The phrase "are determined by" can be replaced with a variety of synonyms to convey the same meaning. Some possible alternatives include "are dictated by," "are established by," "are influenced by," "are controlled by," and "are shaped by." Each of these expressions emphasizes the idea that certain factors or forces are responsible for determining a particular outcome or situation. By choosing the most appropriate synonym, writers can ensure that their message is clear and concise, while also adding variety and nuance to their prose. Ultimately, the choice of synonym will depend on the specific context and tone of the writing.