Abstract Positive dynamical or control systems have all their variables nonnegative. Euler discretization transforms a continuous-time system into on discrete time scale. Some structural properties of the may be preserved by discretization, while other lost. Four fundamental positive are studied in context discretization: positivity, stability, reachability and observability. Both linear nonlin...

We introduce a new general-purpose approach to deep learning on three-dimensional surfaces based the insight that simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust changes in resolution and sampling of surface—a basic property crucial practical applications. Our can be discretized various geometric representations, such as tria...

Abstract A well-known challenge for deformation monitoring is the spatial discretization, i.e. choice of points at which measurements are to be taken. Well-chosen employ prior knowledge yield a significant amount information about certain aspect monitored object. However, such set typically made practically expedient or left measurement instrument itself. We aim derive adaptive discretization s...