Using Participles

I'm still confused about using participles in writing. I know that we should use them sometimes, but I can't figure out when, especially when I'm reading BBC news, or other sources (of reading).

For example, 'despite inflation dropping to zero, it is unlikely we...' And 'with the monetary policy committee still alert to the risk of very low inflation becoming entrenched, a rise...'

Can anyone here help? Thanks in advance!!:)

In both cases, the form is used in a subsidiary phrase, which qualifies the main clause in the sentence.  It could read, for example  'despite the situation that/although inflation has fallen to zero, it is unlikely we...', or  'with the monetary policy committee still alert to the risk that very low inflation may become entrenched, a rise...'.  The writer wants to emphasize that these are regarded as conditions of the main statement, and using the '-ing' form is a concise and convenient way of doing this.  I could have just written :  ' . . and to use the '-ing' form is a concise and convenient way to do this.  In this case, the present participle substitutes for the infinitive.

You can see that this form can easily be avoided if you are not comfortable using it  [ if it is difficult for you to use it ].