  We develop a mathematical model of information transmission across the
biological neural network of the human brain. The overall function of the brain
consists of the emergent processes resulting from the spread of information
through the neural network. The capacity of the brain is therefore related to
the rate at which it can transmit information through the neural network. The
particular transmission model under consideration allows for information to be
transmitted along multiple paths between points of the cortex. The resulting
transmission rates are governed by potential theory. According to this theory,
the brain has preferred and quantized transmission modes that correspond to
eigenfunctions of the classical Steklov eigenvalue problem, with the reciprocal
eigenvalues quantifying the corresponding transmission rates. We take the model
as a basis for testing the hypothesis that the sulcus pattern of the human
brain has evolved to maximize the rate of transmission of information between
points in the cerebral cortex. We show that the introduction of sulci, or cuts,
in an otherwise smooth domain indeed increases the overall transmission rate.
We demonstrate this result by means of numerical experiments concerned with a
spherical domain with a varying number of slits on its surface.
