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"though there exists" is a correct and usable phrase in written English.
It is often used to introduce a contradictory idea or situation. Example: Though there exists a wealth of evidence supporting the theory of climate change, there are still some who deny its existence.
Exact(19)
Though, there exists a farm that I've been interested in visiting for years and have yet to reach upon the life path set before me, The Factor e Farm, part of Marcin Jakubowski's brain child, Open Source Ecology, has alluded me.
Corrugated web profiles are generally used in single story long span structures though there exists limited number of researches about the performance of the connections.
Among these select few, though, there exists a small cadre of experts whose vital role is all too often overlooked: the routers.
Currently, though, there exists no evidence to support this hypothesis.
Though there exists some advanced optimization procedures of the above nonlinear MAXCUT problem, here we use the greedy gradient search to achieve the computational efficiency for practical applications.
Though there exists this case that the primary users start transmitting at the time of the secondary user starting sensing, these do not increase collision probability.
Similar(41)
Though there exist many different approaches to signal (i.e. short sequence) finding, some new study shows that this problem still leaves plenty of room for improvement.
Deletions finding on the HBV whole genome sequences is thus a very important issue though there exist underlying the challenges in mining such big and complex biological data.
Though there exist several sufficient conditions of MP and AMP for the periodic solution problem in literature like [7 9] (for a brief explanation to these conditions, see Section 4.3), an optimal characterization on MP and AMP is not available.
The Supreme Court expanded that question to somehow allow unlimited, anonymous corporate spending on all elections, even though there existed, like, half a century of laws about that already.
Though there exist drugs to treat leishmaniasis infection [31], possible therapies that combine stimulation of the UPR response in Leishmania with leishmanicidal drugs are of considerable interest due to the rapid evolution of these organisms.
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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