Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry

In this paper we show that if $\theta$ is a $T$-design of an association scheme $(\Omega, \mathcal{R})$, and the Krein parameters $q_{i,j}^h$ vanish for some $h \not \in T$ and all $i, j \not \in T$ ($i, j, h \neq 0$), then $\theta$ consists of precisely half of the vertices of $(\Omega, \mathcal{R})$ or it is a $T'$-design, where $|T'|>|T|$. We then apply this result to various problems in finite geometry. In particular, we show for the first time that nontrivial $m$-ovoids of generalised octagons of order $(s, s^2)$ do not exist. We give short proofs of similar results for (i) partial geometries with certain order conditions; (ii) thick generalised quadrangles of order $(s,s^2)$; (iii) the dual polar spaces $\mathsf{DQ}(2d, q)$, $\mathsf{DW}(2d-1,q)$ and $\mathsf{DH}(2d-1,q^2)$, for $d \ge 3$; (iv) the Penttila-Williford scheme. In the process of (iv), we also consider a natural generalisation of the Penttila-Williford scheme in $\mathsf{Q}^-(2n-1, q)$, $n\geqslant 3$.Comment: This paper builds on part of the doctoral work of the second author under the supervision of the first. The second author acknowledges the support of an Australian Government Research Training Program Scholarship and Australian Research Council Discovery Project DP20010195

On Bruen chains

It is known that a Bruen chain of the three-dimensional projective space $\mathrm{PG}(3,q)$ exists for every odd prime power $q$ at most $37$, except for $q=29$. It was shown by Cardinali et. al (2005) that Bruen chains do not exist for $41\le q\leq 49$. We develop a model, based on finite fields, which allows us to extend this result to $41\leqslant q \leqslant 97$, thereby adding more evidence to the conjecture that Bruen chains do not exist for $q>37$. Furthermore, we show that Bruen chains can be realised precisely as the $(q+1)/2$-cliques of a two related, yet distinct, undirected simple graphs

Separating rank 3 graphs

We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not $\mathbb{Q}\mathrm{I}$, groups of affine type

Anthropometric and metabolic correlates of sympathetic nervous system activation in women with polycystic ovary syndrome

Background: Polycystic ovary syndrome (PCOS) is associated with increased metabolic risk and hypertension, which may relate to enhanced sympathetic nervous system (SNS) activation. The cerebral pathways involved in this process are not known. Aims: (1) To compare blood pressure and SNS activation in response to isometric forearm contraction (IFC) between PCOS and control groups. (2) To identify and compare the neuronal signatures of this response. (3) To investigate metabolic and anthropometric correlates of SNS activation. Methods: 20 PCOS (age 29.8 yrs, BMI 26.1 kg/ m²) and 20 matched controls (age 29.7 yrs, BMI 26.1 kg/ m²; p=NS) were studied. Out-of-scanner tests: measurement of mean blood pressure (MAP) and heart rate (HR) responses to 30% IFC for 180 seconds; baseline and post-task catecholamines, and microneurography (MSNA) in a subgroup of 8 PCOS and 8 controls. In-scanner: Blood oxygen level dependent (BOLD) fMRI using an identical block paradigm design for IFC, BOLD signalcorrelating to MAP responses (threshold Z>2.3, corrected cluster threshold p=0.05). Results: IFC elicited an increase in HR and MAP in PCOS and controls but these did not differ between groups (p=0.16[HR] and p=0.06[MAP]). Adrenaline increased significantly post-IFC in PCOS (0.68 to 1.23ng/mL p<0.001) but not in controls (0.77 to 0.99ng/mL p=0.14). MSNA burst frequency increased by 68% in the PCOS group compared to 11.9% in controls (p=0.002). Brain activation indexed by the BOLD signal in response to IFC was significantly greater in the PCOS group compared to the control group in the right orbitofrontal cortex (p<0.0001), left angular gyrus and lateral occipital cortex (p=0.04). When the BOLD signal was separately corrected for insulin sensitivity, BOLD signal in the right orbitofrontal cortex was no longer significant. Conclusions: PCOS is associated with enhanced SNS activation and increased regional brain activation in response to IFC. The right orbitofrontal cortex BOLD signal change in the PCOS group is associated with insulin sensitivity

Acromegaly and the information gap: patient perceptions of the journey from primary to tertiary care

Objective Acromegaly is a rare condition and there is often a long path to diagnosis for many patients. We sought to explore patient’s perceptions and understanding of acromegaly, to examine the quality of communication and find gaps in the information provided at diagnosis. Design A prospective study using qualitative research methodology and grounded theory. A semi-structured interview was conducted with 18 patients treated for acromegaly in a single tertiary centre and verbatim transcripts were thematically analysed for overarching themes. Results Eighteen patients with acromegaly were interviewed. The mean age of participants was 52 (range 30–72). Four overarching themes emerged; (1) Patients rely on online resources to understand acromegaly in the time between diagnosis and tertiary care clinic; (2) There is not enough support available for patients; (3) Patients have a basic understanding of acromegaly and associated conditions, but the long-term impact is underestimated; and (4) Patients initially felt intimidated by the multidisciplinary team panel, but overall found it useful. Conclusion Acromegalic patients have a strong need for information at the point of initial diagnosis, in particular online resources and interaction with other experienced patients. Wider dissemination of patient educational resources into primary and secondary care settings may improve overall patient satisfaction, treatment adherence and subsequent health care provider–patient relationships