Constructing commutative semifields of square order

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semi-fields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187{196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.

The Science and Art of Light

Architecture today often is praised for its tectonics, floating volumes, and sensational, gravity-defying stunts of “starchitecture.” Yet, very so often there is a building that inspires descriptions of the sublime, the experiential, and the power of light and architecture to transcend our expectations. The new Meinel Optical Sciences Research Building, designed by Phoenix-based Richärd+Bauer for the University of Arizona, Tucson, is one of these architectural rarities. Already drawing comparisons to Louis Kahn's 1965 Salk Institute for Biological Studies in La Jolla, California, the indescribable quality of light that characterizes the best of Kahn's work also resonates in Richärd+Bauer's new building. Both an expansion and renovation of the existing College of Optical Sciences facilities, the Meinel building includes teaching and research laboratories, six floors of offices, discussion areas, conference rooms, and an auditorium. The new 47,000 square-foot cast-in-place concrete structure, wrapped on three-sides in copper-alloy panels, harmonizes with the largely brick vocabulary of the campus while reflecting the ethereal quality of the wide Arizona sky. The façade, however, is merely a prelude for what awaits inside—where light and architecture seamlessly combine to create moments of pure awe.

Mixed pixel analysis and assessment for flood mapping

The most difficult operation in flood inundation mapping using optical flood images is to map the ‘wet’ areas where trees and houses are partly covered by water. This can be referred to as a typical problem of the presence of mixed pixels in the images. A number of automatic information extracting image classification algorithms have been developed over the years for flood mapping using optical remote sensing images, with most labelling a pixel as a particular class. However, they often fail to generate reliable flood inundation mapping because of the presence of mixed pixels in the images. To solve this problem, spectral unmixing methods have been developed. In this thesis, methods for selecting endmembers and the method to model the primary classes for unmixing, the two most important issues in spectral unmixing, are investigated. We conduct comparative studies of three typical spectral unmixing algorithms, Partial Constrained Linear Spectral unmixing, Multiple Endmember Selection Mixture Analysis and spectral unmixing using the Extended Support Vector Machine method. They are analysed and assessed by error analysis in flood mapping using MODIS, Landsat and World View-2 images. The Conventional Root Mean Square Error Assessment is applied to obtain errors for estimated fractions of each primary class. Moreover, a newly developed Fuzzy Error Matrix is used to obtain a clear picture of error distributions at the pixel level. This thesis shows that the Extended Support Vector Machine method is able to provide a more reliable estimation of fractional abundances and allows the use of a complete set of training samples to model a defined pure class. Furthermore, it can be applied to analysis of both pure and mixed pixels to provide integrated hard-soft classification results. Our research also identifies and explores a serious drawback in relation to endmember selections in current spectral unmixing methods which apply fixed sets of endmember classes or pure classes for mixture analysis of every pixel in an entire image. However, as it is not accurate to assume that every pixel in an image must contain all endmember classes, these methods usually cause an over-estimation of the fractional abundances in a particular pixel. In this thesis, a subset of adaptive endmembers in every pixel is derived using the proposed methods to form an endmember index matrix. The experimental results show that using the pixel-dependent endmembers in unmixing significantly improves performance.