The horizontal application theory and its influence on freedom of agreement in the law of contract - a South 'African perspective

No Abstrac

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension

Experimental Evolution of Fission Yeast Genomes in Response to Repeated Environmental Changes

Evolutionary biology has mainly relied on comparative studies. Supported by the advances in genomics, several groups are now using microorganisms for experimental evolution studies to directly observe the evolution process and its genetic basis. To understand how cells adapt to an environmental stress, I developed experimental evolution assays during which fission yeast populations were repeatedly exposed to short heat-shocks, followed immediately by ideal growth conditions. Samples were frozen after each selection cycle for subsequent phenotypic and genotypic analyses. In total, I performed 10 independent such experiments for up to 150 selection cycles, including a control experiment with mock-treated samples. In all experiments, except for the mock-treated control, cells acquired a markedly increased survival to heat and other stresses within only 10-20 selection cycles, while during later cycles there was a more subtle but continuous increase in stress resistance. Surprisingly, all populations, including the mock-treated control, also evolved a more rapid re-initiation of exponential growth following heat shock and a more efficient use of the growth medium, reflected by higher biomass in stationary phase. These rapid adaptations seem to be based on DNA variations as the new phenotypes are stable. The cellular phenotypes and global regulation of gene expression of the evolved strains were determined using stress assays and DNA microarrays. Genomes of 96 strains at selected time points over the course of the evolution experiments were sequenced. We analyzed what genetic changes in regulatory and coding regions occurred in the different independent experiments, with the ultimate goal of uncovering the specific changes that are causing the striking alteration in phenotype. In collaboration with Dr. Ville Mustonen, we determined dynamic allele frequency trajectories that had swept through each population. Genetic variation among the parental cells seems to underlie the rapid initial adaptation of new phenotypes. This analysis led to the discovery of a common haplotype consisting of 9 mutations, which is likely associated with the more rapid recovery of growth after heat shock

Temperate southern Australian coastal waters are characterised by surprisingly high rates of nitrogen fixation and diversity of diazotrophs

Biological dinitrogen (N2) fixation is one mechanism by which specific microorganisms (diazotrophs) can ameliorate nitrogen (N) limitation. Historically, rates of N2 fixation were believed to be limited outside of the low nutrient tropical and subtropical open ocean; however, emerging evidence suggests that N2 fixation is also a significant process within temperate coastal waters. Using a combination of amplicon sequencing, targeting the nitrogenase reductase gene (nifH), quantitative nifH PCR, and 15N2 stable isotope tracer experiments, we investigated spatial patterns of diazotroph assemblage structure and N2 fixation rates within the temperate coastal waters of southern Australia during Austral autumn and summer. Relative to previous studies in open ocean environments, including tropical northern Australia, and tropical and temperate estuaries, our results indicate that high rates of N2 fixation (10–64 nmol L−1 d−1) can occur within the large inverse estuary Spencer Gulf, while comparatively low rates of N2 fixation (2 nmol L−1 d−1) were observed in the adjacent continental shelf waters. Across the dataset, low concentrations of NO3/NO2 were significantly correlated with the highest N2 fixation rates, suggesting that N2 fixation could be an important source of new N in the region as dissolved inorganic N concentrations are typically limiting. Overall, the underlying diazotrophic community was dominated by nifH sequences from Cluster 1 unicellular cyanobacteria of the UCYN-A clade, as well as non-cyanobacterial diazotrophs related to Pseudomonas stutzeri, and Cluster 3 sulfate-reducing deltaproteobacteria. Diazotroph community composition was significantly influenced by salinity and SiO4 concentrations, reflecting the transition from UCYN-A-dominated assemblages in the continental shelf waters, to Cluster 3-dominated assemblages in the hypersaline waters of the inverse estuary. Diverse, transitional diazotrophic communities, comprised of a mixture of UCYN-A and putative heterotrophic bacteria, were observed at the mouth and southern edge of Spencer Gulf, where the highest N2 fixation rates were observed. In contrast to observations in other environments, no seasonal patterns in N2 fixation rates and diazotroph community structure were apparent. Collectively, our findings are consistent with the emerging view that N2 fixation within temperate coastal waters is a previously overlooked dynamic and potentially important component of the marine N cycle

Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde

Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.Comment: 20 page

Insectivorous bats are less active near freeways

Traffic disturbances (i.e. pollution, light, noise, and vibrations) often extend into the area surrounding a road creating a 'road-effect zone'. Habitat within the road-effect zone is degraded or, in severe cases, completely unsuitable for wildlife, resulting in indirect habitat loss. This can have a disproportionate impact on wildlife in highly modified landscapes, where remaining habitat is scarce or occurs predominantly along roadside reserves. In this study, we investigated the road-effect zone for insectivorous bats in highly cleared agricultural landscapes by quantifying the change in call activity with proximity to three major freeways. The activity of seven out of 10 species of bat significantly decreased with proximity to the freeway. We defined the road-effect zone to be the proximity at which call activity declined by at least 20% relative to the maximum detected activity. The overall road-effect zone for bats in this region was 307 m, varying between 123 and 890 m for individual species. Given that this road-effect zone exceeds the typical width of the roadside verges (<50 m), it is possible that much of the vegetation adjacent to freeways in this and similar landscapes provides low-quality habitat for bats. Without accounting for the road-effect zone, the amount of habitat lost or degraded due to roads is underestimated, potentially resulting in the loss of wildlife, ecosystem services and key ecosystem processes (e.g. predator-prey or plant-pollinator interactions) from the landscape. We suggest all future environmental impact assessments include quantifying the road-effect zone for sensitive wildlife, in order to best plan and mitigate the impact of roads on the environment. Mitigating the effects of new and existing roads on wildlife is essential to ensure enough high-quality habitat persists to maintain wildlife populations

S-duality and 2d Topological QFT

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure

Rational Terms in Theories with Matter

We study rational remainders associated with gluon amplitudes in gauge theories coupled to matter in arbitrary representations. We find that these terms depend on only a small number of invariants of the matter-representation called indices. In particular, rational remainders can depend on the second and fourth order indices only. Using this, we find an infinite class of non-supersymmetric theories in which rational remainders vanish for gluon amplitudes. This class includes all the "next-to-simplest" quantum field theories of arXiv:0910.0930. This provides new examples of amplitudes in which rational remainders vanish even though naive power counting would suggest their presence.Comment: 10+4 pages. (v2) typos corrected, references adde