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

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

Development of a RAD-Seq Based DNA Polymorphism Identification Software, AgroMarker Finder, and Its Application in Rice Marker-Assisted Breeding

Abstract Rapid and accurate genome-wide marker detection is essential to the marker-assisted breeding and functional genomics studies. In this work, we developed an integrated software, AgroMarker Finder (AMF: http://erp.novelbio.com/AMF), for providing graphical user interface (GUI) to facilitate the recently developed restriction-site associated DNA (RAD) sequencing data analysis in rice. By application of AMF, a total of 90,743 high-quality markers (82,878 SNPs and 7,865 InDels) were detected between rice varieties JP69 and Jiaoyuan5A. The density of the identified markers is 0.2 per Kb for SNP markers, and 0.02 per Kb for InDel markers. Sequencing validation revealed that the accuracy of genome-wide marker detection by AMF is 93%. In addition, a validated subset of 82 SNPs and 31 InDels were found to be closely linked to 117 important agronomic trait genes, providing a basis for subsequent marker-assisted selection (MAS) and variety identification. Furthermore, we selected 12 markers from 31 validated InDel markers to identify seed authenticity of variety Jiaoyuanyou69, and we also identified 10 markers closely linked to the fragrant gene BADH2 to minimize linkage drag for Wuxiang075 (BADH2 donor)/Jiachang1 recombinants selection. Therefore, this software provides an efficient approach for marker identification from RAD-seq data, and it would be a valuable tool for plant MAS and variety protection

Genetic dissection of fruit quality traits in the octoploid cultivated strawberry highlights the role of homoeo-QTL in their control

Fruit quality traits are major breeding targets in the Rosaceae. Several of the major Rosaceae species are current or ancient polyploids. To dissect the inheritance of fruit quality traits in polyploid fleshy fruit species, we used a cultivated strawberry segregating population comprising a 213 full-sibling F1 progeny from a cross between the variety ‘Capitola’ and the genotype ‘CF1116’. We previously developed the most comprehensive strawberry linkage map, which displays seven homoeology groups (HG), including each four homoeology linkage groups (Genetics 179:2045–2060, 2008). The map was used to identify quantitative trait loci (QTL) for 19 fruit traits related to fruit development, texture, colour, anthocyanin, sugar and organic acid contents. Analyses were carried out over two or three successive years on field-grown plants. QTL were detected for all the analysed traits. Because strawberry is an octopolyploid species, QTL controlling a given trait and located at orthologous positions on different homoeologous linkage groups within one HG are considered as homoeo-QTL. We found that, for various traits, about one-fourth of QTL were putative homoeo-QTL and were localised on two linkage groups. Several homoeo-QTL could be detected the same year, suggesting that several copies of the gene underlying the QTL are functional. The detection of some other homoeo-QTL was year-dependent. Therefore, changes in allelic expression could take place in response to environmental changes. We believe that, in strawberry as in other polyploid fruit species, the mechanisms unravelled in the present study may play a crucial role in the variations of fruit quality