Canonical forms for complex matrix congruence and *congruence

Canonical forms for congruence and *congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347-353], based on Sergeichuk's paper [Math. USSR, Izvestiya 31 (3) (1988) 481-501], which employed the theory of representations of quivers with involution. We use standard methods of matrix analysis to prove directly that these forms are canonical. Our proof provides explicit algorithms to compute all the blocks and parameters in the canonical forms. We use these forms to derive canonical pairs for simultaneous congruence of pairs of complex symmetric and skew-symmetric matrices as well as canonical forms for simultaneous *congruence of pairs of complex Hermitian matrices.Comment: 31 page

The TTC 2013 Flowgraphs Case

This case for the Transformation Tool Contest 2013 is about evaluating the scope and usability of transformation languages and tools for a set of four tasks requiring very different capabilities. One task deals with typical model-to-model transformation problem, there's a model-to-text problem, there are two in-place transformation problems, and finally there's a task dealing with validation of models resulting from the transformations. The tasks build upon each other, but the transformation case project also provides all intermediate models, thus making it possible to skip tasks that are not suited for a particular tool, or for parallelizing the work among members of participating teams.Comment: In Proceedings TTC 2013, arXiv:1311.753

Antigenic variation in African trypanosomes

Studies on Variant Surface Glycoproteins (VSGs) and antigenic variation in the African trypanosome, Trypanosoma brucei, have yielded a remarkable range of novel and important insights. The features first identified in T. brucei extend from unique to conserved-among-trypanosomatids to conserved-among-eukaryotes. Consequently, much of what we now know about trypanosomatid biology and much of the technology available has its origin in studies related to VSGs. T. brucei is now probably the most advanced early branched eukaryote in terms of experimental tractability and can be approached as a pathogen, as a model for studies on fundamental processes, as a model for studies on eukaryotic evolution or often all of the above. In terms of antigenic variation itself, substantial progress has been made in understanding the expression and switching of the VSG coat, while outstanding questions continue to stimulate innovative new approaches. There are large numbers of VSG genes in the genome but only one is expressed at a time, always immediately adjacent to a telomere. DNA repair processes allow a new VSG to be copied into the single transcribed locus. A coordinated transcriptional switch can also allow a new VSG gene to be activated without any detectable change in the DNA sequence, thereby maintaining singular expression, also known as allelic exclusion. I review the story behind VSGs; the genes, their expression and switching, their central role in T. brucei virulence, the discoveries that emerged along the way and the persistent questions relating to allelic exclusion in particular

Telling Stories - A History of Growth Management in the Gauteng Province (South Africa)

The sprawled nature of major South African cities can be attributed to a variety of reasons. The 1994 (post-apartheid) political shift, however, prompted cities and regions to plan for more equitable and accessible cities. Together with its three metropolitan municipalities, the Gauteng Province proved to be a pioneer in adopting an urban growth management approach (the Gauteng Urban Edge). Against the backdrop of a Provincial Spatial Development Framework, a Provincial Urban Edge was delineated within which local authorities were awarded the opportunity to refine a custom-made growth management strategy. In the absence of clear provincial direction, these strategies achieved various levels of success. This paper explores the urban growth management movement, its approaches and its expressions as witnessed in the case of Gauteng