Safe Reinforcement Learning Using Black-Box Reachability Analysis
… We represent sets using constrained zonotopes, zonotopes, and intervals, because they
enable efficient Minkowski sum computation (a key part of reachability analysis) [30] and …
enable efficient Minkowski sum computation (a key part of reachability analysis) [30] and …
Scalable Distributed Reachability Analysis for Cyber-Physical Networked Microgrids with Communication Latency
… the dynamic operations of the cyber-physical networked microgrid system, Zonotope
method is adopted in this work. Mathematically, Zonotope is a type of polytope [10], which is a …
method is adopted in this work. Mathematically, Zonotope is a type of polytope [10], which is a …
[HTML][HTML] Limitations of the hyperplane separation technique for bounding the extension complexity of polytopes
M Brugger - Operations Research Letters, 2021 - Elsevier
… graphic zonotopes of … zonotopes of K n . In Section 3.2, we show that the hyperplane
separation bound is at most a constant when applied to our linear description of graphic zonotopes (…
separation bound is at most a constant when applied to our linear description of graphic zonotopes (…
Higher Bruhat orders of types B and C
VI Danilov, AV Karzanov, GA Koshevoy - arXiv preprint arXiv:2107.09462, 2021 - arxiv.org
… , and Ziegler), and on our study of the so-called symmetric cubillages of cyclic zonotopes. …
recall basic facts on cubillages of cyclic zonotopes used in the paper. For details, see [3]. A …
recall basic facts on cubillages of cyclic zonotopes used in the paper. For details, see [3]. A …
Minimizing Low-Rank Quasi-Concave Functions Over Greedy Polytopes
JR Scott - 2020 - oaktrust.library.tamu.edu
We consider the problem of minimizing a function that attains its minimum over a greedy
polytope at one of its vertices. This problem class contains many computationally intractable …
polytope at one of its vertices. This problem class contains many computationally intractable …
[HTML][HTML] Complex Lp affine isoperimetric inequalities
W Wang, L Liu - Advances in Applied Mathematics, 2021 - Elsevier
… Zonoids are defined as limits of zonotopes in the Hausdorff metric, where zonotopes are
Minkowski sum of line segments. Indeed, any origin-symmetric convex body in R 2 is a zonoid. …
Minkowski sum of line segments. Indeed, any origin-symmetric convex body in R 2 is a zonoid. …
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 …
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
… 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 …
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 …
zonotopes for set representation and computation, while for process representation the …
[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 …
P = S 1 + S 2 + … + S w , where w is an integer and S i are segments in E n . Zonotopes are a …