  The subject of study is a neural network with binary neurons, randomly
diluted synapses and variable pattern activity. We look at the system with
parallel updating using a probabilistic approach to solve the one step dynamics
with one condensed pattern. We derive restrictions on the storage capacity and
the mutual information content occuring during the retrieval process. Special
focus is on the constraints on the threshold for optimal performance. We also
look at the effect of noisy updating, giving a dynamical version of the
critical temperature, the corresponding threshold and an approximation for the
time evolution for small temperatures. The description is applicable to the
whole retrieval process in the limit of strong dilution. The analysis is
carried out as exactly as possible and over the full parameter ranges,
generalizing some former results.
