First off, what a fantastic name Corylopsis pauciflora has: buttercup winterhazel. The flowers do look a little bit like buttercups, and have a great creamy yellow color (an unusual contrast to the brighter, more sulphuric yellows you see this time of year). It blooms so early in the spring, it makes sense to have the name winterhazel, too.
Of course, it's hard to make out the specimen of Corylopsis from the plastic flowers that are placed with it. Like garden statuary, I lean against using fake flowers in a garden, but appreciate the better intentions of the gardener.
Corylopsis is a member of the Hamamelidaceae, or witch hazel, family. Like witch hazel, it has a great, irregular, spatula-like leaf. It blooms early in the spring and in the right conditions (not these) it has a loose, sprawling suckering habit. A great specimen of this plant can be found just southwest of the restrooms at the Conservatory Gardens in Central Park.
Corylopsis is derivative of the Greek work for hazel (korylos) and -opsis generally means 'looks like.' If you hear -opsis or -oides in a botanical name, it usually means 'looks like.' Pauciflora literally means 'few flowers.'