2

I am confused about how to use in the presence. Here I have written a sentence in which I think the before presence should be omitted.

This situation might be more critical in the presence of long edges, although we restrict the irregular shape boundary to minimize the complexity.

4

No, it's fine as you've written it.

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2

I disagree with you, I think the word "The" fits here. I think "in presence" is sort of awkward and incorrect. In the presence of is definite, meaning The presence. Presence is a definite article, like The Shirt The Car, The X. It

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