Covariances in Pólya urn schemes

By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.

METAMERISM INDEX OF LED LIGHT ON HALFTONE COLOUR IMAGES

Skin face detection in photo imaging, is an important component of systems for detecting similarities in visual perception, tracing faces through illumination and metamerism. This paper presents an evaluation of the skin perception under standardized conditions of varied light sources: cool-white fluorescent “store light”, 6500K fluorescent “daylight”, and incandescent “home light”, Led light 6500 K, 2700K, 4000K CCT. In cases where the discrepancy is large, the resulting index of metamerism can be misleading. A small index of metamerism and a large change of color under illuminant metamerism has a different interpretation than what is perceived. This has been demonstrated through small colour variations in print through CMYK colors. The implication is that particular indices of metameric should only account for a limited range under different light conditions. The method used in this paper is based on visual perception, which aim to work with a wide variety of individuals, under varying lighting conditions under the influence of standard daylight, but in this case we also used the Led light 6500K correlated colour temperature, and variations of skin color tones, comparing the illuminant metamerism of visual perception based on different reflectance power distributions (SPDs).

Performance Enhancement of Ultra-Thin Nanowire Array Solar Cells by Bottom Reflectivity Engineering

A bottom-reflectivity-enhanced ultra-thin nanowire array solar cell is proposed and studied by 3D optoelectronic simulations. By inserting a small-index MgF2 layer between the polymer and substrate, the absorption is significantly improved over a broad wavelength range due to the strong reabsorption of light reflected at the polymer/MgF2 interface. With a 5 nm-thick MgF2 layer, the GaAs nanowire array solar cell with a height of 0.4–1 μm yields a remarkable conversion efficiency ranging from 14% to 15.6%, significantly higher than conventional structures with a much larger height. Moreover, by inserting the MgF2 layer between the substrate and a part of the nanowire, in addition to between the substrate and polymer, the absorption of substrate right below the nanowire is further suppressed, leading to an optimal efficiency of 15.9%, 18%, and 5.4% for 1 μm-high GaAs, InP, and Si nanowire solar cells, respectively. This work provides a simple and universal way to achieve low-cost high-performance nanoscale solar cells.

The Asaeda–Haagerup fusion categories

The classification of subfactors of small index revealed several new subfactors. The first subfactor above index 4, the Haagerup subfactor, is increasingly well understood and appears to lie in a (discrete) infinite family of subfactors where the \mathbb{Z} /3 \mathbb{Z} symmetry is replaced by other finite abelian groups. The goal of this paper is to give a similarly good description of the Asaeda–Haagerup subfactor which emerged from our study of its Brauer–Picard groupoid. More specifically, we construct a new subfactor {\mathcal{S}} which is a \mathbb{Z} /4 \mathbb{Z} \times \mathbb{Z} /2 \mathbb{Z} analogue of the Haagerup subfactor and we show that the even parts of the Asaeda–Haagerup subfactor are higher Morita equivalent to an orbifold quotient of {\mathcal{S}} . This gives a new construction of the Asaeda–Haagerup subfactor which is much more symmetric and easier to work with than the original construction. As a consequence, we can settle many open questions about the Asaeda–Haagerup subfactor: calculating its Drinfeld center, classifying all extensions of the Asaeda–Haagerup fusion categories, finding the full higher Morita equivalence class of the Asaeda–Haagerup fusion categories, and finding intermediate subfactor lattices for subfactors coming from the Asaeda–Haagerup categories. The details of the applications will be given in subsequent papers.

Relative Difference Sets Partitioned by Cosets

We explore classical (relative) difference sets intersected with the cosets of a subgroup of small index. The intersection sizes are governed by quadratic Diophantine equations. Developing the intersections in the subgroup yields an interesting class of group divisible designs. From this and the Bose-Shrikhande-Parker construction, we obtain some new sets of mutually orthogonal latin squares. We also briefly consider optical orthogonal codes and difference triangle systems.

On products of groups with abelian subgroups of small index

It is proved that every group of the form