… of a zonotope can be find in [25] and [26], but the computation of the zonotopes in this paper
is based on the above mentioned definition. A full description of the zonotopes construction …

… zonotope of the zonotope resulting from the above step. Any technique that calculates the
over-… zonotope is called a zonotope order reduction technique and the resulting zonotope must …

… of n zonotopes. Although there is no “natural” graph to represent the structure of a set of
zonotopes, … This allows us to give a simple application for mixed volumes of zonotopes with few …

The paper has two parts. In the first part we survey the existing results on the cube conjecture
of Las Vergnas. This conjecture claims that the orientation of the matroid of the cube is …

… We will see that, in an appropriate sense, zonotopes form the geometric building blocks for
neural networks (Section 6.2). We then prove that the geometry of the function represented by …

… In this work, the order of a zonotope X refers to the number p of its … a zonotope X is the
Frobenius norm of its generator matrix H (that is, ||H||F = √tr(HT H)). The covariation of a zonotope …

… 1) Reachability using zonotopes: The choice of the representation of the sets Ω0,..., ΩN is …
in [18] the use of zonotopes for the representation of the sets Ω0,..., ΩN . A zonotope Z is a …

… Zonotope with center c ∈ Rn and generators v1,...,vk ∈ Rn … Zonotopes in Reachability …
with X0, U zonotopes, ˆXt is a zonotope for any δ > 0 …

… Following computation algorithm in [18], we can find this reachable set using zonotopes by(5…
H considering that Q is a zonotope and ◊ is zonotope inclusion. For computation of viability …

… , we compute a Lipschitz zonotope in line 5 to provide guarantees. Next, we perform the
reachability recursion in line 6 given the previously computed zonotopes. Note that the Lipschitz …