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

Monte Carlo computer simulations of Venus equilibrium and global resurfacing models

Two models have been proposed for the resurfacing history of Venus: (1) equilibrium resurfacing and (2) global resurfacing. The equilibrium model consists of two cases: in case 1, areas less than or equal to 0.03 percent of the planet are spatially randomly resurfaced at intervals of less than or greater than 150,000 yr to produce the observed spatially random distribution of impact craters and average surface age of about 500 m.y.; and in case 2, areas greater than or equal to 10 percent of the planet are resurfaced at intervals of greater than or equal to 50 m.y. The global resurfacing model proposes that the entire planet was resurfaced about 500 m.y. ago, destroying the preexisting crater population and followed by significantly reduced volcanism and tectonism. The present crater population has accumulated since then with only 4 percent of the observed craters having been embayed by more recent lavas. To test the equilibrium resurfacing model we have run several Monte Carlo computer simulations for the two proposed cases. It is shown that the equilibrium resurfacing model is not a valid model for an explanation of the observed crater population characteristics or Venus' resurfacing history. The global resurfacing model is the most likely explanation for the characteristics of Venus' cratering record. The amount of resurfacing since that event, some 500 m.y. ago, can be estimated by a different type of Monte Carolo simulation. To date, our initial simulation has only considered the easiest case to implement. In this case, the volcanic events are randomly distributed across the entire planet and, therefore, contrary to observation, the flooded craters are also randomly distributed across the planet

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

Atmospheric modelling for NOMAD-UVIS on board the ExoMars Trace Gas Orbiter mission

The Ultraviolet and Visible Spectrometer (UVIS) instrument development process requires the construction of an atmospheric model to provide synthetic UV transmission spectra. We discuss the requirements of the model to enable observational limits to be found, and the potential for certain atmospheric parameters to be further constrained

Explicating the role of partnerships in changing the health and well-being of local communities: a profile of neighbourhood renewal activity focused on promoting health and well-being in Salford and the north west region and the north east of England

This scoping and mapping report is one of three outputs from a project: Explicating the role of partnerships in changing the health and well-being of local communities, one of a number of projects in a larger Higher Education Funding Council Strategic Development Fund project ( HEFCE ) entitled: Urban Regeneration: Making a Difference. This was a collaborative venture between Manchester Metropolitan University, Northumbria University, University of Salford and University of Central Lancashire. Bradford University was an affiliated partner

Reliability considerations in the design, assembly, and testing of the mariner iv power system

Reliability considerations in design, assembly, and testing of Mariner IV power syste

Threats to student evaluative judgement and their management

Students’ capacity for making evaluative judgements of their own work is widely acknowledged as central to their learning within programmes as well as being vital to their subsequent professional practice. In higher education literature, the act of evaluative judgement is usually portrayed as a process of deliberative, analytical reasoning requiring student agency and objectivity, typically scaffolded by points of reference such as explicit criteria, rubrics or exemplars. This article challenges this common portrayal of judgement by drawing attention to research from outside higher education on the role of unconscious factors in judgement and decision-making. Drawing from the field of heuristics and bias studies, the article outlines six unconscious factors that have the potential to distort students’ analytical judgement of their work. A recent challenge to the heuristics and bias approach that radically repositions the place of reasoning in judgement is also considered. Since these unconscious factors have received scant attention in higher education literature, the purpose of this article is to draw attention to them, to identify the challenges they pose to current understandings of evaluative judgement, and to outline their implications for enhancing assessment practic

Improving assessment tasks through addressing our unconscious limits to change

Despite widespread recognition of the need to improve assessment in higher education, assessment tasks in individual courses are too often dominated by conventional methods. While changing assessment depends on many factors, improvements to assessment ultimately depend on the decisions and actions of individual educators. This paper considers research within the ‘heuristics and biases’ tradition in the field of decision-making and judgement which has identified unconscious factors with the potential to limit capacity for such change. The paper focuses on issues that may compromise the process of improving assessment by supporting a reluctance to change existing tasks, by limiting the time allocated to develop alternative assessment tasks, by underestimating the degree of change needed or by an unwarranted overconfidence in assessment design decisions. The paper proposes countering these unconscious limitations to change by requiring justification for changing, or not changing, assessment tasks, and by informal and formal peer review of assessment task design. Finally, an agenda for research on heuristics and biases in assessment design is suggested in order to establish their presence and help counter their influence