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In the following example, is the determiner optional or compulsory?

X is defined by two parameters: scale and time shift.

or

X is defined by two parameters: the scale and the time shift.

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X is defined by two parameters: scale and time shift.

is fine.
In a context that I imagine, I would consider scale and time shift labels. Unless you called the parameters the scale and the time shift elsewhere, you shouldn't use them in your example.

The second example sounds wrong at best. Some more context would be needed to support such a usage.

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