  Quantitative criteria are proposed to identify genes (and sets of genes)
whose expression marks a specific brain region (or a set of brain regions).
Gene-expression energies, obtained for thousands of mouse genes by numerization
of in-situ hybridization images in the Allen Gene Expression Atlas, are used to
test these methods in the mouse brain. Individual genes are ranked using
integrals of their expression energies across brain regions. The ranking is
generalized to sets of genes and the problem of optimal markers of a classical
region receives a linear-algebraic solution. Moreover, the goodness of the
fitting of the expression profile of a gene to the profile of a brain region is
closely related to the co-expression of genes. The geometric interpretation of
this fact leads to a quantitative criterion to detect markers of pairs of brain
regions. Local properties of the gene-expression profiles are also used to
detect genes that separate a given grain region from its environment.
