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The phrase 'establish the connection' is correct and usable in written English.
You can use it to describe the act of creating a relationship or link between two or more things. For example, "When he met the celebrity, he was able to establish a connection with them."
Exact(59)
In the case of the Andrews & Arnold technician, however, they used about 6 feet of twine soaked in salt water (better conductivity than fresh water) that was connected to alligator clips to establish the connection.
By that it will be possible to establish the connection between brain macro (neuronal lineages) and micro (synaptic connectivity) circuitry (Cardona et al., 2009).
If we want young people to fully understand the consequences of sex, it is vital to clearly establish the connection between sex and reproduction from the outset.
She cautioned that this was an observational study, and that more research, particularly in the form of prospective studies, would be needed to firmly establish the connection.
That is why it was such a scandal when Andrew Wakefield failed to declare that his research linking autism and the MMR vaccine was largely funded by people seeking to establish the connection.
It was discouraging that the article about Bloodroot restaurant ("A Vegetarian Spot Where Feminism Is a Main Course," Nov. 17) failed to establish the connection between animal rights and feminism.
Traditionally, causality analysis is performed to establish the connection between different nodes.
It helps the user to establish the connection between different people, places and events.
In addition, we establish the connection between the object-oriented program graph and XML representations.
In a second step, we repeat these tests, but establish the connection before by means of a TCP handshake.
After completion of resource reservation in the target network, the MMT starts to establish the connection in the target network.
More suggestions(18)
reestablish the connection
achieve the connection
define the connection
establish the connectivity
ascertain the connection
establish the relation
establish the linkage
install the connection
establish the linkages
establish the connections
determines the connection
setting the connection
establish the ties
determine the connection
assess the connection
establishes the connection
established the connection
determining the connection
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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