Constructing flag-transitive, point-imprimitive designs

We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.PostprintPeer reviewe

Defining Mentorship in Prehospital Care: A Qualitative Analysis of the Characteristics of Prehospital Mentors

IntroductionThis study sought to begin to define the current understanding of the term mentor within the prehospital environment (emergency medical services or EMS) as described by nomination letters written by mentees for a newly launched prehospital mentor award.MethodsThe John Ross Paramedic Mentor Award was created in the fall of 2015 to recognize outstanding mentors in prehospital care. In the spring of 2016, nineteen nomination letters were received from registered prehospital professionals in Alberta detailing why their mentor should receive the mentor award. Written text from the nominations for this peer nominated award were analyzed using thematic and content analysis (n=19) to identify the current understanding of mentorship in EMS, desirable qualities of prehospital mentors, and what a successful mentoring relationship looks like in the prehospital environment from the perspective of mentees. Demographic data of the mentees and mentors were obtained. ResultsMentees and nominated mentors had varying years of experience, worked in diverse practice areas within prehospital care and represented varying scopes of practice (PCPs and ACPs). Three themes were identified from thematic analysis of the nomination letters 1) nominators seek to emulate their mentors, 2) mentors create a safe and nurturing environment, and 3) mentors act as advocates. In addition, content analysis was used to identify a number of desirable professional and personal traits of prehospital mentors.ConclusionThis study describes the qualities of prehospital mentors and identifies a number of common elements in a successful mentoring relationship (from the perspective of the mentee). These results highlight exceptional mentoring that is already occurring within the prehospital care environment. This research has the potential to provide guidance to those who aim to support both formal and informal mentoring within the prehospital care environment

Primitive decompositions of Johnson graphs

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.Comment: 35 page

Diagonal groups and arcs over groups

Partially supported by Simons Foundation Collaboration Grant 359872 and by Fundacaopara a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) grant PTDC/MAT-PUR/31174/2017. Australian Research Council Discovery Grant DP160102323.In an earlier paper by three of the present authors and Csaba Schneider, it was shown that, for m≥2, a set of m+1 partitions of a set Ω, any m of which are the minimal non-trivial elements of a Cartesian lattice, either form a Latin square (if m=2), or generate a join-semilattice of dimension m associated with a diagonal group over a base group G. In this paper we investigate what happens if we have m+r partitions with r≥2, any m of which are minimal elements of a Cartesian lattice. If m=2, this is just a set of mutually orthogonal Latin squares. We consider the case where all these squares are isotopic to Cayley tables of groups, and give an example to show the groups need not be all isomorphic. For m>2, things are more restricted. Any m+1 of the partitions generate a join-semilattice admitting a diagonal group over a group G. It may be that the groups are all isomorphic, though we cannot prove this. Under an extra hypothesis, we show that G must be abelian and must have three fixed-point-free automorphisms whose product is the identity. (We describe explicitly all abelian groups having such automorphisms.) Under this hypothesis, the structure gives an orthogonal array, and conversely in some cases. If the group is cyclic of prime order p, then the structure corresponds exactly to an arc of cardinality m+r in the (m−1)-dimensional projective space over the field with p elements, so all known results about arcs are applicable. More generally, arcs over a finite field of order q give examples where G is the elementary abelian group of order q. These examples can be lifted to non-elementary abelian groups using p-adic techniques.Publisher PDFPeer reviewe

The geometry of diagonal groups

Part of the work was done while the authors were visiting the South China University of Science and Technology (SUSTech), Shenzhen, in 2018, and we are grateful (in particular to Professor Cai Heng Li) for the hospitality that we received.The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no.EP/R014604/1), where further work on this paper was undertaken. In particular we acknowledge a Simons Fellowship (Cameron) and a Kirk Distinguished Visiting Fellowship (Praeger) during this programme. Schneider thanks the Centre for the Mathematics of Symmetry and Computation of The University of Western Australia and Australian Research Council Discovery Grant DP160102323 for hosting his visit in 2017 and acknowledges the support of the CNPq projects Produtividade em Pesquisa (project no.: 308212/2019-3) and Universal (project no.:421624/2018-3).Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial structures such as affine spaces or Cartesian decompositions, but such structures for diagonal groups have not been studied in general. The main purpose of this paper is to describe and characterise such structures, which we call diagonal semilattices. Unlike the diagonal groups in the O'Nan-Scott theorem, which are defined over finite characteristically simple groups, our construction works over arbitrary groups, finite or infinite. A diagonal semilattice depends on a dimension m and a group T. For m=2, it is a Latin square, the Cayley table of T, though in fact any Latin square satisfies our combinatorial axioms. However, for m≥3, the group T emerges naturally and uniquely from the axioms. (The situation somewhat resembles projective geometry, where projective planes exist in great profusion but higher-dimensional structures are coordinatised by an algebraic object, a division ring.) A diagonal semilattice is contained in the partition lattice on a set Ω, and we provide an introduction to the calculus of partitions. Many of the concepts and constructions come from experimental design in statistics. We also determine when a diagonal group can be primitive, or quasiprimitive (these conditions turn out to be equivalent for diagonal groups). Associated with the diagonal semilattice is a graph, the diagonal graph, which has the same automorphism group as the diagonal semilattice except in four small cases with m<=3. The class of diagonal graphs includes some well-known families, Latin-square graphs and folded cubes, and is potentially of interest. We obtain partial results on the chromatic number of a diagonal graph, and mention an application to the synchronization property of permutation groups.PostprintPeer reviewe

Vertex-primitive groups and graphs of order twice the product of two distinct odd primes

A non-Cayley number is an integer n for which there exists a vertex-transitive graph on n vertices which is not a Cayley graph. In this paper, we complete the determination of the non-Cayley numbers of the form 2pq, where p, q are distinct odd primes. Earlier work of Miller and the second author had dealt with all such numbers corresponding to vertex-transitive graphs admitting an imprimitive subgroup of automorphisms. This paper deals with the primitive case. First the primitive permutation groups of degree 2pq are classified. This depends on the finite simple group classification. Then each of these groups G is examined to determine whether there are any non-Cayley graphs which admit G as a vertex-primitive subgroup of automorphisms, and admit no imprimitive subgroups. The outcome is that 2pq is a non-Cayley number, where

Biogenesis of a Bacterial Organelle: The Carboxysome Assembly Pathway

SummaryThe carboxysome is a protein-based organelle for carbon fixation in cyanobacteria, keystone organisms in the global carbon cycle. It is composed of thousands of subunits including hexameric and pentameric proteins that form a shell to encapsulate the enzymes ribulose 1,5-bisphosphate carboxylase/oxygenase and carbonic anhydrase. Here, we describe the stages of carboxysome assembly and the requisite gene products necessary for progression through each. Our results demonstrate that, unlike membrane-bound organelles of eukaryotes, in carboxysomes the interior of the compartment forms first, at a distinct site within the cell. Subsequently, shell proteins encapsulate this procarboxysome, inducing budding and distribution of functional organelles within the cell. We propose that the principles of carboxysome assembly that we have uncovered extend to diverse bacterial microcompartments

Analysis of the Alaska Volcano Observatory's Response Time to Volcanic Explosions-1989 to 2016

A major goal of volcano monitoring is the rapid identification of volcanic explosions and subsequent warning of associated hazards. Between 1988 and 2016 the Alaska Volcano Observatory (AVO) responded to at least 54 separate volcanic eruptions. During this period, AVO's monitoring program relied principally on seismic and satellite remote sensing data, supplemented with geodetic, gas, and visual observations to track volcanic unrest. In this study we focus on AVO's response time, or the time required for AVO to (1) identify seismic signals associated with large ash-producing volcanic explosions and (2) initiate public warnings. We restrict this analysis to volcanoes monitored by a local seismic network and explosive in character. We focus on the 1989–90 eruption of Redoubt Volcano (VEI 3), the 1992 eruption of Mount Spurr (VEI 4), the 1999 eruption of Shishaldin Volcano (VEI 3), the 2006 eruption of Augustine Volcano (VEI 3) and the 2016 eruption of Pavlof Volcano (VEI 2) as detailed records of the timing of formal warnings are preserved. These eruption sequences allow us to evaluate AVO's response time under a number of monitoring scenarios, including both expected (those with recognized precursory unrest) and surprise eruptions (those without identified precursory unrest) as well as individual and repetitive sequences of explosive events. Recorded response time ranges from ~1 to 86 min. The shorter response times (~1–13 min) were achieved during sequences of explosive events at Redoubt (1989–90), Spurr (1992) and Augustine (2006). The longer response times (31– 86 min) are recorded for unexpected or surprise explosions such as Spurr (August 18, 1992) and Pavlof (2016) and the only or first explosions in an eruptive sequence such as Shishaldin (1999) and Augustine (2006)

Prevalence and corrrelates of 12- month prescription drug misuse in Alberta

Objective: We examined the prevalence and correlates of prescription drug misuse (PDM) in a population-based sample of adults from Alberta. Methods: Data were collected from 3511 adults in Alberta aged 18 years and older in 2002 using a computer-aided telephone survey; the survey response rate was 57.4%. Results: The prevalence of 12-month PDM in Alberta was 8.2% in 2002. Opiates were the most frequently misused drug class, followed by sedatives, stimulants, and tranquilizers. Current disability was particularly associated with PDM. Odds of PDM were also elevated among adult students and adults with a high school diploma relative to adults with a post-secondary degree. Past-year problem gambling, illicit drug use, and alcohol use and dependence were each associated with PDM, while past-year binge drinking and daily smoking were not. Conclusions: Findings suggest PDM was an important public health concern in Alberta in 2002. Estimates suggest prescription use and misuse have increased substantially in Canada since that time. There is an urgent need for an ongoing assessment of this evolving problem so that effective prevention and therapeutic strategies can be developed.Ye

Biochemical characterization of predicted Precambrian RuBisCO

The antiquity and global abundance of the enzyme, RuBisCO, attests to the crucial and longstanding role it has played in the biogeochemical cycles of Earth over billions of years. The counterproductive oxygenase activity of RuBisCO has persisted over billions of years of evolution, despite its competition with the carboxylase activity necessary for carbon fixation, yet hypotheses regarding the selective pressures governing RuBisCO evolution have been limited to speculation. Here we report the resurrection and biochemical characterization of ancestral RuBisCOs, dating back to over one billion years ago (Gyr ago). Our findings provide an ancient point of reference revealing divergent evolutionary paths taken by eukaryotic homologues towards improved specificity for CO2, versus the evolutionary emphasis on increased rates of carboxylation observed in bacterial homologues. Consistent with these distinctions, in vivo analysis reveals the propensity of ancestral RuBisCO to be encapsulated into modern-day carboxysomes, bacterial organelles central to the cyanobacterial CO2 concentrating mechanism