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Several attempts have been made to informally define the robustness property of watermarking.
We define the robustness of a level set homology class of a function f : double-struck X → ℝ as the magnitude of a perturbation necessary to kill the class.
Here, the pass that returns with ĩ, w ~ and the failure, ⊥ can be used to define two potential variants, robust and fragile respectively, of watermarking schemes for different P. Another variant, semi-fragile watermarking scheme can also be defined considering a suitable subset of P. Thus, we define the robustness property in Definition 4.6 considering detection ability at three different levels.
To define the robustness of a behavior, it is more convenient to reason with a positive notion that describes how good the (possibly perturbed) system performs, i.e. satisfies a dynamical property.
The aims of the study were firstly to apply novel culture methods in order to access to the largest cultured bacterial diversity, and secondly to better define the robustness of the community for 3 important functions: As III) oxidation, cellulose degradation and cobalamine biosynthesis.
Thus, to define the robustness of a specific biological outcome requires understanding for a cell type the degree to which several alternative signalling pathways can substitute for each other to execute qualitatively distinct RTK-driven responses, and distinguishing permissive from non-permissive pathways.
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(This is how we defined the robustness property in Definition 4.6).
Particularly, we defined the robustness and security properties of watermarking using the sets of (signal and image based) processing techniques and possible attacks, respectively.
To compare the effect of the quality of network to our method with prioritization, we defined the robustness as investigating changes in the prediction capacity of the DDA scores when the network was perturbed.
(ii) Next, while moving down the sorted VC list, we defined the robustness score (R ) in order to identify how far the genes can be selected to form our prognostic gene signature.
Overall robustness We define the overall robustness as the impact that all possible failure sequences might have, in average, on the system.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com