Deformations of symmetric CMC surfaces in the 3-sphere

In this paper we numerically construct CMC deformations of the Lawson minimal surfaces $\xi_{g,1}$ using a spectral curve and a DPW approach to CMC surfaces in spaceforms.Comment: 17 pages, 5 figure

The Violation of Representation: Art, Argento and the Rape-Revenge Film

Considering the moral controversies surrounding films such as I Spit on Your Grave (Meir Zarch, 1976) and Baise-Moi (Virginie Despentes and Coralie Trinh-Thi, 2000), the rape-revenge film is often typecast as gratuitous and regressive. But far from dismissing rape-revenge in her foundational book Men, Women and Chain Saws: Gender in the Modern Horror Film (1992), Carol J. Clover suggests that these movies permit unique insight into the representation of gendered bodies on screen. In Images of Rape: The 'Heroic' Tradition and Its Alternatives(1999), art historian Diane Wolfthal demonstrates that contradictory representations of sexual violence co-existed long before the advent of the cinematic image, and a closer analysis of films that fall into the rape-revenge category reveals that they too resist a singular classification. Despite the broadness of the rape-revenge category, however, these films predominantly involve some kind of visceral skirmish between victim/villain, good/evil, female/male and right/wrong, and the desire for vengeance upon which their narratives rely provides a widely shared melodramatic foundation. The ideological leanings, thematic cores and moral messages of any given text hinge upon its representational mechanics-in this instance, how film formally constructs meaning-and can thus shift radically from text to text, despite the uniformity of the trope itself

Constant mean curvature surfaces based on fundamental quadrilaterals

We describe the construction of CMC surfaces with symmetries in $\mathbb S^3$ and $\mathbb R^3$ using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials.Comment: 22 pages, 30 figure

Phenotypic response to selection for protein in maize kernels

Long-term, divergent selection for protein concentration in maize grain has been conducted at the University of Illinois since 1896. Grain protein concentration in maize and other cereal crops is strongly associated with productivity, nutritional quality, and processing characteristics. Although grain protein concentration responds to selection in maize, the genetic basis for that response is largely unknown. The proteins that responded most to selection were the alpha-zeins, a class of the abundant seed storage proteins that are lacking in several essential amino acids. Thus, efforts to increase the nutritional quality of maize grain have focused on decreasing the zein proteins. The genomic organization of zein genes, however, limits genetic analysis and the effectiveness of selection for variation in zein accumulation. Developing a method to directly monitor changes in alpha zein accumulation while concurrently maintaining the accumulation of other seed proteins could enable more effective selection for improvements in yield, nutrition, and sustainability. The Illinois Long-Term Selection Experiment (ILTSE) was remarkably successful in changing the protein concentration in the grain. The Illinois High Protein (IHP) population is the only original population still undergoing selection. IHP has now undergone 116 cycles of selection, and represents the biological extreme for protein concentration in maize kernels. Although IHP does not appear to be responding to selection, the variance for grain nitrogen concentration has not decreased. Response to selection has also ceased in Illinois Reverse High Protein (IRHP), but the phenotypic variance in this population was low. Two new IRHP populations were started from IHP cycle 100, and despite no further response to forward selection in IHP, response to reverse selection is documented here. IRHP2 has shown a more dramatic response to selection than has IRHP3, but a genotyping analysis shows patterns that might suggest an unintentional cross with the original IRHP. IHP continues to be grown to serve as a control for two new reverse selection populations, the first replicated aspect of this study since its inception. The biological extreme for low protein was achieved by the Illinois Low Protein (ILP) population 50 years ago, and this feat has since been replicated by the Illinois Reverse High Protein (IRHP) population despite initial selection for 47 years for higher protein concentration. Selection has ceased in both of these populations. The Illinois Reverse Low Protein (IRLP) population continues to slowly respond to selection at a rate similar to what IHP did. In addition to tracking the phenotypic response to selection, recent advances in technology allowed for genotyping a representative subset of the ILTSE populations genome-wide. Analyses revealed relatedness and genetic structuring within the protein populations which mirrored the protein concentration phenotype. A transgenic reporter line was utilized to visualize the accumulation of a specific alpha-zein. The red fluorescent protein (RFP) gene was attached to the 3’ end of the Floury2 (FL2) gene with its native promoter, allowing a quick, nondestructive assessment of the accumulation of that alpha-zein in a maize kernel. This FL2-RFP reporter line has been used to document variation due to genetic, epigenetic, and environmental sources. A first experiment with a set of hybrids grown in paired high and low nitrogen environments showed that FL2-RFP responded to available nitrogen supply in a similar manner to protein concentration. The relationships between FL2-RFP accumulation and six other important agronomic traits was investigated in a population of hybrids that varied greatly for alpha-zein accumulation. The FL2-RFP phenotype showed the most variation among the measured traits, but surprisingly was not strongly correlated with either grain protein concentration or other agronomic traits. These results suggest that selection for changes in FL2-RFP accumulation can be achieved without affecting other aspects of hybrid performance. Finally, observations from prior studies with protein selection in the Illinois Long-Term Selection Experiment and other work raise the possibility that epigenetic factors may contribute to phenotypic variation in alpha-zein accumulation. This hypothesis was directly addressed through the creation and analysis of a population where the FL2-RFP reporter was introgressed into the B73 inbred line and crossed to a B73 near-isogenic line harboring the mediator of paramutation (mop1) mutation. The mop1 gene encodes the RNA-dependent RNA polymerase required for RNA-dependent DNA methylation, and loss of mop1 was predicted to alter known epigenetic marks. This population of “epigenetic near-isogenic lines” (epiNILs) produced a high frequency of phenotypic variants with reduced fitness that were not observed in the control population, including significant variation in FL2-RFP intensity. Selection was largely effective in stabilizing these phenotypic variants. High-density genotyping of 90 epi-NILs revealed all were indeed like B73 except for two genomic regions around mop1and FL2-RFP. Hybrids were created with these epiNILs to establish a heritability estimate for the FL2-RFP trait in this population. A strong narrow-sense heritability estimate of 0.84 was obtained for the FL2-RFP phenotype. Largely, the FL2-RFP phenotype explained most of the variation present when all three red, green, and blue channels were averaged, but this composite phenotype was not highly correlated with grain protein concentration; instead, a contrast between the green and red channels correlated more strongly with the total protein concentration. The FL2-RFP reporter could be used in breeding programs to increase the number of individuals which are monitored for alpha-zein accumulation. The insights into the makeup of the FL2-RFP phenotype allow for selection indices to be built and utilized differently based on the goals of that breeding program