Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). It defines an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. The free energy of the model is exactly calculated in the thermodynamic limit. The model describes quantum fluctuations of circle patterns and the associated discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In particular, in the quasi-classical limit the model precisely describe the geometry of integrable circle patterns with prescribed intersection angles.Comment: 26 pages, 18 color figures, minor correction

Spatially and Temporally Distinct Encoding of Muscle and Kinematic Information in Rostral and Caudal Primary Motor Cortex

The organizing principle of human motor cortex does not follow an anatomical body map, but rather a distributed representational structure in which motor primitives are combined to produce motor outputs. Electrophysiological recordings in primates and human imaging data suggest that M1 encodes kinematic features of movements, such as joint position and velocity. However, M1 exhibits well-documented sensory responses to cutaneous and proprioceptive stimuli, raising questions regarding the origins of kinematic motor representations: are they relevant in top-down motor control, or are they an epiphenomenon of bottom-up sensory feedback during movement? Here we provide evidence for spatially and temporally distinct encoding of kinematic and muscle information in human M1 during the production of a wide variety of naturalistic hand movements. Using a powerful combination of high-field functional magnetic resonance imaging and magnetoencephalography, a spatial and temporal multivariate representational similarity analysis revealed encoding of kinematic information in more caudal regions of M1, over 200 ms before movement onset. In contrast, patterns of muscle activity were encoded in more rostral motor regions much later after movements began. We provide compelling evidence that top-down control of dexterous movement engages kinematic representations in caudal regions of M1 prior to movement production

Elemental distributions within multiphase quaternary Pb chalcogenide thermoelectric materials determined through three-dimensional atom probe tomography

Nanostructured multiphase p-type lead chalcogenides have shown the highest efficiencies amongst thermoelectric materials. However, their electronic transport properties have been described assuming homogenous distribution of dopants between phases. Here, we have analyzed elemental distributions in precipitates and matrices of nanostructured multiphase quaternary Pb chalcogenides doped to levels below and above the solubility limit of the matrix, using three-dimensional atom probe tomography. We demonstrate that partitioning of sodium and selenium occur between the matrix and secondary phase in both lightly- and heavily-doped compounds and that the concentrations of sodium and selenium in precipitates are higher than those in the matrices. This can contribute to the transport properties of such multiphase compounds The sodium concentration reached ~3 at% in sulfur-rich (PbS) precipitates and no nano precipitates of Na-rich phases were observed within either phase, a result that is supported by high resolution TEM analysis, indicating that the solubility limit of sodium in PbS is much higher than previously thought. However, non-equilibrium segregation of sodium is identified at the precipitates/matrix interfaces. These findings can lead to further advances in designing and characterizing multiphase thermoelectric materials

Tritium Beta Decay, Neutrino Mass Matrices and Interactions Beyond the Standard Model

The interference of charge-changing interactions, weaker than the V-A Standard Model (SM) interaction and having a different Lorentz structure, with that SM interaction, can, in principle, produce effects near the end point of the Tritium beta decay spectrum which are of a different character from those produced by the purely kinematic effect of neutrino mass expected in the simplest extension of the SM. We show that the existence of more than one mass eigenstate can lead to interference effects at the end point that are stronger than those occurring over the entire spectrum. We discuss these effects both for the special case of Dirac neutrinos and the more general case of Majorana neutrinos and show that, for the present precision of the experiments, one formula should suffice to express the interference effects in all cases. Implications for "sterile" neutrinos are noted.Comment: 32 pages, LaTeX, 6 figures, PostScript; full discussion and changes in notation from Phys. Lett. B440 (1998) 89, nucl-th/9807057; submitted to Phys. Rev.

Neutrino Clustering in the Galaxy with a Global Monopole

In spherically symmetric, static spacetime, we show that only j=1/2 fermions can satisfy both Einstein's field equation and Dirac's equation. It is also shown that neutrinos are able to have effective masses and cluster in the galactic halo when they are coupled to a global monopole situated at the galactic core. Astronomical implications of the results are discussed.Comment: 8 pages, Revtex

Low-mass dark matter search results from full exposure of PandaX-I experiment

We report the results of a weakly-interacting massive particle (WIMP) dark matter search using the full 80.1\;live-day exposure of the first stage of the PandaX experiment (PandaX-I) located in the China Jin-Ping Underground Laboratory. The PandaX-I detector has been optimized for detecting low-mass WIMPs, achieving a photon detection efficiency of 9.6\%. With a fiducial liquid xenon target mass of 54.0\,kg, no significant excess event were found above the expected background. A profile likelihood analysis confirms our earlier finding that the PandaX-I data disfavor all positive low-mass WIMP signals reported in the literature under standard assumptions. A stringent bound on the low mass WIMP is set at WIMP mass below 10\,GeV/c$^2$, demonstrating that liquid xenon detectors can be competitive for low-mass WIMP searches.Comment: v3 as accepted by PRD. Minor update in the text in response to referee comments. Separating Fig. 11(a) and (b) into Fig. 11 and Fig. 12. Legend tweak in Fig. 9(b) and 9(c) as suggested by referee, as well as a missing legend for CRESST-II legend in Fig. 12 (now Fig. 13). Same version as submitted to PR

The Higgs resonance shape in gluon fusion: Heavy Higgs effects

We study the influence of two--loop radiative corrections of enhanced electroweak strength on Higgs production at the LHC. We consider Higgs production by the gluon fusion mechanism, with the subsequent decay of the Higgs boson into a pair of Z bosons, and incorporate the resonance shape corrections up to order $(g^2 \, m_H^2 / m_W^2)^2$. We take into account the full $g g \rightarrow Z Z$ process and the $q \bar{q} \rightarrow Z Z$ background, as well as the subsequent decay of the Z pair into leptons. We also discuss the theoretical uncertainty related to the use of the equivalence theorem in this process