Zero-One Designs Produce Small Hard SAT Instances

Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0,1) designs (PB01Ds) are introduced as an extension of balanced incomplete block designs (BIBDs) and (0,1) designs. Also, (0,1) difference sets are introduced as an extension of certain cyclical difference sets. Constructions based on (0,1) difference sets enable generation of PB01Ds over a much wider range of parameters than is possible for BIBDs. Building upon previous work of Spence, it is shown how PB01Ds lead to small, very hard, unsatisfiable formulas. A new three-dimensional form of combinatorial block design is introduced, and leads to small, very hard, satisfiable formulas. The methods are validated on solvers that performed well in the SAT 2009 and earlier competitions.

Latanoprost for open-angle glaucoma (UKGTS): a randomised, multicentre, placebo-controlled trial

Background
Treatments for open-angle glaucoma aim to prevent vision loss through lowering of intraocular pressure, but to our knowledge no placebo-controlled trials have assessed visual function preservation, and the observation periods of previous (unmasked) trials have typically been at least 5 years. We assessed vision preservation in patients given latanoprost compared with those given placebo.

Methods
In this randomised, triple-masked, placebo-controlled trial, we enrolled patients with newly diagnosed open-angle glaucoma at ten UK centres (tertiary referral centres, teaching hospitals, and district general hospitals). Eligible patients were randomly allocated (1:1) with a website-generated randomisation schedule, stratified by centre and with a permuted block design, to receive either latanoprost 0·005% (intervention group) or placebo (control group) eye drops. Drops were administered from identical bottles, once a day, to both eyes. The primary outcome was time to visual field deterioration within 24 months. Analyses were done in all individuals with follow-up data. The Data and Safety Monitoring Committee (DSMC) recommended stopping the trial on Jan 6, 2011 (last patient visit July, 2011), after an interim analysis, and suggested a change in primary outcome from the difference in proportions of patients with incident progression between groups to time to visual field deterioration within 24 months. This trial is registered, number ISRCTN96423140.

Findings
We enrolled 516 individuals between Dec 1, 2006, and March 16, 2010. Baseline mean intraocular pressure was 19·6 mm Hg (SD 4·6) in 258 patients in the latanoprost group and 20·1 mm Hg (4·8) in 258 controls. At 24 months, mean reduction in intraocular pressure was 3·8 mm Hg (4·0) in 231 patients assessed in the latanoprost group and 0·9 mm Hg (3·8) in 230 patients assessed in the placebo group. Visual field preservation was significantly longer in the latanoprost group than in the placebo group: adjusted hazard ratio (HR) 0·44 (95% CI 0·28–0·69; p=0·0003). We noted 18 serious adverse events, none attributable to the study drug.

Interpretation
This is the first randomised placebo-controlled trial to show preservation of the visual field with an intraocular-pressure-lowering drug in patients with open-angle glaucoma. The study design enabled significant differences in vision to be assessed in a relatively short observation period