Specifying the Hamiltonian functionals generates the evolution equations for these state variables from the Poisson brackets.
In that case we say that generates the evolution family.
The loss of photosynthesis has occurred often in eukaryotic evolution, even more than its acquisition, which occurred at least nine times independently and which generated the evolution of the supergroups Archaeplastida, Rhizaria, Chromalveolata and Excavata.
The Hamiltonian operator, acting on quantum states, would then generate the dynamical evolution.
See Hopenhayn (1992) [Section 5] for a general characterization of stochastic processes that can generate the observed evolutions of productivity.
and moreover, H ˜ and H are equivalent and generate the same time evolution.
To the contrary, the standard description of a CA does not take the space-time evolution for granted: it takes the automaton's initial conditions as given, and generates the system evolution over time via the CA transition function.
A system which is apparently but not sensitively dependent on initial conditions will be unpredictable to us, but there will exist an algorithm that, given some finite specification of the initial conditions, generates the future evolution of the system perfectly.
The master equation is linear, and can be written in a Schrödinger-type form
There is no tandem repeat of Vtg genes found in the genomes of genus Culex, Aedes or Ochlerotatus, suggesting that gene conversion rather than unequal crossover generated the concerted evolution of Vtg genes in these mosquito species.
