Dependent Dirichlet Process Rating Model (DDP-RM)

Typical IRT rating-scale models assume that the rating category threshold parameters are the same over examinees. However, it can be argued that many rating data sets violate this assumption. To address this practical psychometric problem, we introduce a novel, Bayesian nonparametric IRT model for rating scale items. The model is an infinite-mixture of Rasch partial credit models, based on a localized Dependent Dirichlet process (DDP). The model treats the rating thresholds as the random parameters that are subject to the mixture, and has (stick-breaking) mixture weights that are covariate-dependent. Thus, the novel model allows the rating category thresholds to vary flexibly across items and examinees, and allows the distribution of the category thresholds to vary flexibly as a function of covariates. We illustrate the new model through the analysis of a simulated data set, and through the analysis of a real rating data set that is well-known in the psychometric literature. The model is shown to have better predictive-fit performance, compared to other commonly used IRT rating models.Comment: 2 tables and 5 figure

ASCA Slew Survey

We are systematically analyzing ASCA GIS data taken during the satellite attitude maneuver operation. Our motivation is to search for serendipitous hard X-ray sources and make the ASCA Slew Survey catalog. During its operational life from 1993 February to 2000 July, ASCA carried out more than 2,500 maneuver operations, and total exposure time during the maneuver was ~415 ksec after data screening. Preliminary results are briefly reported.Comment: Proceedings for "X-ray surveys in the light of new observations", Santander (Spain), 2002 September. 1 pag

Index theorem for topological heterostructure systems

We apply the Niemi-Semenoff index theorem to an s-wave superconductor junction system attached with a magnetic insulator on the surface of a three-dimensional topological insulator. We find that the total number of the Majorana zero energy bound states is governed not only by the gapless helical mode but also by the massive modes localized at the junction interface. The result implies that the topological protection for Majorana zero modes in class D heterostructure junctions may be broken down under a particular but realistic condition.Comment: 8 pages, 3 figure

Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach

Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)]. A standard approach for the calculation of topological invariants associated with defects is to deal with the spatial inhomogeneity raised by defects within a semiclassical approximation. In this paper, we propose a full quantum formulation for the topological invariants characterizing line defects in three-dimensional insulators with no symmetry by using the Green's function method. On the basis of the full quantum treatment, we demonstrate the existence of a nontrivial topological invariant in the topological insulator-ferromagnet tri-junction systems, for which a semiclassical approximation fails to describe the topological phase. Also, our approach enables us to study effects of electron-electron interactions and impurity scattering on topological insulators with spatial inhomogeneity which gives rise to the Axion electrodynamics responses.Comment: 15 pages, 3 figure

Nonlinear Generalizations of Tucker's Theorem on Inequality Systems

This note is to prove Tucker's theorem on linear inequalities based on the proof method of minimax theorems which uses Kakutani's fixed point theorem. One device is necessary to convert the minimax theorems to Tucker's formulation. This is a slight restriction on the image sets when creating a set-valued map. We also present nonlinear generalizations of Tucker's theorem employing the same method. All we need is that the set of variable values for which an objective function attains its maximum is convex. This objective function is a convex combination of functions. We also present a proof of the fact that a local characterization of inequality systems, when a given mapping is differentiable, can be made global provided the mapping is concave