Optimal sizes of dendritic and axonal arbors in a topographic projection

I consider a topographic projection between two neuronal layers with different densities of neurons. Given the number of output neurons connected to each input neuron (divergence) and the number of input neurons synapsing on each output neuron (convergence) I determine the widths of axonal and dendritic arbors which minimize the total volume of axons and dendrites. Analytical results for one-dimensional and two-dimensional projections can be summarized qualitatively in the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology and connectivity are known. The rule may be used to infer connectivity of neurons from their morphology.Comment: 8 pages, 7 figures, submitted to Nature Neuroscienc

Understanding the dynamics of fractional edge states with composite fermions

Fractional edge states can be viewed as integer edge states of composite fermions. We exploit this to discuss the conductance of the fractional quantized Hall states and the velocity of edge magnetoplasmons.Comment: 3 pages, revte