Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proo...

Artificially regulating gene expression is an important step in developing new treatment for system-level disease such as cancer. In this paper, we propose a method to regulate gene expression based on sampled-data measurements of gene products concentrations. Inherent noisy behaviour of Gene regulatory networks are modeled with stochastic nonlinear differential equation. To synthesize feed...

We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly, but that a properly weighted version of the trace-norm regularizer works well with non-uniform sampling. We show that the weighted trace-norm regularization indeed yields significant gains on the highly non-uniformly sampled Netflix dataset.

Based on the synchronous language elements introduced in Modelica 3.3, a library is described to utilize the new features in a convenient way for graphical model definition of sampled data systems. The library has elements to define periodic clocks and event clocks that trigger elements to sample, subsample or super-sample partitions synchronously. Optionally, quantization effects, computationa...