1.
A. Erikson's theory explains the fluctuations in the figures for this period
B. Erikson's theory provides an explanation of the fluctuations in the figures for this period.
2.
A. Cheng's theory emphasises the importance of extensive reading in language acquisition
B. Cheng's theory puts emphasis on the importance of extensive reading in language acquisition.
For 1: B is less concise as MCS says, but I think "provides an explanation" leaves more room for error in a scientific report, as people could interpret "explains" to mean that the explanation is the only possibility.
For 2: I can't see any difference in meaning between the two, so I'd go with the shorter A.
If I can give a suggestion, I think 'data' fits better than 'figures'.
A- Is more formal. It is more concise.
