#### Filter Results:

#### Publication Year

1997

2007

#### Publication Type

#### Co-author

#### Publication Venue

Learn 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)

Head-waving, a spontaneously occurring exploratory and appetitive behavior of the marine mollusc Aplysia, provides an opportunity to examine mechanisms of learning expressed in a nonreflexive behavior. The present study explores nonassociative and associative forms of learned modification of head-waving produced using an aversive stimulus as reinforcement.… (More)

- D. Burkholder, M. Fukushima H. Kesten, D. Stroock S. Varadhan, K. Burdzy R. Carmona G. Lawler, D. Aldous M. Barlow, R. Bass J. Bertoin +13 others

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)

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)

- ‹
- 1
- ›