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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 numerizationof in-situ hybridization images in the Allen Gene Expression Atlas, are used totest these methods in the mouse brain. Individual genes are ranked usingintegrals of their expression energies across brain regions. The ranking isgeneralized to sets of genes and the problem of optimal markers of a classicalregion receives a linear-algebraic solution. Moreover, the goodness of thefitting of the expression profile of a gene to the profile of a brain region isclosely related to the co-expression of genes. The geometric interpretation ofthis fact leads to a quantitative criterion to detect markers of pairs of brainregions. Local properties of the gene-expression profiles are also used todetect genes that separate a given grain region from its environment.

Marker Genes for Anatomical Regions in the Brain: Insights from the Allen Gene Expression Atlas