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The phrase "the channels through which" is correct and commonly used in written English.
It is typically used to refer to the avenues or means through which something is conveyed or communicated. Example: "The internet and social media have become the main channels through which companies promote their products and services."
Exact(60)
For developing economies, the channels through which inequality might drag down growth seem clear.
They also raise important questions about the channels through which it impacts economic growth and human development.
But those who don't might change their minds if they altered the channels through which their opinions came.
[We've got] the framework, the channels through which people have got to come if they really think they have something to say.
And we need to strengthen and broaden the channels through which democracy can be practiced, including the role of the media.
And you need to understand the channels through which subprime defaults could spread to the wider economy.America's residential mortgage market is huge.
Developers finally silenced the noise by removing some louvers in a cooling tower to widen the channels through which the wind whistled.
It injures the cells that line arteries and stimulates the growth of smooth muscle cells; both effects can result in lesions that narrow the channels through which blood flows.
However, Supporter Ownership Week is designed to highlight the channels through which things can be taken further, and Supporters Direct hopes a crowdfunding appeal can attract both financial support and attention.
Efforts to seal the channels through which the mud is escaping are unlikely to succeed, and it is impossible to tell how much fluid remains underground, according to a University of Oslo geology team.
The letter acknowledge such concerns, but argues that the best way to address them is to promote responsible, transparent and accountable systems in line with existing regulations, rather than by closing down the channels through which funds are sent.
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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