If a sentence starts with a modifier (for instance a participle), this should refer to the subject of the main clause. If it doesn't it is called a dangling modifier, a very common error.
*Examining this concept more thoroughly, it becomes apparent that a wide range of definitions is being used.
When this concept is examined more thoroughly, it becomes more apparent....
*Passing the building, the vandalism became visible.
As we passed the building, the vandalism became visible.
*To understand the causes, vandalism has been extensively investigated.
To understand the causes, researchers have extensively investigated vandalism.
*After studying the problem, vandals are now thought to share certain characteristics.
After studying the problem, researchers think that vandals share certain characteristics.
*When destructive, researchers have learned that vandals are more likely to be in groups.
When vandals are destructive, researchers have learned, they are more likely to be in groups.
Revise most dangling modifiers in one of two ways, depending on what you want to emphasize in the sentence.
*To express themselves, graffiti decorate walls.
To express themselves, some youths decorate walls with graffiti..
Because some youths need to express themselves, graffiti decorate walls.