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"parallel emergence" is a correct and usable phrase in written English.
You could use it to refer to the occurrence of two or more similar or related events occurring at the same time. For example, "The parallel emergence of new technologies and changing consumer trends have led to a radical transformation in the marketplace."
Exact(14)
In this study, we investigate potential antipredator adaptations that have emerged following the parallel emergence of two different ecotypes of a freshwater isopod (Asellus aquaticus) in lakes in southern Sweden.
Hence the parallel emergence of shamanism throughout the prehistoric world.
What is at work today is linked to a general erosion of the ethical value of privacy and a parallel emergence of a widespread sense of entitlement to look at – or to make use of – the lives of others.
While the scientists were struck by the parallel emergence of the cat images, as well as human faces and body parts in specific memory regions of their computer model, Dr. Ng said he was cautious about drawing parallels between his software system and biological life.
In this way, Clifford believed, it would be possible to explain why the genesis of complex material structures in the course of evolution is accompanied by the parallel emergence of higher forms of sentience and mental activity.
The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then solve for a regression or classification output by means of a mathematical pseudoinverse operation.
Similar(46)
The divergence of the TNFR families in vertebrates has been suggested to parallel the emergence of the adaptive immune system.
The spontaneity of jazz music and its adaptations to local culture over time around the globe parallel the emergence and export of new diseases from their seedbeds to audiences the world over.
Can it be a coincidence that this awareness parallels the emergence of an aesthetic that seems, somehow, to remind us of warehouses and factories — but, with all that burnished wood and polished metal, of warehouses and factories at rest, from another time, at their most impossibly beautiful?
I also began noticing the far greater prevalence of what I've thought of as masculine styling by women, which Chinese friends say parallels the emergence of what they call a unisex style that has become very popular among young men.
The development of the commercial theatre, perceived by Vasari in the 16th century as an extraordinary innovation, parallels the emergence of the commedia companies, known for at least a century and a half as performers of commedia mercenaria (mercenary commedia), commedia all'improvviso (improvised commedia), commedia delle maschere (mask commedia), and, in France, as the comédie italienne.
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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