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

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 strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Gain More for Less: The Surprising Benefits of QoS Management in Constrained NDN Networks

Quality of Service (QoS) in the IP world mainly manages forwarding resources, i.e., link capacities and buffer spaces. In addition, Information Centric Networking (ICN) offers resource dimensions such as in-network caches and forwarding state. In constrained wireless networks, these resources are scarce with a potentially high impact due to lossy radio transmission. In this paper, we explore the two basic service qualities (i) prompt and (ii) reliable traffic forwarding for the case of NDN. The resources we take into account are forwarding and queuing priorities, as well as the utilization of caches and of forwarding state space. We treat QoS resources not only in isolation, but correlate their use on local nodes and between network members. Network-wide coordination is based on simple, predefined QoS code points. Our findings indicate that coordinated QoS management in ICN is more than the sum of its parts and exceeds the impact QoS can have in the IP world