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In (4), we transform the objective function (2) into finding the optimal transmit powers and rates that maximize the minimal normalized average rate.
We optimized the parameters from all models to get the minimal normalized point process distance between predicted and actual boundaries in each sentence.
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So, from now on, when referring to the geodesic joining two points, we mean the unique minimal normalized one.
So from now on, a geodesic means the unique minimal normalized one.
The described approach includes an exhaustive search procedure to find the group cluster parameters that resulted in an optimal clustering of the group data, by finding a clustering solution with a minimal normalized cut cost [20].
Then (operatorname{exp}_{x} T _{x}Erightarrow E) is a diffeomorphism, and for any two points (x, yin E), there exists a unique minimal normalized geodesic (gamma_{x,y}=operatorname{exp}_{x}toperatorname{exp}_{x}^{-1}y) for every (tin[0,1]) joining x to y.
Using a 1.75-fold change and a minimal normalized signal of 100 as cutoff we obtained 1338 significantly regulated probe sets, of which 335 were up- and 1003 down-regulated (supplemental Table S1).
The reads were trimmed to a minimal length of 25 bases resulting in an average size of 35 bases and maximum of 71 bases and aligned with a minimal normalized score = 4.5 [ 10].
The minimal material volume (normalized) is also given in closed form by a simple function of ρ and q, namely, V= q ρ-1/q-ρ1/q).
In order to standardize the analyzed profiles across all neurons, the stimulus strength was normalized according to the minimal step current required to reach AP-threshold (the membrane potential above which an action potential is initiated).
Cluster assignments were further fine-tuned by a script that found the true centroid of each cluster, as defined by the sequence with minimal average normalized Hamming distance to every other sequence in the cluster.
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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