The main result of this paper is the determination of all pairwise non-isomorphic trade sets of volume at most 10 which can appear in Steiner triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks.
We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction… (More)
This is a preprint of an article accepted for publication in Discrete Mathematics c 2002 (copyright owner as specified in the journal). Abstract A Steiner triple system, STS(v), is said to be χ-chromatic if the points can be coloured using χ colours, but no fewer, such that no block is monochromatic. All known 3-chromatic STS(v) are also equitably… (More)
Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all have chromatic index 10, except for 4 075 designs with… (More)
We investigate the conditions under which a Steiner triple system can have a 2-or 3-existentially closed block intersection graph.
OBJECTIVE Recent studies have shown an increased risk for cognitive impairment and dementia in patients with diabetes. An association between diabetic retinopathy (DR) and retinal microvasculature disease and cognitive impairment has been reported as potential evidence for a microvascular component to the cognitive impairment. It was hypothesized that… (More)
PURPOSE To assess the caregiver burden and factors determining the burden in patients receiving ranibizumab therapy for neovascular AMD (nAMD). METHODS This is a cross-sectional questionnaire survey of 250 matched patient caregiver dyads across three large ophthalmic treatment centres in United Kingdom. The primary outcome was the subjective caregiver… (More)
OBJECTIVE Annual diabetic eye screening has been implemented in England since 2008. This study aimed to estimate changes in the detection of retinopathy in the first 4 years of the program. RESEARCH DESIGN AND METHODS Participants included 32,340 patients with type 2 diabetes resident in three London boroughs with one or more screening records between… (More)
PURPOSE The purpose of this study was to examine the relationship between metabolic and inflammatory markers in patients with diabetic retinopathy (DR). METHODS 208 adult patients with type 2 diabetes participated in this study and were categorized into (1) mild nonproliferative diabetic retinopathy (NPDR) without clinically significant macular edema… (More)
This is a preprint of an article accepted for publication in Mathematica Slovaca c 2006 (copyright owner as specified in the journal). Abstract We construct a 2-chromatic Steiner system S(2, 4, 100) in which every block contains three points of one colour and one point of the other colour. The existence of such a design has been open for over 25 years. A… (More)