Request #555

There’s a YA book I would have read sometime around 2008-2012 I think I’ve been trying to find for years. I remember very little of it other than time travel was a key plot point. Someone in the book explain time as the stones in a diamond ring, where all moments exist at the same time, and we constantly jumping from stone to stone. There was a group of kids in it and part of the plot is that they did this big presentation or poster board about why people yawn, and how it is contagious. There’s a homeless man involved who is generally viewed as being crazy and I think referred to as “quackers” but in the end is ultimately revealed to have traveled back through time to save one of the kids from being hit and killed by a car, sacrificing himself in the process – he may have even been an older version of one of the kids from another timeline. And I remember the cover having a big red dot on top of a map. This is so vague, hopefully someone can help!