The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

Voltage-dependent Block of the Cystic Fibrosis Transmembrane Conductance Regulator Cl- Channel by Two Closely Related Arylaminobenzoates

The gene defective in cystic fibrosis encodes a Cl- channel, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is blocked by diphenylamine-2-carboxylate (DPC) when applied extracellularly at millimolar concentrations. We studied the block of CFTR expressed in Xenopus oocytes by DPC or by a closely related molecule, flufenamic acid (FFA). Block of whole-cell CFTR currents by bath-applied DPC or by FFA, both at 200 µM, requires several minutes to reach full effect. Blockade is voltage dependent, suggesting open-channel block: currents at positive potentials are not affected but currents at negative potentials are reduced. The binding site for both drugs senses ~40% of the electric field across the membrane, measured from the inside. In single-channel recordings from excised patches without blockers, the conductance was 8.0 ± 0.4 pS in symmetric 150 mM Cl^-. A subconductance state, measuring ~60% of the main conductance, was often observed. Bursts to the full open state lasting up to tens of seconds were uninterrupted at depolarizing membrane voltages. At hyperpolarizing voltages, bursts were interrupted by brief closures. Either DPC or FFA (50 µM) applied to the cytoplasmic or extracellular face of the channel led to an increase in flicker at V_m =-100 mV and not at V_m = +100 mV, in agreement with whole-cell experiments. DPC induced a higher frequency of flickers from the cytoplasmic side than the extracellular side. FFA produced longer closures than DPC; the FFA closed time was roughly equal (~ 1.2 ms) at -100 mV with application from either side. In cell-attached patch recordings with DPC or FFA applied to the bath, there was flickery block at V_m = -100 mV, confirming that the drugs permeate through the membrane to reach the binding site. The data are consistent with the presence of a single binding site for both drugs, reached from either end of the channel. Open-channel block by DPC or FFA may offer tools for use with site-directed mutagenesis to describe the permeation pathway

Polynomial sequences for bond percolation critical thresholds

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. P03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, p_c(4,6,12)=0.69377849... and p_c(3^4,6)=0.43437077..., compared with Parviainen's numerical results of p_c \approx 0.69373383 and p_c \approx 0.43430621 . These deviations are of the order 10^{-5}, as is standard for this method, although they are outside Parviainen's typical standard error of 10^{-7}. Deriving thresholds in this way for a given lattice leads to a polynomial with integer coefficients, the root in [0,1] of which gives the estimate for the bond threshold. I show how the method can be refined, leading to a sequence of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.Comment: submitted to Journal of Statistical Mechanic

Nunalleq, Stories from the Village of Our Ancestors:Co-designing a multivocal educational resource based on an archaeological excavation

This work was funded by the UK-based Arts and Humanities Research Council through grants (AH/K006029/1) and (AH/R014523/1), a University of Aberdeen IKEC Award with additional support for travel and subsistence from the University of Dundee, DJCAD Research Committee RS2 project funding. Thank you to the many people who contributed their support, knowledge, feedback, voices and faces throughout the project, this list includes members of the local community, colleagues, specialists, students, and volunteers. If we have missed out any names we apologize but know that your help was appreciated. Jimmy Anaver, John Anderson, Alice Bailey, Kieran Baxter, Pauline Beebe, Ellinor Berggren, Dawn Biddison, Joshua Branstetter, Brendan Body, Lise Bos, Michael Broderick, Sarah Brown, Crystal Carter, Joseph Carter, Lucy Carter, Sally Carter, Ben Charles, Mary Church, Willard Church, Daniele Clementi, Annie Cleveland, Emily Cleveland, Joshua Cleveland, Aron Crowell, Neil Curtis, Angie Demma, Annie Don, Julia Farley, Veronique Forbes, Patti Fredericks, Tricia Gillam, Sean Gleason, Sven Haakanson, Cheryl Heitman, Grace Hill, Diana Hunter, Joel Isaak, Warren Jones, Stephan Jones, Ana Jorge, Solveig Junglas, Melia Knecht, Rick Knecht, Erika Larsen, Paul Ledger, Jonathan Lim Soon, Amber Lincoln, Steve Luke, Francis Lukezic, Eva Malvich, Pauline Matthews, Roy Mark, Edouard Masson-MacLean, Julie Masson-MacLean, Mhairi Maxwell, Chuna Mcintyre, Drew Michael, Amanda Mina, Anna Mossolova, Carl Nicolai Jr, Chris Niskanen, Molly Odell, Tom Paxton, Lauren Phillips, Lucy Qin, Charlie Roberts, Chris Rowe, Rufus Rowe,Chris Rowland, John Rundall, Melissa Shaginoff, Monica Shah, Anna Sloan, Darryl Small Jr, John Smith, Mike Smith, Joey Sparaga, Hannah Strehlau, Dora Strunk, Larissa Strunk, Lonny Strunk, Larry Strunk, Robbie Strunk, Sandra Toloczko, Richard Vanderhoek, the Qanirtuuq Incorporated Board, the Quinhagak Dance Group and the staff at Kuinerrarmiut Elitnaurviat. We also extend our thanks to three anonymous reviewers for their valuable comments on our paper.Peer reviewedPublisher PD

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Science religion encounters, epistemic trespass, neighbourliness and overlapping domains: theorisation and quantitative evidence of extent

This study advances a concept of science religion encounter (SRE), with preliminary theorisation and shares findings on the extent and nature of such encounters reported by secondary religious education and science teachers. SREs are interdisciplinary engagements in classrooms involving subject knowledge from more than one subject. The researchers hypothesised they may arise unexpectedly, when a pupil asks a question, or be teacher-planned and intended. This article further elaborates the concept of SRE with reference to the concepts of ‘epistemic trespassing’ (ET), epistemic neighbourliness, and overlapping domains, introducing these to the field of education. The study is contextualised in the school classroom with quantitative data gathered among beginning and experienced teachers measuring whether this ET in SRE topics enter the classroom via ‘spontaneity’ or via a ‘deliberateness’. This clarifies the different roles a teacher may play and offers considerations for teacher development when navigating an SRE in ways that potentially reduce lost learning

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

A case of a severe reaction following the use of bisphosphonates in a patient with osteogenesis imperfecta

We present a case of an unusual delayed multi-systemic reaction, following treatment with pamidronate. Although serious adverse reactions have been reported with pamidronate use, such a severe reaction, late in the course of pamidronate treatment, has not been described before. An 11-month-old boy with severe and complex osteogenesis imperfecta (OI) presented with hyperpyrexia and respiratory distress 10 days after his fifth cycle of pamidronate. He had significant derangement of his biochemical parameters including a positive urine myoglobin. His respiratory distress was out of proportion to his chest radiograph changes. Bilevel positive airway pressure (BiPAP) and paediatric intensive care (PICU) admission were required. He was extensively investigated to exclude other diagnoses, but all of these investigations were negative. The reaction resembled rhabdomyolysis. He made a full recovery with only supportive management

Science and RE teachers' perspectives on the purpose of RE on the secondary school curriculum in England

Renewed interest in curriculum in English schooling over the past decade has emanated from a particular focus on the place and role of knowledge in the classroom. Significant changes in policy and examination specifications have led to changes in religious education (RE). However, little is known about teachers' perspectives on the purpose of RE. We asked teachers of science and RE what they understood as the purpose of RE on the school curriculum. Data from 10 focus groups and a survey with 276 secondary teachers demonstrated that many secondary teachers of science have a different understanding to RE teachers of the purpose of RE on the school curriculum. Findings also show a lack of consensus from RE teachers on the purpose of RE, suggesting the impact of the knowledge turn in RE is not as strong as the Ofsted Research Review implies. Findings are significant as little is known about how knowledge works across disciplinary boundaries in schools. If students are to come to a full understanding of how knowledge works, teachers need to have some understanding of how knowledge is being constructed and utilised in other curriculum subjects. Knowledge of the intended purpose of RE is important for respectful co-existence of subjects on the curriculum and essential when RE is declining as a subject in secondary schools

Exact Casimir Interaction Between Semitransparent Spheres and Cylinders

A multiple scattering formulation is used to calculate the force, arising from fluctuating scalar fields, between distinct bodies described by $\delta$-function potentials, so-called semitransparent bodies. (In the limit of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We obtain expressions for the Casimir energies between disjoint parallel semitransparent cylinders and between disjoint semitransparent spheres. In the limit of weak coupling, we derive power series expansions for the energy, which can be exactly summed, so that explicit, very simple, closed-form expressions are obtained in both cases. The proximity force theorem holds when the objects are almost touching, but is subject to large corrections as the bodies are moved further apart.Comment: 5 pages, 4 eps figures; expanded discussion of previous work and additional references added, minor typos correcte