In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coefficients of the polynomials. We further address...

Lyapunov functions are an important tool to determine the basin of attraction of equilibria in Dynamical Systems through their sublevel sets. Recently, several numerical construction methods for Lyapunov functions have been proposed, among them the RBF (Radial Basis Function) and CPA (Continuous Piecewise Affine) methods. While the first method lacks a verification that the constructed function...

We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information about the underlying space, such as the distance function, the distance to a measure, the kNN density estimator, the kernel density estimator, and the kerne...

Abstract Sublevel shrinkage (SLSh) is an underground mining method similar to sublevel caving (SLC) but with continuous backfilling from the top. It features a top-down sequence production drifts orientated in longitudinal or transverse way orebody. Fan drilling and blasting done drifts, where ore then drawn. While drawing, backfill introduced at top flows down by gravity, which supports walls ...