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Several lines of evidence suggest that excitatory synaptic transmission contributes to the maturation of precise neuronal connections. In the present study we determined whether the specific innervation pattern of single inhibitory arborizations was dependent upon neuronal activity during development. A homogeneous group of glycinergic inhibitory neurons in… (More)

Following Lyons (1990, [4]) we define a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric… (More)

We consider a random walk on Z in a stationary and ergodic random environment, whose states are called types of the vertices of Z. We nd conditions for which the speed of the random walk is positive. In the case of a Markov chain environment with nitely many states, we give an explicit formula for the speed and for the asymptotic proportion of time spent at… (More)

Following Lyons (1990, 4]) we deene a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric… (More)

1. Abstract Given a set of points and their mutual similarities we want to find clusters of similar points and separate distant or dissimilar points. Spectral clustering methods (see [4], [13] for a survey) have in common that they use piecewise (almost) constant eigenvectors of matrices derived from the mutual distances or similarities of the points to be… (More)

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