Deep learning has transformed the way we think of software and what it can do. But deep
neural networks are fragile and their behaviors are often surprising. In many settings, we need …

… The reachable set is produced by partitioning time into small intervals, linearizing the dynamics
in each time interval, then overapproximating the reachable set with a zonotope for each …

… a particular level of probability) via a zonotope representation, then predict the reachability of
all … In this work, we use the zonotope to represent all sets. In general, a zonotope Z ∈ Rn is …

… II we introduce zonotopes and reachability analysis of linear … Zonotopes The advantage of
zonotopes as a set-… of an operation involving zonotopes is again a zonotope. In the following …

… The cones of any real central hyperplane arrangement induce a fan that is the normal fan
of a zonotope. Moreover, choosing one of the regions of that fan as the base region induces a …

Deep neural networks (DNNs) have been applied in safety-critical domains such as self driving
cars, aircraft collision avoidance systems, malware detection, etc. In such scenarios, it is …

… In this study, the size of the residual zonotope ℛ k + 1 is described by the P -radius. Then,
the robustness condition can be formulated by minimizing the P -radius. The FD observer for …

… Second, we consider the estimated zonotope width of the GSIO. If no order-reduction step is
… We define the width of estimated intervals and zonotopes of the first and second subsystems …

… Table B.1 gives Whitney numbers of the first and of the second kind for several four-dimensional
zonotopes. Face … Namely, for subgraphs of Kr+1 representing zonotopes we have [56] …

… In particular, a zonotope always has a center of symmetry. A zonoid is a limit of a sequence
of zonotopes in the Hausdorff metric. We need a generalization of the notion of zonotope to …