Identities and exponential bounds for transfer matrices

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity, If the block tridiagonal matrix is invertible, it is shown that half of the singular values of the transfer matrix have a lower bound exponentially large in the length of the chain, and the other half have an upper bound that is exponentially small. This is a consequence of a theorem by Demko, Moss and Smith on the decay of matrix elements of inverse of banded matrices.Comment: To appear in J. Phys. A: Math. and Theor. (Special issue on Lyapunov Exponents, edited by F. Ginelli and M. Cencini). 16 page

Determinants of Block Tridiagonal Matrices

An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).Comment: 8 pages, final form. To appear on Linear Algebra and its Application

Hedin's equations and enumeration of Feynman's diagrams

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GW approximation.Comment: Revised published version, 3 pages, no figure

Fundamental structure of steady plastic shock waves in metals

The propagation of steady plane shock waves in metallic materials is considered. Following the constitutive framework adopted by R. J. Clifton [Shock Waves and the Mechanical Properties of Solids, edited by J. J. Burke and V. Weiss (Syracuse University Press, Syracuse, N.Y., 1971), p. 73] for analyzing elastic–plastic transient waves, an analytical solution of the steady state propagation of plastic shocks is proposed. The problem is formulated in a Lagrangian setting appropriate for large deformations. The material response is characterized by a quasistatic tensile (compression) test (providing the isothermal strain hardening law). In addition the elastic response is determined up to second order elastic constants by ultrasonic measurements. Based on this simple information, it is shown that the shock kinetics can be quite well described for moderate shocks in aluminum with stress amplitude up to 10 GPa. Under the later assumption, the elastic response is assumed to be isentropic, and thermomechanical coupling is neglected. The model material considered here is aluminum, but the analysis is general and can be applied to any viscoplastic material subjected to moderate amplitude shocks. Comparisons with experimental data are made for the shock velocity, the particle velocity and the shock structure. The shock structure is obtained by quadrature of a first order differential equation, which provides analytical results under certain simplifying assumptions. The effects of material parameters and loading conditions on the shock kinetics and shock structure are discussed. The shock width is characterized by assuming an overstress formulation for the viscoplastic response. The effects on the shock structure of strain rate sensitivity are analyzed and the rationale for the J. W. Swegle and D. E. Grady [J. Appl. Phys. 58, 692 (1985)] universal scaling law for homogeneous materials is explored. Finally, the ability to deduce information on the viscoplastic response of materials subjected to very high strain rates from shock wave experiments is discussed

Intima-Media Thickness: Setting a Standard for a Completely Automated Method of Ultrasound Measurement

The intima - media thickness (IMT) of the common carotid artery is a widely used clinical marker of severe cardiovascular diseases. IMT is usually manually measured on longitudinal B-Mode ultrasound images. Many computer-based techniques for IMT measurement have been proposed to overcome the limits of manual segmentation. Most of these, however, require a certain degree of user interaction. In this paper we describe a new completely automated layers extraction (CALEXia) technique for the segmentation and IMT measurement of carotid wall in ultrasound images. CALEXia is based on an integrated approach consisting of feature extraction, line fitting, and classification that enables the automated tracing of the carotid adventitial walls. IMT is then measured by relying on a fuzzy K-means classifier. We tested CALEXia on a database of 200 images. We compared CALEXia performances to those of a previously developed methodology that was based on signal analysis (CULEXsa). Three trained operators manually segmented the images and the average profiles were considered as the ground truth. The average error from CALEXia for lumen - intima (LI) and media - adventitia (MA) interface tracings were 1.46 ± 1.51 pixel (0.091 ± 0.093 mm) and 0.40 ± 0.87 pixel (0.025 ± 0.055 mm), respectively. The corresponding errors for CULEXsa were 0.55 ± 0.51 pixels (0.035 ± 0.032 mm) and 0.59 ± 0.46 pixels (0.037 ± 0.029 mm). The IMT measurement error was equal to 0.87 ± 0.56 pixel (0.054 ± 0.035 mm) for CALEXia and 0.12 ± 0.14 pixel (0.01 ± 0.01 mm) for CULEXsa. Thus, CALEXia showed limited performance in segmenting the LI interface, but outperformed CULEXsa in the MA interface and in the number of images correctly processed (10 for CALEXia and 16 for CULEXsa). Based on two complementary strategies, we anticipate fusing them for further IMT improvement

Strong exciton binding in quantum structures through remote dielectric confinement

We propose a new type of hybrid systems formed by conventional semiconductor nanostructures with the addition of remote insulating layers, where the electron-hole interaction is enhanced by combining quantum and dielectric confinement over different length scales. Due to the polarization charges induced by the dielectric mismatch at the semiconductor/insulator interfaces, we show that the exciton binding energy can be more than doubled. For conventional III-V quantum wires such remote dielectric confinement allows exciton binding at room temperature.Comment: 4 pages, 3 PostScript figures embedded, best printed in color. Uses RevTex, multicol, and psfig styles. To appear in Phys. Rev. Let

On conformally recurrent manifolds of dimension greater than 4

Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak's theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is nonzero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel - Debever - Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.Comment: Title changed and typos corrected. 14 page

Spatial Correlation Robust Inference with Errors in Location or Distance

This paper presents results from a Monte Carlo study concerning inference with spatially dependent data. We investigate the impact of location/distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances. Nonparametric estimators are quite robust to such errors, method of moments estimators perform surprisingly well, and MLE estimators are very poor. We also present and evaluate a specification test based on a parametric bootstrap that has good power properties for the types of measurement error we consider.