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Although the responses of trees to flooding seem to be manifold, variability within an ecosystem is greater than that between ecosystems despite widely differing species/genera/families dominating the respective floodplains.
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Coupled physical-biological models offer a framework for diagnosis of these manifold contributions to variability in Alexandrium populations in the Gulf of Maine (GOM).
A great variability induces a multi-manifold parameter space which disturbs the AAM convergence.
Example 2 (variability along lower-dimensional manifolds) Consider the genetic toggle switch [ 29], where two proteins X1 and X2 mutually repress the other protein's expression (illustrated in Figure 5).
We need a view manifold to accommodate the view-induced shape variability for different targets.
The identity manifold captures both inter-class and intra-class variability of target shapes, while a hemispherical view manifold is involved to account for the variability of viewpoints.
The merits of considering uncertainties are manifold: it allows for assessing the reliability and variability of the response(s) and, most importantly, it provides information to increase the reliability and to improve the design as well as the fidelity of the prediction.
As shown in Figure 1, the 1-D identity manifold captures both inter-class and intra-class shape variability.
Specifically, the identity manifold was proposed to capture both inter-class and intra-class shape variability among different target types.
Understanding the nature and mechanism of such variability, which is commonly referred to as 'transcriptional noise', has manifold functional consequences [ 37].
The requirements of video analysis techniques are manifold, such as dealing with cluttered background, camera motion, occlusion, and geometric and photometric variability, [1, 4, 5].
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CEO of Professional Science Editing for Scientists @ prosciediting.com