Geometric Path Enumeration for Equivalence Verification of Neural Networks

S Teuber, MK Büning, P Kern… - 2021 IEEE 33rd …, 2021 - ieeexplore.ieee.org
… The sets are represented through generalized star sets or zonotopes which we define below…
the time spent per zonotope or we can try to reduce the number of zonotopes which have to …

Effective Certification of Monotone Deep Equilibrium Models

MN Müller, R Staab, M Fischer, M Vechev - arXiv preprint arXiv …, 2021 - arxiv.org
… the containment of an improper M-Zonotope (red) in a proper M-Zonotope (green), by …
3b we show how the proper M-Zonotope can be decomposed into their Box and Zonotope

[PDF][PDF] Process Performance Verification Using Viability Theory. Processes 2021, 9, 482

… Because of simplicity and efficient computations, the proposed algorithms are based on
zonotopes for set representation and computation, while for process representation the …

Robust bounded feasibility verification of piecewise affine systems via reachability computations

R Desimini, M Prandini - IFAC-PapersOnLine, 2019 - Elsevier
… The ratio r/h is the order of the zonotope. Intervals in Rh are zonotopes. The propagation
of … values in a zonotope leads to a zonotope (closure property of zonotopes with respect to …

[HTML][HTML] Characterization of the three-dimensional multiple translative tiles

M Han, K Sriamorn, Q Yang, C Zong - Advances in Mathematics, 2022 - Elsevier
… We call it a zonotope if it is a Minkowski sum of finite number of segments. In other words,
P = S 1 + S 2 + … + S w , where w is an integer and S i are segments in E n . Zonotopes are a …

Continuous GPS Authentication with Chimera using Stochastic Reachability Analysis

T Mina, A Kanhere, S Kousik, G Gao - … Meeting of the Satellite Division of …, 2021 - ion.org
… We similarly maintain a pair of probabilistic zonotopes (p-zonotopes) on the receiver
state error, one based on the variance and bounded biases from the unauthenticated GPS …

Guaranteed Estimation and Distributed Control of Vehicle Formations

RA García Rodríguez, L Orihuela, P Millán… - International Journal of …, 2020 - idus.us.es
… a zonotope, ie X ∩ S, or after the intersection of two zonotopes, ie X1 ∩ X2, can be enclosed
by a new zonotope. With some abuse of notation, we will refer this new zonotope Z as Z …

Topology of Cycles in Pseudolinear Programs

NE Mnev - Journal of Mathematical Sciences, 2004 - Springer
… A)op is representable by a tiling of a generic zonotope by parallelepipeds. The low-dimensional
tilings of zonotopes by parallelepipeds have a special value as local models for physical …

[HTML][HTML] Efficient implementation of Carathéodory's theorem for the single machine scheduling polytope

R Hoeksma, B Manthey, M Uetz - Discrete applied mathematics, 2016 - Elsevier
… We obtain this result by exploiting the fact that the scheduling polytope is a zonotope, and
by the observation that its barycentric subdivision has a simple, linear description. The actual …

Robust fault detection and isolation based on finite-frequency H-/H∞ unknown input observers and zonotopic threshold analysis

M Zhou, Z Cao, Y Wang - IEEE/CAA Journal of Automatica …, 2019 - ieeexplore.ieee.org
zonotope fault detection methods do not take fault sensitivity index into consideration …
based on zonotopes that rigorously consider the unknown disturbance bounds is proposed to …