Transience and recurrence of random walks on percolation clusters in an ultrametric space

We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)}, \delta>-1$, with $c_k=C_0+C_1\log k+C_2k^\alpha$, non-negative constants $C_0, C_1, C_2$, and $\alpha>0$. Percolation was proved in Dawson and Gorostiza (2013) for $\delta0$, with $\alpha>2$. In this paper we improve the result for the critical case by showing percolation for $\alpha>0$. We use a renormalization method of the type in the previous paper in a new way which is more intrinsic to the model. The proof involves ultrametric random graphs (described in the Introduction). The results for simple (nearest neighbour) random walks on the percolation clusters are: in the case $\delta<1$ the walk is transient, and in the critical case $\delta=1, C_2>0,\alpha>0$, there exists a critical $\alpha_c\in(0,\infty)$ such that the walk is recurrent for $\alpha<\alpha_c$ and transient for $\alpha>\alpha_c$. The proofs involve graph diameters, path lengths, and electric circuit theory. Some comparisons are made with behaviours of random walks on long-range percolation clusters in the one-dimensional Euclidean lattice.Comment: 27 page

GDL: a model infrastructure for a regional digital library

This brief article describes the early days of the Glasgow Digital Library (GDL), when it was a cross-sectoral and city-wide collaborative initiative involving Strathclyde, Glasgow and Caledonian Universities, as well as Glasgow City Libraries and Archives and the Glasgow Colleges Group

Hierarchical equilibria of branching populations

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $\Omega_N$ consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit $N\to\infty$ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls $B^{(N)}_\ell$ of hierarchical radius $\ell$ converge to a backward Markov chain on $\mathbb{R_+}$. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.Comment: 62 page

Mode-Coupling Theory of Colloids with Short-range Attractions

Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the usual repulsive hard core, two intersecting liquid-glass transition lines appear, one of which extends to low densities, while the other one, at high densities, shows a re-entrant behaviour. In the glassy region a new type of transition appears between two different types of glasses. The complex phenomenology can be described in terms of higher order glass transition singularities. The various glass phases are characterised by means of their viscoelastic properties. The glass driven by attractions has been associated to particle gels, and the other glass is the well known repulsive colloidal glass. These correspondences, in associations with the new predictions of glassy behaviour mean that such phenomena may be expected in colloidal systems with, for example, strong depletion or other short-ranged attractive potentials.Comment: 17 pages, 8 figure

Characterization of Mauritius parakeet (Psittacula eques) microsatellite loci and their cross-utility in other parrots (Psittacidae, Aves).

We characterized 21 polymorphic microsatellite loci in the endangered Mauritius parakeet (Psittacula eques). Loci were isolated from a Mauritius parakeet genomic library that had been enriched separately for eight different repeat motifs. Loci were characterized in up to 43 putatively unrelated Mauritius parakeets from a single population inhabiting the Black River Gorges National Park, Mauritius. Each locus displayed between three and nine alleles, with the observed heterozygosity ranging between 0.39 and 0.96. All loci were tested in 10 other parrot species. Despite testing few individuals, between seven and 21 loci were polymorphic in each of seven species tested

Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops

This is an exploratory study of the lightest non-singlet scalar $q\bar q$ state on the lattice with two dynamical quarks. Domain Wall fermions are used for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$ and N_f=2. Since this statistical error-bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the Partially Quenched ChPT and find it describes lattice correlators well. The leading unphysical contribution in Partially Quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass 1.51(19) GeV from the partially quenched correlators is consistent with the dynamical result and has appreciably smaller error-bar.Comment: 23 pages, 8 figure

SPEIR: Scottish Portals for Education, Information and Research. Final Project Report: Elements and Future Development Requirements of a Common Information Environment for Scotland

The SPEIR (Scottish Portals for Education, Information and Research) project was funded by the Scottish Library and Information Council (SLIC). It ran from February 2003 to September 2004, slightly longer than the 18 months originally scheduled and was managed by the Centre for Digital Library Research (CDLR). With SLIC's agreement, community stakeholders were represented in the project by the Confederation of Scottish Mini-Cooperatives (CoSMiC), an organisation whose members include SLIC, the National Library of Scotland (NLS), the Scottish Further Education Unit (SFEU), the Scottish Confederation of University and Research Libraries (SCURL), regional cooperatives such as the Ayrshire Libraries Forum (ALF)1, and representatives from the Museums and Archives communities in Scotland. Aims; A Common Information Environment For Scotland The aims of the project were to: o Conduct basic research into the distributed information infrastructure requirements of the Scottish Cultural Portal pilot and the public library CAIRNS integration proposal; o Develop associated pilot facilities by enhancing existing facilities or developing new ones; o Ensure that both infrastructure proposals and pilot facilities were sufficiently generic to be utilised in support of other portals developed by the Scottish information community; o Ensure the interoperability of infrastructural elements beyond Scotland through adherence to established or developing national and international standards. Since the Scottish information landscape is taken by CoSMiC members to encompass relevant activities in Archives, Libraries, Museums, and related domains, the project was, in essence, concerned with identifying, researching, and developing the elements of an internationally interoperable common information environment for Scotland, and of determining the best path for future progress