Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q)

A flock of a quadratic cone of PG(3,q) is a partition of the non-vertex points into plane sections. It was shown by Thas in 1987 that to such flocks correspond generalized quadrangles of order (q2,q), previously constructed algebraically by Kantor (q odd) and Payne (q even). In 1999, Thas gave a geometrical construction of the generalized quadrangle from the flock via a particular set of elliptic quadrics in PG(3,q). In this paper we characterise these sets of elliptic quadrics by a simple property, construct the generalized quadrangle synthetically from the properties of the set and strengthen the main theorem of Thas 1999.S.G. Barwick, Matthew R. Brown and Tim Penttilahttp://www.elsevier.com/wps/find/journaldescription.cws_home/622862/description#descriptio

Isomorphisms of groups related to flocks

A truly fruitful way to construct finite generalized quadrangles is through the detection of Kantor families in the general 5-dimensional Heisenberg group over some finite field . All these examples are so-called "flock quadrangles". Payne (Geom. Dedic. 32:93-118, 1989) constructed from the Ganley flock quadrangles the new Roman quadrangles, which appeared not to arise from flocks, but still via a Kantor family construction (in some group of the same order as ). The fundamental question then arose as to whether (Payne in Geom. Dedic. 32:93-118, 1989). Eventually the question was solved in Havas et al. (Finite geometries, groups, and computation, pp. 95-102, de Gruyter, Berlin, 2006; Adv. Geom. 26:389-396, 2006). Payne's Roman construction appears to be a special case of a far more general one: each flock quadrangle for which the dual is a translation generalized quadrangle gives rise to another generalized quadrangle which is in general not isomorphic, and which also arises from a Kantor family. Denote the class of such flock quadrangles by . In this paper, we resolve the question of Payne for the complete class . In fact we do more-we show that flock quadrangles are characterized by their groups. Several (sometimes surprising) by-products are described in both odd and even characteristic

A Validated Model for Sudden Cardiac Death Risk Prediction in Pediatric Hypertrophic Cardiomyopathy

Background: Hypertrophic cardiomyopathy is the leading cause of sudden cardiac death (SCD) in children and young adults. Our objective was to develop and validate a SCD risk prediction model in pediatric hypertrophic cardiomyopathy to guide SCD prevention strategies. Methods: In an international multicenter observational cohort study, phenotype-positive patients with isolated hypertrophic cardiomyopathy 70% prediction accuracy and incorporates risk factors that are unique to pediatric hypertrophic cardiomyopathy. An individualized risk prediction model has the potential to improve the application of clinical practice guidelines and shared decision making for implantable cardioverter defibrillator insertion. Registration: URL: https://www.clinicaltrials.gov; Unique identifier: NCT0403679