We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse zonotopes can represent nonconvex sets and are generalizations polytopes, Taylor models. Operations like Minkowski sum, quadratic mapping, reduction the size be computed with complexity w.r.t. dimension system. In particular, reachability analysis nonlinear systems, wrapping effe...

In many private set operations, a set is represented by a polynomial over a ring Zσ for a composite integer σ, where Zσ is the message space of some additive homomorphic encryption. While it is useful for implementing set operations with polynomial additions and multiplications, a polynomial representation has a limitation due to the hardness of polynomial factorizations over Zσ. That is, it is...

The Visual Information Retrieval (VIR) area requires robust implementations achieved trough mathematical representations for images or data sets. The implementation of a mathematical modeling goes from the corpus image selection, an appropriate descriptor method, a segmentation approach and the similarity metric implementation whose are treated as VIR elements. The goal of this research is to f...

Let (G, D) be a permutation representation of a finite group G acting on a finite set D. The cycle index of this representation is a polynomial P(G, D; Xl ,..., x,~) in several variables xl ,..., x~ with rational numbers as coefficients (see [1]). The restriction, made in [1], that the representation (G, D) is faithful, is unnecessary and we put no restriction on (G, D) whatsoever. We replace e...