A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

An extended view of the Pisces Overdensity from the SCUSS survey

SCUSS is a u-band photometric survey covering about 4000 square degree of the South Galactic Cap, reaching depths of up to 23 mag. By extending around 1.5 mag deeper than SDSS single-epoch u data, SCUSS is able to probe much a larger volume of the outer halo, i.e. with SCUSS data blue horizontal branch (BHB) stars can trace the outer halo of the Milky Way as far as 100-150 kpc. Utilizing this advantage we combine SCUSS u band with SDSS DR9 gri photometric bands to identify BHB stars and explore halo substructures. We confirm the existence of the Pisces overdensity, which is a structure in the outer halo (at around 80 kpc) that was discovered using RR Lyrae stars. For the first time we are able to determine its spatial extent, finding that it appears to be part of a stream with a clear distance gradient. The stream, which is ~5 degrees wide and stretches along ~25 degrees, consists of 20-30 BHBs with a total significance of around 6sigma over the background. Assuming we have detected the entire stream and that the progenitor has fully disrupted, then the number of BHBs suggests the original system was similar to smaller classical or a larger ultra-faint dwarf galaxy. On the other hand, if the progenitor still exists, it can be hunted for by reconstructing its orbit from the distance gradient of the stream. This new picture of the Pisces overdensity sheds new light on the origin of this intriguing system.Comment: 8 pages, 4 figures, accepted by Ap

The role of C2 in nanocrystalline diamond growth

This paper presents findings from a study of nanocrystalline diamond (NCD) growth in a microwave plasma chemical vapour deposition (CVD) reactor. NCD films were grown using Ar/H2/CH4 and He/H2/CH4 gas compositions. The resulting films were characterised using Raman spectroscopy, scanning electron microscopy and atomic force microscopy. Analysis revealed an estimated grain size of the order of 50 nm, growth rates in the range 0.01 to 0.3 um/h and sp3 and sp2 bonded carbon content consistent with that expected for NCD. The C2 Swan band was probed using cavity ring-down spectroscopy (CRDS) to measure the absolute C2 (a) number density in the plasma during diamond film growth. The number density in the Ar/H2/CH4 plasmas was in the range 2 to 4 x 10^12 cm-3, but found to be present in quantities too low to measure in the He/H2/CH4 plasmas. Optical emission spectrometry (OES) was employed to determine the relative densities of the C2 excited state (d) in the plasma. The fact that similar NCD material was grown whether using Ar or He as the carrier gas suggests that C2 does not play a major role in the growth of nanocrystalline diamond.Comment: 39 pages, 11 figure

Integrable Kondo impurity in one-dimensional q-deformed t−Jt-J models

Integrable Kondo impurities in two cases of the one-dimensional q-deformed $t-J$ models are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.Comment: 17 pages, RevTex, No figures, final version to appear in J. Phys.

Exact diagonalization of the generalized supersymmetric t-J model with boundaries

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.Comment: Latex file, 32 page

Exact solution and surface critical behaviour of open cyclic SOS lattice models

We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigen-spectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter $\lambda=\pi/L$, the finite-size corrections to the eigen-spectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, $\alpha_s=2-L/2\ell$ and $\alpha_1=1-L/\ell$, where $\ell=1,2,\cdots,L-1$ coprime to $L$. These results are in agreement with the scaling relations $\alpha_s=\alpha_b+\nu$ and $\alpha_1=\alpha_b-1$.Comment: 13 pages, LaTeX, to appear in J. Phys.

Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries

The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.Comment: Only LaTex file; no figur

Integrability of the Heisenberg Chains with Boundary Impurities and Their Bethe Ansatz

In this paper, we show the integrability of spin-1/2 XXZ Heisenberg chain with two arbitrary spin boundary Impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these models are obtained by the means of Bethe ansatz method.Comment: 13 pages, latex, no figures, to be appeared in J.Phys.

Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure