This invention is an oligomer-based analog neural network (ANN) comprising weight and saturation oligomers, the concentrations of which are selected such that activation of the ANN by a set of input oligomers generates a set of output oligomers, the sequences and relative concentrations of which are dependent on the sequences and relative concentrations of the input oligomers. The invention further includes methods for using such an ANN for solving any problems amenable to solution by a trained neural network. A preferred embodiment of the claimed invention is a DNA-based ANN that accepts cDNA molecules as inputs and analyzes the gene expression profile of the cells from which the cDNA is derived. The DNA-based ANN is typically trained with a computer to identify the weights giving accurate mapping of the inputs to the outputs; and the concentrations of weight oligomers of the DNA-based ANN are then selected accordingly.