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We investigate the interplay between the local and asymptotic geometry of a set
and the geometry of model sets
, which approximate
locally uniformly on small scales. The framework for local set approximation developed in this paper unifies and extends ideas of Jones, Mattila and Vuorinen, Reifenberg, and Preiss. We indicate several applications of this framework to variational problems that arise in geometric measure theory and partial differential equations. For instance, we show that the singular part of the support of an
-dimensional asymptotically optimally doubling measure in
) has upper Minkowski dimension at most
It is unknown whether prodromal services improve outcomes in those who go on to develop psychosis, and whether these patients are demographically different from the overall first-episode population.
To compare sociodemographic features, duration of untreated psychosis, hospital admission and frequency of compulsory treatment in the first year after the onset of psychosis in patients who present to prodromal services with patients who did not present to services until the first episode of psychosis.
We compared two groups of patients with first-episode psychosis: one who made transition after presenting in the prodromal phase and the other who had presented with a first episode.
The patients who had presented before the first episode were more likely to be employed and less likely to belong to an ethnic minority group. They had a shorter duration of untreated psychosis, and were less likely to have been admitted to hospital and to have required compulsory treatment.
Patients who develop psychosis after being engaged in the prodromal phase have a better short-term clinical outcome than patients who do not present until the first episode. Patients who present during first episodes may be more likely to have sociodemographic features associated with relatively poor outcomes.
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