In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Let k be a number field and letM be a simple k-algebra with center k of rank n, i.e. dimk(M) = n 2. Fix a k-involution x 7→ xτ on M , i.e. (xy)τ = yτxτ as well as (xτ )τ = x and xτ = x when x ∈ k. We will assume that M and τ are defined over the ring of integers O of k. The standard example will be the algebra of n× n matrices Matn(k) and x τ = xt the transposed matrix. For any ringR over k let...

objective: micrornas (mirnas) are single-stranded small rnas 18-25 nucleotides in length that regulate gene expression through translational inhibition and mrna cleavage. aberrant expression of mirnas contribute to several diseases. this has increased interest in profiling the expressions of these molecules. real-time quantitative pcr (rq-pcr) is a sensitive, quantitative technique for gene exp...

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations stochastic, quenched and deterministic are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous sta...