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In this paper, by solving a maximum hemispherical partitioning problem raised from a weighted Gaussian image, an optimization algorithm is proposed to partition a free-form surface into two sub-patches and simultaneously report the optimal representative normals.
In the learning stage, the hyperparameters C v,n and C w,n of the state-space model in (7) are estimated by solving a maximum likelihood (ML) problem (see Section 4.1 for more details).
SCISSORS attempts to clean up these regions by solving a maximum subarray problem.
Finding an optimal set of edges can be done by solving a maximum weight-matching problem on a related graph.
Finding an optimal set of edges is done by solving a maximum weight-matching problem in a bipartite graph, where vertices with greater indegree than outdegree constitute one part, and the vertices with greater outdegree than indegree are the other.
The estimation of the parameters a, b is done by solving a maximum likelihood problem min a, b L (a, b ), where L (a, b ) = ∑ i = 1 N (t i log (p i ) + (1 - t i ) log (1 - p i ) ) and p i = 1 1 + exp (a · f i + b ), f i = f (x i ), t i = N + + 1 N + + 2 if y i = 1 1 N - + 2 if y i = - 1, i = 1, …, N, where N+, N- are the sizes of the positive and negative class respectively.
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In MTreeMix, the estimation of a single tree is based on solving a maximum weight branching problem by a combinatorial algorithm.
On the other hand, the impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains and some parameters are fixed.
Noticeably, when the impulsive interval is fixed, the impulsive gain can reach a proper value by adjusting itself; when the impulsive gain is fixed, we can estimate the impulsive interval by solving a sequence of maximum value problems.
Noticeably, the impulsive gains can adjust themselves to proper values in terms of the updating laws, and intervals can be estimated by solving a sequence of maximum value problems.
According to the discussions in Remarks 1 and 2, the impulsive gains or instants can adjust themselves to proper values or be estimated by solving a sequence of maximum value problems.
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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