Optimization and abstraction: a synergistic approach for analyzing neural network robustness

G Anderson, S Pailoor, I Dillig… - Proceedings of the 40th …, 2019 - dl.acm.org
… and red zonotopes, while in the powerset domain we keep the blue and red zonotopes
separate… The final images show how the second affine transformation affects all three zonotopes. …

[PDF][PDF] Complexity of experimental designs and polynomial models via Betti numbers

H Maruri, H Wynn… - SAMSI Transition …, 2009 - researchgate.net
… Using the zonotope theory we can (theoretically) find candidate w-vectors. • Betti numbers
for the Stanley-Reisner ideal and its Artinian closure (adjoint the quadratics a 2 ,b 2 ,...): △, β(I…

DIO-based robust fault estimation observer for discrete-time switched systems with unknown input*

Y Yang, Y Wu, D Du - 2020 35th Youth Academic Annual …, 2020 - ieeexplore.ieee.org
zonotopes, e(t) is also bounded in a zonotope denoted by Ω = 〈0,H(k)〉, where H(k) ∈ R(nx+nf
)×r . According to (11), the generator matrix H(k) of the zonotope Ω … zonotopes, we have …

[HTML][HTML] Adaptive reachability algorithms for nonlinear systems using abstraction error analysis

M Wetzlinger, A Kulmburg, A Le Penven… - Nonlinear Analysis: Hybrid …, 2022 - Elsevier
… Furthermore, the simplification of the set representation is tackled by limiting the Hausdorff
distance between the original and reduced sets; we demonstrate this for zonotopes. Both …

Reachability analysis for managing platoons at intersections

IB Makhlouf, H Diab… - … Conference on Control …, 2013 - ieeexplore.ieee.org
… For the computation of reachable sets we use our method based on zonotopes as approximation
sets. We show how decisions to manage the platoon at the intersection under safety …

Discriminant coamoebas through homology

M Passare, F Sottile - Journal of Commutative Algebra, 2013 - projecteuclid.org
… defined over the real numbers and define its associated zonotope chain. Our main result is a
… ) the coamoeba and zonotope chains map to the coamoeba AB and the zonotope ZB, and a …

Robust identification and fault diagnosis using set-membership approaches

J Blesa - 2011 - dialnet.unirioja.es
… form and complex shapes (zonotopes and polytopes) for … systems with uncertain parameters
bounded by a zonotope. … in parameters was bounded by a zonotope, whereas in the method …

Zonotopic Reachability Analysis for an Unmanned Helicopter

HG Harno, Y Kim - 2019 19th International Conference on …, 2019 - ieeexplore.ieee.org
… of a zonotope can be written as Z = (g0, g1, . . . , ge). From Definition 1, a zonotope is a special
polytope that is convex and symmetric with respect to its center. The zonotope is favorable …

[PDF][PDF] МАТЕМАТИКА И МАТЕМАТИЧЕСКО ОБРАЗОВАНИЕ, 2005 MATHEMATICS AND EDUCATION IN MATHEMATICS, 2005

SM Markov, AC da Rocha Costa, GP Dimuro - math.bas.bg
… with zonotopes in the plane, and more specifically, the inclusion relation between zonotopes
in the plane. Our purpose is to use only the implicit presentation of zonotopes as Minkowski …

[PDF][PDF] Hyperplane arrangements, hypercubes and mixed graphs

G Gordon - CONGRESSUS NUMERANTIUM, 1997 - researchgate.net
… We conclude by briefly exploring the connections between our hybrid mixed graphs and
zonotopes, root systems corresponding to subgroups and the group theoritic structure of the …