High-resolution three-dimensional views of membrane-associated clathrin and cytoskeleton in critical-point-dried macrophages.

We obtained high-resolution topographical information about the distribution of clathrin and cytoskeletal filaments on cytoplasmic membrane surfaces of macrophages spreading onto glass coverslips by both critical-point drying of broken-open cells and preparation of rotary platinum replicas. Irregular patches of the adherent ventral surface of the plasma membrane were exposed in these cells, and large areas of these exposed membranes were covered with clathrin-coated patches, pits, and vesicles. Various amounts of cytoskeleton were attached to the plasma membranes of these spreading cells, either as distinct starlike foci, or as individual filaments and bundles radiating out from the cytoskeletal meshwork. In newly adherent cells a well developed Golgi-GERL complex, characterized by smooth, dish-like cisternae associated with rough endoplasmic reticulum, was observed. There were many coated vesicles budding off from the Golgi cisternae, and these were predominantly of the large type (150 nm) usually associated with the plasma membrane. In critical-point-dried samples, both cytoskeleton and membranes were preserved in detail comparable to that of quick-frozen samples, after appropriate fixation. Rotary replication of critical-point-dried cells provides a rapid, easily controlled, and generally easy to perform method for obtaining samples of exposed membrane large enough to permit quantification of membrane-associated clathrin and cytoskeleton under various experimental conditions

Validity of the expected Euler characteristic heuristic

We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f^x, derived from the original process f.Comment: Published at http://dx.doi.org/10.1214/009117905000000099 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial

We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our results to exceptional Jacobi polynomials.Comment: 15 pages; validity of the conjecture was extende

Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

Out-of-plane dielectric constant and insulator-superconductor transition in Bi_2Sr_2Dy_{1-x}Er_xCu_2O_8 single crystals

The out-of-plane dielectric constant of the parent insulator of the high-temperature superconductor Bi_2Sr_2(Dy,Er)Cu_2O_8 was measured and analysed from 80 to 300 K in the frequency range of 10^6-10^9 Hz. All the samples were found to show a fairly large value of 10-60, implying some kind of charge inhomogeneity in the CuO_2 plane. Considering that the superconducting sample Bi_2Sr_2(Ca,Pr)Cu_2O_8 also shows a similar dielectric constant, the charge inhomogeneity plays an important role in the insulator-superconductor transition.Comment: RevTex4 format, 5 pages, 3 figures, submitted to J. Phys. Condens. Ma

Absence of lattice strain anomalies at the electronic topological transition in zinc at high pressure

High pressure structural distortions of the hexagonal close packed (hcp) element zinc have been a subject of controversy. Earlier experimental results and theory showed a large anomaly in lattice strain with compression in zinc at about 10 GPa which was explained theoretically by a change in Fermi surface topology. Later hydrostatic experiments showed no such anomaly, resulting in a discrepancy between theory and experiment. We have computed the compression and lattice strain of hcp zinc over a wide range of compressions using the linearized augmented plane wave (LAPW) method paying special attention to k-point convergence. We find that the behavior of the lattice strain is strongly dependent on k-point sampling, and with large k-point sets the previously computed anomaly in lattice parameters under compression disappears, in agreement with recent experiments.Comment: 9 pages, 6 figures, Phys. Rev. B (in press

Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2