A. J. Wilkie

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Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of(More)
Let F be a collection of holomorphic functions and let R(PR(F)) denote the reduct of the structure Ran to the ordered field operations together with the set of proper restrictions (see below) of the real and imaginary parts of all functions in F . We ask the question: Which holomorphic functions are locally definable (ie have their real and imaginary parts(More)
BACKGROUND Public health officials of the Tibet Autonomous Region (TAR) of China requested a survey of blindness, eye diseases, and eye care service utilisation to assist the development of a 10 year blindness prevention and treatment plan. The objective of the survey was to determine the prevalence of blindness and visual impairment, as well as cataract(More)
The work in this paper has been motivated by two questions from the theory of o-minimality (see for instance [6]): (1) Does every o-minimal expansion of the real field admit analytic cell decomposition? (2) Does there exist a “largest” o-minimal expansion M of the real field, in the sense that any other o-minimal expansion of the real field is a reduct of(More)
AIMS The frequency of the Taq I A alleles (A1 and A2) of the D2 dopamine receptor (DRD2) gene was examined in Caucasian post-traumatic stress disorder (PTSD) patients and controls. RESULTS In 91 PTSD patients, the frequency of the A1 allele was higher (P = 6.12 x 10(-3)) than in the 51 controls. In the 38 PTSD harmful drinkers (>or=60 g alcohol/day), A1(More)
BACKGROUND A recently published, population based survey of the Tibet Autonomous Region (TAR) of China reported on low vision, blindness, and blinding conditions. This paper presents detailed findings from that survey regarding cataract, including prevalence, cataract surgical coverage, surgical outcome, and barriers to use of services. METHODS The Tibet(More)