Geometrical Frustration: A Study of 4d Hard Spheres

The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio

On colouring point visibility graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4

Pathotype-specific QTL for stem rust resistance in Lolium perenne

A genetic map populated with RAD and SSR markers was created from F1 progeny of a stem rust-susceptible and stem rust-resistant parent of perennial ryegrass (Lolium perenne). The map supplements a previous map of this population by having markers in common with several other Lolium spp. maps including EST-SSR anchor markers from a consensus map published by other researchers. A QTL analysis was conducted with disease severity and infection type data obtained by controlled inoculation of the population with each of two previously characterized pathotypes of Puccinia graminis subsp. graminicola that differ in virulence to different host plant genotypes in the F1 population. Each pathotype activated a specific QTL on one linkage group (LG): qLpPg1 on LG7 for pathotype 101, or qLpPg2 on LG1 for pathotype 106. Both pathotypes also activated a third QTL in common, qLpPg3 on LG6. Anchor markers, present on a consensus map, were located in proximity to each of the three QTL. These QTL had been detected also in previous experiments in which a genetically heterogeneous inoculum of the stem rust pathogen activated all three QTL together. The results of this and a previous study are consistent with the involvement of the pathotype-specific QTL in pathogen recognition and the pathotype-nonspecific QTL in a generalized resistance response. By aligning the markers common to other published reports, it appears that two and possibly all three of the stem rust QTL reported here are in the same general genomic regions containing some of the L. perenne QTL reported to be activated in response to the crown rust pathogen (P. coronata).Keywords: Ryegrass population, Fescue festuca pratensis, Disease resistance, Puccinia coronata resistance, SSR markers, Multiflorum lam., Crown rust, Self incompatibility, F-SP Lolii, Linkage mapKeywords: Ryegrass population, Fescue festuca pratensis, Disease resistance, Puccinia coronata resistance, SSR markers, Multiflorum lam., Crown rust, Self incompatibility, F-SP Lolii, Linkage ma

Effects of the Mycoparasite Sphaerellopsis filum on Overwintering Survival of Stem Rust in Perennial Ryegrass

Sphaerellopsis filum is a mycoparasite of Puccinia graminis subsp. graminicola, a rust fungus that causes widespread crop damage on perennial ryegrass grown for seed. In observations taken over the winter months, S. filum was found naturally colonizing 2% of P. graminis subsp. graminicola uredinia on first-year plantings and 25% of the uredinia on second-year plantings of perennial ryegrass. In controlled experiments conducted in glasshouses and growth chambers, S. filum applied to rust-inoculated plants reduced the lifetime spore production of P. graminis subsp. graminicola pustules by half, from 39,000 to 18,000 spores/pustule. Mist duration, temperature, and P. graminis subsp. graminicola pustule age at the time of S. filum inoculation had significant effects on the proportion of P. graminis subsp. graminicola pustules infected by S. filum. Fifty percent of all P. graminis subsp. graminicola pustules were infected when S. filum was inoculated onto erumpent pustules and incubated above 5°C for 48 h while exposed to mist. Plants inoculated with both fungi under controlled conditions and then planted into the field had a significantly greater proportion of P. graminis subsp. graminicola pustules infected with S. filum, and a significantly reduced P. graminis subsp. graminicola overwintering population, compared with plants inoculated with P. graminis subsp. graminicola only. First-year stands of perennial ryegrass treated in the field with monthly applications of S. filum had more than 10 times the proportion of pustules infected with S. filum and 50% less P. graminis subsp. graminicola disease compared with the nontreated controls. In comparison, plants with one application of fungicide during the winter had 98% lower P. graminis subsp. graminicola severity than the P. graminis subsp. graminicola-only control There were no effects of S. filum or fungicide application on rust severity in 2- or 3-year-old perennial ryegrass stands

Infection of Brachypodium distachyon by Formae Speciales of Puccinia graminis: Early Infection Events and Host-Pathogen Incompatibility

Puccinia graminis causes stem rust, a serious disease of cereals and forage grasses. Important formae speciales of P. graminis and their typical hosts are P. graminis f. sp. tritici (Pg-tr) in wheat and barley, P. graminis f. sp. lolii (Pg-lo) in perennial ryegrass and tall fescue, and P. graminis f. sp. phlei-pratensis (Pg-pp) in timothy grass. Brachypodium distachyon is an emerging genetic model to study fungal disease resistance in cereals and temperate grasses. We characterized the P. graminis- Brachypodium pathosystem to evaluate its potential for investigating incompatibility and non-host resistance to P. graminis. Inoculation of eight Brachypodium inbred lines with Pg-tr, Pg-lo or Pg-pp resulted in sporulating lesions later accompanied by necrosis. Histological analysis of early infection events in one Brachypodium inbred line (Bd1-1) indicated that Pg-lo and Pg-pp were markedly more efficient than Pg-tr at establishing a biotrophic interaction. Formation of appressoria was completed (60–70% of germinated spores) by 12 h post-inoculation (hpi) under dark and wet conditions, and after 4 h of subsequent light exposure fungal penetration structures (penetration peg, substomatal vesicle and primary infection hyphae) had developed. Brachypodium Bd1-1 exhibited pre-haustorial resistance to Pg-tr, i.e. infection usually stopped at appressorial formation. By 68 hpi, only 0.3% and 0.7% of the Pg-tr urediniospores developed haustoria and colonies, respectively. In contrast, development of advanced infection structures by Pg-lo and Pg-pp was significantly more common; however, Brachypodium displayed post-haustorial resistance to these isolates. By 68 hpi the percentage of urediniospores that only develop a haustorium mother cell or haustorium in Pg-lo and Pg-pp reached 8% and 5%, respectively. The formation of colonies reached 14% and 13%, respectively. We conclude that Brachypodium is an apt grass model to study the molecular and genetic components of incompatiblity and non-host resistance to P. graminis

On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States

We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in \C^n which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.Comment: 29 pages, LaTe

The Use and Role of Predictive Systems in Disease Management

Disease predictive systems are intended to be management aids. With a few exceptions, these systems typically do not have direct sustained use by growers. Rather, their impact is mostly pedagogic and indirect, improving recommendations from farm advisers and shaping management concepts. The degree to which a system is consulted depends on the amount of perceived new, actionable information that is consistent with the objectives of the user. Often this involves avoiding risks associated with costly disease outbreaks. Adoption is sensitive to the correspondence between the information a system delivers and the information needed to manage a particular pathosystem at an acceptable financial risk; details of the approach used to predict disease risk are less important. The continuing challenge for researchers is to construct tools relevant to farmers and their advisers that improve upon their current management skill. This goal requires an appreciation of growers’ decision calculus in managing disease problems and, more broadly, their overall farm enterprise management.Keywords: plant pathogen, IPM adoption, diffusion theory, disease control, disease forecastin