Before revision:  Data in biology are often sampled sparsely in time , therefore a method is developed to compute a temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator .
After revision:  Data in biology are often sampled sparsely in time . Therefore we compute what we call the temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator .