  In this paper, we introduce tiled graphs as models of learning and maturing
processes. We show how tiled graphs can combine graphs of learning spaces or
antimatroids (partial hypercubes) and maturity models (total orders) to yield
models of learning processes. For the visualization of these processes it is a
natural approach to aim for certain optimal drawings. We show for most of the
more detailed models that the drawing problems resulting from them are
NP-complete. The terse model of a maturing process that ignores the details of
learning, however, results in a polynomially solvable graph drawing problem. In
addition, this model provides insight into the process by ordering the subjects
at each test of their maturity. We investigate extremal and random instances of
this problem, and provide exact results and bounds on their optimal crossing
number.
  Graph-theoretic models offer two approaches to the design of optimal maturity
models given observed data: (1) minimizing intra-subject inconsistencies, which
manifest as regressions of subjects, is modeled as the well-known feedback arc
set problem. We study the alternative of (2) finding a maturity model by
minimizing the inter-subject inconsistencies, which manifest as crossings in
the respective drawing. We show this to be NP-complete.
