We want to sketch the support of a probability measure on Euclidean space from samples that have been drawn from the measure. This problem is closely related to certain manifold learning problems, where one assumes that the sample points are drawn from a manifold that is embedded in Euclidean space. Here we propose to sketch the support of the probability measure (that does not need to be a man...

We prove two continuity theorems for the Lyapunov exponents of the maximal entropy measure of polynomial automorphisms of C. The first continuity result holds for any family of polynomial automorphisms of constant dynamical degree. The second result is the continuity of the upper exponent for families degenerating to a 1-dimensional map.

Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance cons...

Recent changes in the organisation of primary health care have increased the range of professionals that patients may encounter, leading to renewed interest in the importance of continuity of care. To assess whether organisational changes have had an impact on continuity, it is necessary to define and measure the term. Researchers seeking to assess continuity face many conceptual and practical ...

In [10] we introduced a new notion of isomorphisms for topological measure spaces, which preserve almost sure continuity of mappings, almost sure convergence of random variables, and weak convergence of probability measures. The main thrust of that paper is the construction of an isomorphism from a Polish space with a nonatomic Borel probability measure to the unit Lebesgue interval (I, *). App...