Generating function equation has been derived for the probability distribution of the number of nodes with k ≥ 0 outgoing lines in randomly evolving special trees defined in an earlier paper arXiv:condmat/0205650. The stochastic properties of the end-nodes (k = 0) have been analyzed, and it was shown that the relative variance of the number of end-nodes vs. time has a maximum when the evolution...

JCB • VOLUME 171 • NUMBER 3 • 2005 406 Divided identities in the niche o maintain a stem cell niche at a fixed size, the niche exerts control over both cell differentiation (how many cells functionally leave the niche) and cell division. G. Venugopala Reddy and Elliot Meyerowitz (Caltech, Pasadena, CA) now show that, in the growing shoots of plants, these two control points are separable in bot...

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv: cond-mat/0211092) have been investigated in the case when the continuous time parameter converges to infinity. Equations for generating functions of the number of nodes and end-nodes in a stationary (i.e. infinitely old) tree have been derived. In order ...

A graph G is randomly planar if every planar embedding of every connected subgraph of G can be extended to a planar embedding of G. We classify these graphs.

A twisted hypercube of dimension k is created from two twisted hypercubes of dimension k − 1 by adding a matching joining their vertex sets, with the twisted hypercube of dimension 0 consisting of one vertex and no edges. We generate random twisted hypercube by generating the matchings randomly at each step. We show that, asymptotically almost surely, joining any two vertices in a random twiste...

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled M p models and found that they flow in two decoupled M p−1 models, in the infra-red limit. This result is then extend to the case with M randomly coupled M p models, which will flow toward M decoupled M p−1 .

We consider the problem of generating a colouring of the random graph Gn,p uniformly at random using a natural Markov chain algorithm: the Glauber dynamics. We assume that there are β∆ colours available, where ∆ is the maximum degree of the graph, and we wish to determine the least β = β(p) such that the distribution is close to uniform in O(n log n) steps of the chain. This problem has been pr...