying "glueball" spectrum.The Euclidean string tension and mass gap decrease exponentially at weakcoupling in excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure

Hemispheric shape of European and Japanese brains : 3-D MRI analysis of intersubject variability, ethnical and gender differences

Hemispheric shape is studied using magnetic resonance imaging and 3-D reconstructions in right-handed, male and female, European and Japanese subjects. Japanese hemispheres are relatively shorter, but wider than European hemispheres. Regions of maximal intersubject variability in hemispheric shape are present in the occipital and temporal lobes in each sample. Deviations from this general pattern are found in the (i) right inferior parietal lobule (European hemispheres are more variable than Japanese), (ii) lower third of the pre- and postcentral gyri (female Japanese hemispheres are less variable than the other samples), (iii) right inferior frontal gyrus (male European hemispheres are more variable than the other samples), and (iv) polar part of the frontal lobe (female European hemispheres are less variable than the other samples). The distribution of intersubject variability between the hemispheres is less asymmetric in female than male brains. Male Japanese hemispheres are shorter but wider than female Japanese hemispheres, whereas European hemispheres show the inverse gender relations. These results demonstrate that hemispheric shape shows a considerable intersubject variability, which is not randomly distributed over the cortical surface but displays distinct regions of higher variability. Despite this intersubject variability significant interethnic- and gender-related differences in hemispheric shape are present, which may be relevant if individual brains have to be warped to a single or mean reference brain or realistic brain models are to be constructed

Mapping of human and macaque sensorimotor areas by integrating architectonic, transmitter receptor, MRI and PET data.

The human and macaque sensorimotor cortex was subdivided into numerous areas by a correlative analysis based on cytoarchitectonics, myeloarchitecture and the distribution of transmitter receptors. Receptor densities and laminar distribution patterns differ not only between motor and somatosensory regions, but also between different areas within these regions of the cortex. Changes in receptor distribution often match architectonically defined borders. Receptor findings provide new criteria for a more detailed mapping in the human brain which cannot be achieved by cytoarchitectonic analysis alone. Morphological data on these areas were integrated with functional data from positron emission tomography (PET) on the basis of a recently developed computerised brain atlas. The central sulcus marks the border between (1) the agranular motor cortex with a generally low density of glutamatergic, muscarinic, GABAergic and serotoninergic receptors, and (2) the granular somatosensory cortex with higher densities of these receptors. Rostral to the primary motor cortex, 2 isocortical areas are found on the mesial cortex which probably represent the functionally defined supplementary motor areas (SMA) SMA-proper (caudally) and pre-SMA (rostrally). Below SMA-proper the areas 24d (macaque) and the caudal cingulate motor area cmc (human) are located in the cingulate sulcus. Both regions correspond to the 'posterior cingulate motor areas' of recent PET studies and to the posterior part of the agranular cingulate cortex of architectonic studies. Below pre-SMA the area 24c (macaque) and the rostral cingulate motor area cmr (human) are located in the cingulate sulcus; they correspond to the 'anterior cingulate motor areas' of recent PET observations and to the anterior part of the agranular cingulate cortex of architectonic studies. Homologous sensorimotor areas can be defined in both species on the basis of common architectonic features