On the omega-limit sets of tent maps

For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta for i=0,1, ...,n-1. It is known that every omega-limit set is internally chain transitive; in earlier work it was shown that for X a shift of finite type, a closed subset D of X is internally chain transitive if and only if D is an omega-limit set for some point in X, and that the same is also true for the tent map with slope equal to 2. In this paper, we prove that for tent maps whose critical point c=1/2 is periodic, every closed, internally chain transitive set is necessarily an omega-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an omega-limit set. Together, these results lead us to conjecture that for those tent maps with shadowing (or pseudo-orbit tracing), the omega-limit sets are precisely those sets having internal chain transitivity.Comment: 17 page

The incidence of nominal and real wage rigidities in Great Britain: 1978–1998

This paper analyzes the extent of rigidities in wage setting in Great Britain over the 1980s and 1990s. Our estimation strategy, which generalizes the work of Altonji and Devereux (2000), models the notional wage growth distribution--the distribution of nominal wage growth that would occur in the absence of rigidities in pay--while allowing for the presence of measurement error in the data. The model then allows for the possibility that the nominal wage growth of a fraction of the workforce may be subject to a nominal or real downward rigidity. Our model suggests that real rigidities in wage setting are more prevalent than nominal rigidities, although the incidence of these real wage rigidities has fallen gradually over time. If firms cannot cut real wages in response to negative demand shocks they may resort to laying off workers. Our results support this microfoundation of the wage-unemployment Phillips curve: Workers who are more likely to be protected from wage cuts are also more likely to lose their jobs.Wages - Great Britain

Shadowing and Expansivity in Sub-Spaces

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval, in which context some of our results can be extended.Comment: 18 page

The omega-limit sets of quadratic Julia sets

In this paper we characterize \w-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that quadratic maps with dendritic Julia sets have shadowing, and also that for all such maps, a closed invariant set is an \w-limit set of a point if, and only if, it is internally chain transitive.Comment: 24 page

Applied linguistics and mathematics education: More than words and numbers

The preceding set of papers has explored various aspects of the role of language in mathematics education. The papers reflect the work of individual contributors. An important part of our collaboration, however, has been the conversation between us. This paper reflects aspects of that conversation, as we draw together some of the themes that have emerged during our work. In particular, we discuss some of the implications of our analyses for theory, policy, practice and inter-disciplinarity in mathematics education and applied linguistics

Marking machinima : a case study in assessing student use of a Web 2.0 technology

The model of learning best suited to the future may be one which sees learning as the process of managing the different kinds of participation an individual might have in complex social systems. Learning capability and engagement is thus dependent on the relationship between an individual identity and social systems. We report on the incorporation of machinima, a Web 2.0 technology, as part of an interdisciplinary and collaborative project where the focus is not on the mastery of the tools or the acquisition of predetermined knowledge, but on the development of learning engagement. We provide the case study of a pilot project involving students across two Arts disciplines collaborating via the game, World of Warcraft, to produce an animated adaptation of one of Geoffrey Chaucer\u27s Canterbury Tales. Their contributions were differently assessed according to the pre-existing requirements of their home disciplines. We argue that the assessment in such projects, in conjunction with innovations and experimentation with Web 2.0 technologies, should shift from an emphasis on product to process. We believe that this has a sound pedagogical and theoretical foundation, and also fits better with the increasingly digitalised, unfixed and interdisciplinary world that students will face on graduation. <br /

The role of ECL2 in CGRP receptor activation: a combined modelling and experimental approach

The calcitonin gene-related peptide (CGRP) receptor is a complex of a calcitonin receptor-like receptor (CLR), which is a family B G-protein-coupled receptor (GPCR) and receptor activity modifying protein 1. The role of the second extracellular loop (ECL2) of CLR in binding CGRP and coupling to Gs was investigated using a combination of mutagenesis and modelling. An alanine scan of residues 271–294 of CLR showed that the ability of CGRP to produce cAMP was impaired by point mutations at 13 residues; most of these also impaired the response to adrenomedullin (AM). These data were used to select probable ECL2-modelled conformations that are involved in agonist binding, allowing the identification of the likely contacts between the peptide and receptor. The implications of the most likely structures for receptor activation are discussed.</jats:p

Towards semi-automatic data-type translation for parallelism in Erlang

As part of our ongoing research programme into programmer-in-the-loop parallelisation, we are studying the problem of introducing alternative data structures to support parallelism. Automated support for data structure transformations makes it easier to produce the best parallelisation for some given program, or even to make parallelisation feasible. We use a refactoring approach to choose and introduce these transformations for specific algorithmic skeletons, structured forms of parallelism that capture common patterns of parallelism. Our approach integrates with the Wrangler refactoring tool for Erlang, and uses the advanced Skel [4] skeleton library for Erlang. This library has previously been shown to give good parallelisations for a number of applications, including a multi-agent system [1] where we have achieved speedups of up to 142.44 on a 61-core machine with 244 threads. We have investigated three widely-used Erlang data structures: lists, binary structures and ETS (Erlang Term Storage) tables. In general, we have found that ETS tables deliver the best parallel performance for the examples that we have considered. However, our results show that simple lists may deliver similar performance to the use of ETS tables, and better performance than using binary structures. This means that we cannot blindly choose to implement a single optimisation as part of the compilation process. Our approach also allows the use of new (possibly user-defined) data structures and other transformations in future, giving a high level of flexibility and generality.Postprin

Explanation and Quasi-Miracles in Narrative Understanding: The Case of Poetic Justice

This is the peer reviewed version of the following article: Craig Bourne, and Emily Caddick Bourne, ‘Explanation and Quasi‐miracles in Narrative Understanding: The Case of Poetic Justice’, Dialectica, Vol. 71 (4): 563-579, January 2018, which has been published in final form at https://doi.org/10.1111/1746-8361.12201. Under embargo until 29 January 2020. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.David Lewis introduced the idea of a quasi-miracle to overcome a problem in his initial account of counterfactuals. Here we put the notion of a quasi-miracle to a different and new use, showing that it offers a novel account of the phenomenon of poetic justice, where characters in a narrative get their due by happy accident (for example, when the murderer of King Mitys happens to be crushed by a falling statue of Mitys). The key to understanding poetic justice is to see what makes poetically just events remarkable coincidences. We argue that remarkable coincidence is to be understood in terms of a distinctive type of experience quasi-miracles offer. Cases of poetic justice offer a dual awareness of the accidental nature of the events and of a non-accidental process, involving intention, which it appears would explain them. We also extend this account to incorporate how we might experience magic tricks. An account of poetic justice as quasi-miraculous allows us to account for the experience of encounters with poetic justice, as involving the incongruity of seeing design in accident.Peer reviewedFinal Accepted Versio

Purification and characterization of phycocyanin from the marine cyanobacterium Synechococcus sp. IO9201

This paper describes a suitable method for the optimum extraction and isolation of phycocyanin from the cyanobacterium Synechococcus sp. IO9201 isolated from Caribbean waters. Phycocyanin from this microorganism was purified to homogeneity and some of its properties were investigated. The purification steps consisted of extraction, hydrophobic interaction chromatography and ion exchange chromatography. Freezing at −21°C-thawing at 4°C, using an alkaline buffer was the best method for extracting phycocyanin from Synechococcus sp. IO9201. The best extraction was obtained using butyl-sepharose resin for hydrophobic interaction chromatography and 0.05 M Tris-HCl (pH = 7) containing 10% ethanol for phycocyanin elution. Finally, phycocyanin was further purified by ion exchange chromatography using Q-sepharose and eluted with a complex isocratic system. The estimated molecular weight of the phycocyanin purified from Synechococcus sp. IO9201 was 102 000 daltons by gel filtration and the isoelectric point was 4.6. When analyzed by SDS-PAGE, Synechococcus sp. IO9201 phycocyanin migrated as two bands having an apparent molecular weight of 21 360 and 18 980 Da. The first band corresponds to β phycocyanin subunits, whereas the second corresponds to α phycocyanin subunits. So, this phycocyanin was characterized as (αCPCβCPC)3