[HTML][HTML] A survey of safety and trustworthiness of deep neural networks: Verification, testing, adversarial attack and defence, and interpretability

X Huang, D Kroening, W Ruan, J Sharp, Y Sun… - Computer Science …, 2020 - Elsevier
… A zonotope Z consists of constraints in the form of z i = a i + ∑ j = 1 m b i j ϵ j , where a i ,
b i j are real constants and ϵ j ∈ [ l j , u j ] . The conjunction of these constraints expresses a …

Set-Based B-Series

J Alexandre dit Sandretto - Mathematics, 2022 - mdpi.com
… Indeed, a polytope can be described by the intersection of a finite number of zonotopes [47].
Let us define an initial condition Y 0 enclosed by a polytope P 0 . If P 0 = Z 0 ∩ Z 1 ∩ ⋯ ∩ Z …

Kinematic Stability based AFG-RRT* Path Planning for Cable-Driven Parallel Robots

UA Mishra, M Métillon, S Caro - 2021 IEEE International …, 2021 - ieeexplore.ieee.org
… , T becomes a special type of polytope in wrench space called the zonotope, given by …
Mathematically, the Hyperplane Shifting Method (HSM) [8] is implemented to convert the zonotope, …

Computation of the Available Force Set of a 3-RPRR Kinematically Redundant Planar Parallel Manipulator

M Arsenault, R Boudreau… - Journal of …, 2021 - asmedigitalcollection.asme.org
… 3, the vertex’s location in the wrench space is thus confined to a zonotope whose edges
are parallel to lines L q i ⁠, which are defined as being parallel to the q i vectors. …

[PDF][PDF] ISOPERIMETRIC PROBLEMS FOR THREE-DIMENSIONAL PARALLELOHEDRA AND TRANSLATIVE, CONVEX MOSAICS

Z LÁNGI - researchgate.net
… can be defined as the Minkowski sums of at most six segments with prescribed linear
dependencies between the generating segments, and thus, they are a subclass of zonotopes. …

Transformed sparse grids for high-dimensional models

C Schnick - 2021 - elib.uni-stuttgart.de
… After we obtained a zonotope Zp, the next step is to determine how to go from this zonotope
… To achieve this, the zonotope Zp is first encased in an r-dimensional hypercube, called the …

On the capacity of MIMO optical wireless channels

L Li, SM Moser, L Wang… - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space
optical intensity channel under a per-input-antenna peak-power constraint and a total …

Resilience of Linear Systems to Partial Loss of Control Authority

JB Bouvier, M Ornik - arXiv preprint arXiv:2209.08034, 2022 - arxiv.org
zonotope of center 0 and generators Bi, the columns of B. Similarly, CW = (0,C1,...,Cp). However,
Z is not a zonotope … build an underapproximation of Z with a symmetric zonotope (0,g1,..…

[HTML][HTML] The r-signed Birkhoff transform

R Ehrenborg - Discrete Mathematics, 2021 - Elsevier
… of a hyperplane arrangement and the associated zonotope. That is, when applying the …
entry of the flag f -vector of the zonotope in terms of the associated intersection lattice also holds …

Contribution au pronostic des systèmes complexes. Application aux systèmes énergétiques

A Al Mohamad - 2021 - tel.archives-ouvertes.fr
… Kalman étendu augmenté) et ensembliste (par zonotopes), en proposant un filtre de Kalman
… A noter que les zonotopes sont adoptés pour leurs calculs simples en plus de leur capacité …