Fluxoid formation: size effects and non-equilibrium universality

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek scaling exponent was reported for spontaneous fluxoid production in a single isolated superconducting Nb loop, albeit with low density. Using analytic approximations backed up by Langevin simulations, we argue that densities as small as these are too low to be attributable to scaling, and are conditioned by the small size of the loop. We also reflect on the physical differences between slow quenches and small rings, and derive some criteria for these differences, noting that recent work on slow quenches does not adequately explain the anomalous behaviour seen here.Comment: 7 pages, 4 figures, presentation given at CMMP 201

Highly syntenic and yet divergent: a tale of two Theilerias

The published genomic sequences of the two major host-transforming Theileria species of cattle represent a rich resource of information that has allowed novel bioinformatic and experimental studies into these important apicomplexan parasites. Since their publication in 2005, the genomes of T. annulata and T. parva have been utilised for a diverse range of applications, ranging from candidate antigen discovery to the identification of genetic markers for population analysis. This has led to advancements in the quest for a sub-unit vaccine, while providing a greater understanding of variation among parasite populations in the field. The unique ability of these Theileria species to induce host cell transformation is the subject of considerable scientific interest and the availability of full genomic sequences has provided new insights into this area of research. This article reviews the data underlying published comparative analyses, focussing on the general features of gene expression, the major Tpr/Tar multi-copy gene family and a re-examination of the predicted macroschizont secretome. Codon usage between the Theileria species is reviewed in detail, as this underpins ongoing comparative studies investigating selection at the intra- and inter-species level. The TashAT/TpshAT family of genes, conserved between T. annulata and T. parva, encodes products targeted to the host nucleus and has been implicated in contributing to the transformed bovine phenotype. Species-specific expansion and diversification at this critical locus is discussed with reference to the availability, in the near future, of genomic datasets which are based on non-transforming Theileria species

Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance

Genomic islands of divergence in the Yellow Tang and the Brushtail Tang Surgeonfishes.

The current ease of obtaining thousands of molecular markers challenges the notion that full phylogenetic concordance, as proposed by phylogenetic species concepts, is a requirement for defining species delimitations. Indeed, the presence of genomic islands of divergence, which may be the cause, or in some cases the consequence, of speciation, precludes concordance. Here, we explore this issue using thousands of RAD markers on two sister species of surgeonfishes (Teleostei: Acanthuridae), Zebrasoma flavescens and Z.&nbsp;scopas, and several populations within each species. Species are readily distinguished based on their colors (solid yellow and solid brown, respectively), yet populations and species are neither distinguishable using mitochondrial markers (cytochrome c oxidase 1), nor using 5193 SNPs (pairwise Φst&nbsp;=&nbsp;0.034). In contrast, when using outlier loci, some of them presumably under selection, species delimitations, and strong population structure follow recognized taxonomic positions (pairwise Φst&nbsp;=&nbsp;0.326). Species and population delimitation differences based on neutral and selected markers are likely due to local adaptation, thus being consistent with the idea that these genomic islands of divergence arose as a consequence of isolation. These findings, which are not unique, raise the question of a potentially important pathway of divergence based on local adaptation that is only evident when looking at thousands of loci

The number of conjugacy classes in pattern groups is not a polynomial function

A famous open problem due to Graham Higman asks if the number of conjugacy classes in the group of n x n unipotent upper triangular matrices over the q-element field can be expressed as a polynomial function of q for every fixed n. We consider the generalization of the problem for pattern groups and prove that for some pattern groups of nilpotency class two the number of conjugacy classes is not a polynomial function of q