483 research outputs found
On the motifs distribution in random hierarchical networks
The distribution of motifs in random hierarchical networks defined by
nonsymmetric random block--hierarchical adjacency matrices, is constructed for
the first time. According to the classification of U. Alon et al of network
superfamilies by their motifs distributions, our artificial directed random
hierarchical networks falls into the superfamily of natural networks to which
the class of neuron networks belongs. This is the first example of ``handmade''
networks with the motifs distribution as in a special class of natural networks
of essential biological importance.Comment: 7 pages, 5 figure
On scale-free and poly-scale behaviors of random hierarchical network
In this paper the question about statistical properties of
block--hierarchical random matrices is raised for the first time in connection
with structural characteristics of random hierarchical networks obtained by
mipmapping procedure. In particular, we compute numerically the spectral
density of large random adjacency matrices defined by a hierarchy of the
Bernoulli distributions on matrix elements, where
depends on hierarchy level as (). For the spectral density we clearly see the free--scale
behavior. We show also that for the Gaussian distributions on matrix elements
with zero mean and variances , the tail of the
spectral density, , behaves as for and , while for
the power--law behavior is terminated. We also find that the vertex
degree distribution of such hierarchical networks has a poly--scale fractal
behavior extended to a very broad range of scales.Comment: 11 pages, 6 figures (paper is substantially revised
First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an
ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+,
satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We
construct and examine a random variable \tau (\omega) that has the meaning the
first passage times. Also, we obtain a formula for the mean number of returns
on the interval (0,t] and give its asymptotic estimates for large t.Comment: 20 page
A p-Adic Model of DNA Sequence and Genetic Code
Using basic properties of p-adic numbers, we consider a simple new approach
to describe main aspects of DNA sequence and genetic code. Central role in our
investigation plays an ultrametric p-adic information space which basic
elements are nucleotides, codons and genes. We show that a 5-adic model is
appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance,
is also suitable for genetic code and for a more advanced employment in
genomics. We find that genetic code degeneracy is related to the p-adic
distance between codons.Comment: 13 pages, 2 table
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