From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding result for a Lipschitz-continuous function between two such manifolds. That is, we outline the construction of a simplicial map which recovers the induced maps o...

Let (Xi)i∈N be a sequence of independent and identically distributed random variables with values in the set N0 of non-negative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1, . . . , Xn} of the first n values. We obtain necessary and sufficient conditions in terms of ...