Pattern-specific neural network design

We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let genuine Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed notbefore, butduring the learning phase.     

Codings of graphs with binary edge labels

LetG(V,E) be a graph. A mappingf:E{0,1} ^m is called a (binary) coding ofG, if the induced mapping , assigns different vectors to the vertices. For the Boolean sum,f is called aB-code, and for the mod 2 sum anM-code. Letm _B (G) resp.m _M (G) be the smallest lengthm for whichB-codes resp.M-codes are possible. Trivially,m _B (G),m _M (G) log₂|V|. Improving results of Z. Tuza we showm _B (G)log₂|V| + 1,m _M (G)log₂|V|+4.     

Dipole transition matrix elements for certain classes of potential models

We prove results about vanishing and nonvanishing of radial dipole matrix elements for certain classes of spherically symmetric potentials. A basic tool is a new sum rule based on Ehrenfest's law and the superposition principle for solutions of the Schrödinger equation.