  We give a new approach to coding sequence (CDS) density estimation in genomic
analysis based on the topological pressure, which we develop from a well known
concept in ergodic theory. Topological pressure measures the "weighted
information content" of a finite word, and incorporates 64 parameters which can
be interpreted as a choice of weight for each nucleotide triplet. We train the
parameters so that the topological pressure fits the observed coding sequence
density on the human genome, and use this to give ab initio predictions of CDS
density over windows of size around 66,000bp on the genomes of Mus Musculus,
Rhesus Macaque and Drososphilia Melanogaster. While the differences between
these genomes are too great to expect that training on the human genome could
predict, for example, the exact locations of genes, we demonstrate that our
method gives reasonable estimates for the "coarse scale" problem of predicting
CDS density.
  Inspired again by ergodic theory, the weightings of the nucleotide triplets
obtained from our training procedure are used to define a probability
distribution on finite sequences, which can be used to distinguish between
intron and exon sequences from the human genome of lengths between 750bp and
5,000bp. At the end of the paper, we explain the theoretical underpinning for
our approach, which is the theory of Thermodynamic Formalism from the dynamical
systems literature. Mathematica and MATLAB implementations of our method are
available at http://sourceforge.net/projects/topologicalpres/.
