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Next, we introduce expanded paths, where a negative path [ A i, B m, A j ] ¯ is converted into two expanded paths [ A i,B m,A j ] and [ A j,B m,A i ] that are positive.
After the initial path was generated, we continued optimization for 451 more optimization steps, while gradually expanding the path to 185 beads.
where the second equality is obtained by expanding the path gain a, as given in Equation (7) (see also Equations (32) to (35) in [10] for further details on the derivation of the log-likelihood function fML).
While Korenblat, who is also the former president of the International Mountain Bicycling Association, is currently working with the NPS on expanding bike paths and lanes within the parks, she believes that "little pockets of creativity" are responsible for some of the most innovative changes.
For a fragment S k i 1, i 2, …, i k j 1, j 2, …, j k with a total of P paths that include all expanded negative paths and all positive paths of S k i 1, i 2, …, i k j 1, j 2, …, j k, the generation of the path graph Φ has time complexity O (P (P − 1 ) ).
This framework is based on the Carbon Flux Path (CFP) approach, a mixed-integer linear program that expands classical path finding techniques by considering additional biophysical constraints.
Both (mathsf {NN}) and (mathsf {DENN}) expand a path.
Consider the (i+1 th iteration to expand the path by adding one more node.
And then let us learn from such deliberateness as - in order for us to continue to Lean In effectively and expand the path further for more women - we need to (not just) Lean In but Stay In and that takes the same courage, tenacity, intelligence, aggressiveness, and effective leadership exhibited by the men who opened those initial doors to us.
The nodes of Φ correspond uniquely to the expanded negative paths and the positive paths of a fragment S k i 1, i 2, …, i k j 1, j 2, …, j k.
To summarize, we generate a digraph Φ with the following properties: ● The nodes Φ i of Φ are the expanded negative paths and the positive paths of a given fragment S k i 1, i 2, …, i k j 1, j 2, …, j k. ● A directed edge (Φ i, Φ j ) exists if and only if the end species node of the path corresponding to Φ i is the starting species node of the path corresponding to Φ j.
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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