Conway groupoids, regular two-graphs and supersimple designs

A $2-(n,4,\lambda)$ design $(\Omega, \mathcal{B})$ is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym$(\Omega)$ called a "Conway groupoid". The construction generalizes Conway's construction of the groupoid $M_{13}$. It turns out that several infinite families of groupoids arise in this way, some associated with 3-transposition groups, which have two additional properties. Firstly the set of collinear point-triples forms a regular two-graph, and secondly the symmetric difference of two intersecting lines is again a line. In this paper, we show each of these properties corresponds to a group-theoretic property on the groupoid and we classify the Conway groupoids and the supersimple designs for which both of these two additional properties hold.Comment: 17 page

The feasibility of measuring calprotectin from a throat swab as a marker of infections caused by group A streptococcus: a case–control feasibility study

Background Most people with sore throat do not benefit from antibiotic treatment, but nearly three-quarters of those presenting in primary care are prescribed antibiotics. A test that is predictive of bacterial infection could help guide antibiotic prescribing. Calprotectin is a biomarker of neutrophilic inflammation, and may be a useful marker of bacterial throat infections.Aim To assess the feasibility of measuring calprotectin from throat swabs, and assess whether individuals with sore throats likely to be caused by streptococcal infections have apparently higher throat calprotectin levels than other individuals with sore throat and healthy volunteers.Design & setting A proof of concept case–control study was undertaken, which compared primary care patients with sore throats and healthy volunteers.Method Baseline characteristics and throat swabs were collected from 30 primary care patients with suspected streptococcal sore throat, and throat swabs were taken from 10 volunteers without sore throat. Calprotectin level determination and rapid antigen streptococcal testing were conducted on the throat swab eluents. Calprotectin levels in the following groups were compared: volunteers without a sore throat; all patients with a sore throat; patients with a sore throat testing either negative or positive for streptococcal antigen; and those with lower and higher scores on clinical prediction rules for streptococcal sore throat.Results Calprotectin was detected in all throat swab samples. Mean calprotectin levels were numerically higher in patients with sore throat compared with healthy volunteers, and sore throat patients who had group A streptococci antigen detected compared with those who did not.Conclusion Calprotectin can be measured from throat swab samples and levels are consistent with the hypothesis that streptococcal infection leads to higher throat calprotectin levels. This hypothesis will be tested in a larger study.leukocyte L1 antigen complexpharyngitisanti-bacterial agentsgroup A streptococciprimary health carecalprotectinsore throatantibiotic

Conway Groupoids and Completely Transitive Codes

To each supersimple $2-(n,4,\lambda)$ design \De one associates a `Conway groupoid,' which may be thought of as a natural generalisation of Conway's Mathieu groupoid $M_{13}$ which is constructed from $\mathbb{P}_3$. We show that \Sp_{2m}(2) and 2^{2m}.\Sp_{2m}(2) naturally occur as Conway groupoids associated to certain designs. It is shown that the incidence matrix associated to one of these designs generates a new family of completely transitive $\mathbb{F}_2$-linear codes with minimum distance 4 and covering radius 3, whereas the incidence matrix of the other design gives an alternative construction of a previously known family of completely transitive codes. We also give a new characterization of $M_{13}$ and prove that, for a fixed $\lambda > 0,$ there are finitely many Conway groupoids for which the set of morphisms does not contain all elements of the full alternating group

Generating groups using hypergraphs

To a set B of 4-subsets of a set Ω of size n, we introduce an invariant called the ‘hole stabilizer’ which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd's ‘15-puzzle’. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs (Ω,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n,4,λ) designs with λ⩽2⁠

EPICOG-SCH: A brief battery to screen cognitive impact of schizophrenia in stable outpatients

Brief batteries in schizophrenia, are needed to screen for the cognitive impact of schizophrenia. We aimed to validate and co-norm the Epidemiological Study of Cognitive Impairment in Schizophrenia (EPICOG-SCH) derived brief cognitive battery. A cross-sectional outpatient evaluation was conducted of six-hundred-seventy-two patients recruited from 234 centers. The brief battery included well-known subtests available worldwide that cover cognitive domains related to functional outcomes: WAIS-III-Letter-Number-Sequencing-LNS, Category Fluency Test-CFT, Logical-Memory Immediate Recall-LM, and Digit-Symbol-Coding-DSC. CGI-SCH Severity and WHO-DAS-S were used to assess clinical severity and functional impairment, respectively. Unit Composite Score (UCS) and functional regression-weighted Composite Scores (FWCS) were obtained; discriminant properties of FWCS to identify patients with different levels of functional disability were analyzed using receiver-operating characteristic (ROC) technique. The battery showed good internal consistency, Cronbach's alpha = 0.78. The differences between cognitive performance across CGI-SCH severity level subscales ranged from 0.5 to 1 SD. Discriminant capacity of the battery in identifying patients with up to moderate disability levels showed fair discriminant accuracy with areas under the curve (AUC) > 0.70, p < 0.0001. An FWCS mean cut-off score ≥ 100 showed likelihood ratios (LR) up to 4.7, with an LR+ of 2.3 and a LR− of 0.5. An FWCS cut-off ≥ 96 provided the best balance between sensitivity (0.74) and specificity (0.62). The EPICOG-SCH proved to be a useful brief tool to screen for the cognitive impact of schizophrenia, and its regression-weighted Composite Score was an efficient complement to clinical interviews for confirming patients' potential functional outcomes and can be useful for monitoring cognition during routine outpatient follow-up visits