Chern-Simons theory and three-dimensional surfaces

There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the surface geometry. Remarkably, at a classical level, they are equivalent. In particular, it will be shown that their stress tensors differ only by a null contribution. Their Euler-Lagrange equations provide identical constraints on the normal curvature. A new identity for the Cotton tensor is associated with the triviality of the Chern-Simons theory for embedded hypersurfaces implied by this equivalence. The corresponding null surface stress capturing this information will be constructed explicitly.Comment: 10 pages, unnecessary details removed, typos fixed, references adde

Phrenology report of Francis Cotton by A.S. Hamilton, Tasmania 1856

Phrenology report in 1856 by A.S. Hamilton on Francis Cotton who assumed the name William Thompson and the dress of a 'seafaring man ... so as to prevent if possible, any personal knowledge or bias through an oral report.

Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale

The detection of sound begins when energy derived from acoustic stimuli deflects the hair bundles atop hair cells. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental challenge to the ear's high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification. Here we demonstrate that a complementary part involves the fluid-structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors stabilize the structure, further reducing the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid-structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.Comment: 21 pages, including 3 figures. For supplementary information, please see the online version of the article at http://www.nature.com/natur

Determinants of patient recruitment in a multicenter clinical trials group: trends, seasonality and the effect of large studies

BACKGROUND: We examined whether quarterly patient enrollment in a large multicenter clinical trials group could be modeled in terms of predictors including time parameters (such as long-term trends and seasonality), the effect of large trials and the number of new studies launched each quarter. We used the database of all clinical studies launched by the AIDS Clinical Trials Group (ACTG) between October 1986 and November 1999. Analyses were performed in two datasets: one included all studies and substudies (n = 475, total enrollment 69,992 patients) and the other included only main studies (n = 352, total enrollment 57,563 patients). RESULTS: Enrollment differed across different months of the year with peaks in spring and late fall. Enrollment accelerated over time (+27 patients per quarter for all studies and +16 patients per quarter for the main studies, p < 0.001) and was affected by the performance of large studies with target sample size > 1,000 (p < 0.001). These relationships remained significant in multivariate autoregressive modeling. A time series based on enrollment during the first 32 quarters could forecast adequately the remaining 21 quarters. CONCLUSIONS: The fate and popularity of large trials may determine the overall recruitment of multicenter groups. Modeling of enrollment rates may be used to comprehend long-term patterns and to perform future strategic planning

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure