The goal of this paper is to study geometric and extremal properties the convex body BF(M), which unit ball Lipschitz-free Banach space associated with a finite metric M. We investigate ℓ1 ℓ∞-sums, in particular we characterize spaces such that BF(M) Hanner polytope. also whose are isometric. discuss extreme volume product P(M)=|BF(M)|⋅|BF(M)∘|, when number elements M fixed. show if P(M) maxima...

We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. three modules and combine them to obtain two network architectures, coined R-VPNet LA-VPNet. The distinct feature of the proposed models is that they are intrinsic volume-preserving. In addition, corresponding approximation theorems proved, which theoretically guarantee expre...