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To explore and compare the characteristics of frequent attenders to the ED at an Australian and a Canadian tertiary hospitals by utilising a network analysis approach.We conducted a retrospective population-based study using administrative data over the 2018 and 2019 calendar years. Participants were from a tertiary hospital in Melbourne, Australia, and Toronto, Canada. Frequent attenders were defined as patients with four or more visits in 12 months. Characteristics of younger (18-39 years), middle-aged (40-69 years) and older (70 years and older) frequent attenders were described using descriptive statistics and network analyses.Younger frequent attenders were characterised by mental illness and substance use, while older frequent attenders had high rates of physical (including chronic) diseases. Middle-aged frequent attenders were characterised by a combination of mental and physical illnesses. These findings were observed at both hospitals. Across all age groups, the network analyses between the Melbourne and Toronto hospitals were different. Among older frequent attender visits, more diagnoses were associated with high triage acuity at the Toronto hospital than at the Melbourne hospital. Some associations were similar at both sites, for example, the negative correlation between high triage acuity and joint pain.Younger, middle-aged and older frequent attenders have distinct characteristics, made readily apparent by using network analyses. Future interventions to reduce ED visits should consider the heterogeneity of frequent attenders who have needs specific to their age, presenting problems and jurisdiction.

The aim of the present study was to describe the burden of patients presenting to the ED with symptoms occurring after receiving a COVID-19 vaccination.This was a retrospective cohort study performed over a 4-month period across two EDs. Participants were eligible for inclusion if it was documented in the ED triage record that their ED attendance was associated with the receipt of a COVID-19 vaccination. Data regarding the type of vaccine (Comirnaty or ChAdOx1) were subsequently extracted from their electronic medical record. Primary outcome was ED length of stay (LOS) and secondary outcomes included requests for imaging and ED disposition destination.During the study period of 22 February 2021 to 21 June 2021, 632 patients were identified for inclusion in the present study, of which 543 (85.9%) had received the ChAdOx1 vaccination. The highest proportion of COVID-19 vaccine-related attendances occurred in June 2021 and accounted for 21 (8%) of 262 total daily ED attendances. Patients who had an ED presentation related to ChAdOx1 had a longer median ED LOS (253 vs 180 min, P 0.001) compared to Comirnaty and a higher proportion had haematology tests and imaging requested in the ED. Most patients (n = 588, 88.8%) were discharged home from the ED.There was a notable proportion of ED attendances related to recent COVID-19 vaccination administration, many of which were associated with lengthy ED stays and had multiple investigations. In the majority of cases, the patients were able to be discharged home from the ED.

To assess the feasibility of an ED presenting complaint (PC) tool that categorised all ED PCs into 10 categories.A retrospective analysis of 1445 consecutive patient encounters was conducted. The primary outcome was the frequency of use of the 10 PC categories.Of the 1203 patient encounters meeting inclusion criteria, the PC tool was completed by clinicians in 574 (47.7%). When completed, the tool's 10 options were selected for most presentations (72.3%).The PC tool captured the majority of presenting complaints in 10 categories. External validation is recommended.

Funding: R.A. Bailey and Peter J. Cameron are grateful to Shanghai Jiao Tong University for funding, from the National Science Foundation of China (11671258) and STCSM (17690740800), a research visit where part of this study was done. Alexander L. Gavrilyuk was supported by BK21plus Center for Math Research and Education at Pusan National University, Republic of Korea. Sergey V. Goryainov was supported by the National Science Foundation of China, STCSM (17690740800) and RFBR (17‐51‐560008).

This paper addresses the question of whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having −1 as multiplier is both a necessary and sufficient condition for the construction to work. Using this, we are able to give a new infinite family of triple arrays. We use an alternative version of the construction to analyze the case of non-abelian difference sets, for which we prove a sufficient condition for giving triple arrays. We do a computer search for such non-abelian difference sets, but have not found any examples satisfying the given condition.

This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand, and by the Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.

The base size of a permutation group, and the metric dimension of a graph, are two of a number of related parameters of groups, graphs, coherent configurations and association schemes. They have been repeatedly re-defined with different terminology in various different areas, including computational group theory and the graph isomorphism problem. We survey results on these parameters in their many incarnations, and propose a consistent terminology for them. We also present some new results, including on the base sizes of wreath products in the product action, and on the metric dimension of Johnson and Kneser graphs.

We give two constructions of a balanced incomplete-block design discovered by van Lint: the design has parameters (13,39,15,5,5), and has repeated blocks and an automorphism group of order 240. One of these methods can be generalized to produce a large class of designs with the properties of the title. © 2006 Wiley Periodicals, Inc. J Combin Designs

This paper introduces the concept of orbit-homogeneity of permutation groups: a group $G$ is orbit- $t$ -homogeneous if two sets of cardinality $t$ lie in the same orbit of $G$ whenever their intersections with each $G$ -orbit have the same cardinality. For transitive groups, this coincides with the usual notion of $t$ -homogeneity. This concept is also compatible with the idea of partition transitivity introduced by Martin and Sagan. Further, this paper shows that any group generated by orbit- $t$ -homogeneous subgroups is orbit- $t$ -homogeneous, and that the condition becomes stronger as $t$ increases up to $\lfloor n/2\rfloor$ , where $n$ is the degree. So any group $G$ has a unique maximal orbit- $t$ -homogeneous subgroup $\Omega_t(G)$ , and $\Omega_t(G)\le\Omega_{t-1}(G)$ . Some structural results for orbit- $t$ -homogeneous groups, and a number of examples, are also given.

The paper defines a new type of product of association schemes (and of the related objects, permutation groups and orthogonal block structures), which generalizes the direct and wreath products (which are referred to as 'crossing' and 'nesting' in the statistical literature). Given two association schemes for , each having an inherent partition (that is, a partition whose equivalence relation is a union of adjacency relations in the association scheme), a product of the two schemes is defined, which reduces to the direct product if or , and to the wreath product if and , where and are the relation of equality and the universal relation on . The character table of the crested product is calculated, and it is shown that, if the two schemes and have formal duals, then so does their crested product (and a simple description of this dual is given). An analogous definition for permutation groups with intransitive normal subgroups is created, and it is shown that the constructions for association schemes and permutation groups are related in a natural way. The definition can be generalized to association schemes with families of inherent partitions, or permutation groups with families of intransitive normal subgroups. This time the correspondence is not so straightforward, and it works as expected only if the inherent partitions (or orbit partitions) form a distributive lattice. The paper concludes with some open problems.

It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on ν points, in such a way that all automorphisms of U can be extended to V, for every admissible ν satisfying ν > g(u). We find exponential upper and lower bounds for g. © 2005 Wiley Periodicals, Inc. J Combin Designs.

A transitive nite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and ane group constructions. A brief historical introduction and a survey of known elusive groups are also included. In a sequel, Giudici has determined all the quasiprimitive elusive groups. Part of the motivation for studying this class of groups was a conjecture due to Maru si c, Jordan and Klin asserting that there is no elusive 2-closed permutation group. It is shown that the constructions given will not build counterexamples to this conjecture.

1 The use of trap crops to reduce green vegetable bug (GVB) Nezara viridula (L.) (Heteroptera: Pentatomidae) damage to process sweet corn Zea mays (L.) was investigated in three field experiments. 2 In the first season, small plots (2.7 m by 10 m) of white mustard Sinapis alba (L.) with pea Pisum sativum (L.) were sown along a crop border and compared with sweet corn alone. 3 In the second season, black mustard Brassica nigra (L.) was sown at two sowing dates (14 days apart) and compared with a sweet corn control, to examine how the maturity of the trap crop affected numbers of GVB trapped. 4 A field scale experiment was also conducted to determine the effectiveness of black mustard as a trap crop to protect larger areas of sweet corn from GVB. 5 In all three experiments, GVB populations were much higher on the trap crops compared with the sweet corn. 6 In both small plot experiments, GVB were contained largely within the trap crop for 2 weeks until the sweet corn was harvested. 7 The field scale experiment demonstrated the efficacy of the trap cropping technique to protect larger areas of crop from GVB. 8 Percentages of damaged sweet corn cobs in the outside row of fields protected by a trap crop were 0% and 1%, respectively, compared with 11% and 22% in control fields. 9 Trap cropping is recommended as an effective strategy to manage this insect. Options for cultivating or spraying the trap crops to reduce bug survival are discussed.

It is usually assumed that an infinite design is a design with infinitely many points. This encompasses a myriad of structures, some nice and others not. In this paper we consider examples of structures that we would not like to call designs, and investigate additional conditions that exclude such anomalous structures. In particular, we expect a design to be regular, the complement of a design to be a design, and a t-design to be an s-design for all 0 b.

Background: In 1999, a new major trauma system was proposed for the state of Victoria, Australia. The guidelines for the new system were aimed at delivering major trauma cases to definitive trauma care in the least time possible. The aim of the present study was to analyse the potential effect of this system on Victoria’s ambulance services. Methods: The present study modelled the workload of major trauma cases in Victoria’s ambulance service for one year pre- and post-introduction of the guidelines. Cases were analysed regarding whether their first hospital destination would change under the proposed guidelines, and, subsequently, whether they would require interhospital transport to a higher level trauma service. The impact on the ambulance services was modelled as annual changes in distances travelled due to predicted changes in hospital destinations. Results: Analysis of the predicted changes indicated that, in general, Victoria"s metropolitan and rural road ambulance crews would not be greatly affected. However, some metropolitan road crews may have to travel extra distances for up to 110 cases per year. The major impact was on air retrieval crews, where the annual number of interhospital transfers is predicted to increase from approximately 150 to 330. Conclusions: The present study demonstrated that most of the impact of a new trauma system on Victoria"s ambulance services could be readily absorbed into the current workload. However, it also highlighted areas affected disproportionately within the ambulance services; in particular, air retrieval. Such studies are important to enable the effective implementation of new trauma systems.

A permutation group is cofinitary if any non-identity element fixes only finitely many points. This paper presents a survey of such groups. The paper has four parts. Sections 1-6 develop some basic theory, concerning groups with finite orbits, topology, maximality, and normal subgroups. Sections 7-12 give a variety of constructions, both direct and from geometry, combinatorial group theory, trees, and homogeneous relational structures. Sections 13-15 present some generalisations of sharply fc-transitive groups, including an orbit-counting result with a character-theoretic flavour. The final section treats some miscellaneous topics. Several open problems are mentioned.

Large sets of Steiner systems S(t,k,n) exist for all finite t and k with t < k and all infinite n. The vector space analogues exist over a field F for all finite t and k with t < k provided that either v or F is infinite, and n ⩾ 2k − t + 1. This inequality is best possible. © 1995 John Wiley & Sons, Inc.

P. J. CAMERO ANN MD. DEZA1. IntroductionThe lattic oef flats of a matroid or combinatorial geometr cay n be regarde d as asublattice (with rank function) of the lattice of subsets of a set, having the property that,given an element of rank r of the lattice and a point outside it, a unique element of rankr+1 covers both. This paper develop a theorsy of permutation geometries, whic arhesimilarly defined object ins the semilattice of subpefmiitations (partia 1-l 1 mappings)on a set.As well as providing this basic analogy, raatroid theor is relatey d in other ways toour theor oyf permutation geometries In. the semilattice of all subpermutations th, einterval consistin ogf all elements below a given bound is a lattice isomorphi tco thelattice of all subsets of a set. In a permutation geometry, any such lower interva ils thelattice of flats of a matroid.The set of subpermutations, as well as being a semilattice, has additional structure:it is an inverse semigroup, where maximal element (thse permutations) form a group.The most interesting permutatio annd thos geometriese to whic wh e, give mostattention, are the ones whose maximal elements a for subgroum p of the symmetricgroup. (We call a group which arises in this way a geometric group.) Our results includethe determination of doubly transitive geometric groups, and some examples which arenot doubly transitive.Connections also exist with the theories of permutation cliques, sharp permutationgroups, and Jordan groups.The author ars e gratefu tl o C Landaue. r for helpfu l remarks.2. SubpermutationsLet N = {1, 2,...,«}. A subpermutation c of N is a bijection between subset osf N;its height \\c\\ is the cardinalit oy f it domais n c (or of it range)s I. f c and d aresubpermutations, we write c ^ d, and say c is covered by d, if c is the restriction of d to asubset of d. The meet c A d of two subpermutations c and d is the subpermutation edefined on the set of points{iecn d\c{i) = d(i)}and equal to each of c and d on its domain. The inverse c~

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both within group theory and outside. The purpose of this article is to consider the theory of finite permutation groups with the assumption that the finite simple groups are known, and to examine questions such as: which problems are solved or solvable under this assumption, and what important problems remain?

There are several methods for constructing snarks (cubic graphs with chromatic index 4). We study the reverse process of splitting a snark into smaller snarks which compose it. We also introduce the notion of a prime snark.

Il existe une fonction entiere f ayant la propriete que quand G est un groupe de permutation premier sur un ensemble fini Ω, si Gα est le stabiliseur du point α dans Ω et si d est la longueur d'une Gα-orbite dans Ω-{α}, alors |Gα|≤f(d)

Whitney's theorem on line graphs is extended to the class of generalized line graphs defined by Hoffman.