8 research outputs found
Conductivity fluctuations in polymer's networks
Polymer's network is treated as an anisotropic fractal with fractional
dimensionality D = 1 + \epsilon close to one. Percolation model on such a
fractal is studied. Using the real space renormalization group approach of
Migdal and Kadanoff we find threshold value and all the critical exponents to
be strongly nonanalytic functions of \epsilon, e.g. the critical exponent of
the conductivity was obtained to be \epsilon^{-2}\exp(-1-1/\epsilon). The main
part of the finite size conductivities distribution function at the threshold
was found to be universal if expressed in terms of the fluctuating variable,
which is proportional to the large power of the conductivity, but with
dimensionally-dependent low-conductivity cut-off. Its reduced central momenta
are of the order of \exp(-1/\epsilon) up to the very high order.Comment: 7 pages, one eps figure, uses epsf style, to be published in Proc. of
LEES-97 (Physica B
Principles of statistical mechanics of random networks
We develop a statistical mechanics approach for random networks with
uncorrelated vertices. We construct equilibrium statistical ensembles of such
networks and obtain their partition functions and main characteristics. We find
simple dynamical construction procedures that produce equilibrium uncorrelated
random graphs with an arbitrary degree distribution. In particular, we show
that in equilibrium uncorrelated networks, fat-tailed degree distributions may
exist only starting from some critical average number of connections of a
vertex, in a phase with a condensate of edges.Comment: 14 pages, an extended versio
Bloggers Behavior and Emergent Communities in Blog Space
Interactions between users in cyberspace may lead to phenomena different from
those observed in common social networks. Here we analyse large data sets about
users and Blogs which they write and comment, mapped onto a bipartite graph. In
such enlarged Blog space we trace user activity over time, which results in
robust temporal patterns of user--Blog behavior and the emergence of
communities. With the spectral methods applied to the projection on weighted
user network we detect clusters of users related to their common interests and
habits. Our results suggest that different mechanisms may play the role in the
case of very popular Blogs. Our analysis makes a suitable basis for theoretical
modeling of the evolution of cyber communities and for practical study of the
data, in particular for an efficient search of interesting Blog clusters and
further retrieval of their contents by text analysis
Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks
A lot of previous work showed that the sectional mean first-passage time
(SMFPT), i.e., the average of mean first-passage time (MFPT) for random walks
to a given hub node (node with maximum degree) averaged over all starting
points in scale-free small-world networks exhibits a sublinear or linear
dependence on network order (number of nodes), which indicates that hub
nodes are very efficient in receiving information if one looks upon the random
walker as an information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been addressed
yet. In this paper, we study random walks on the class of Koch networks with
scale-free behavior and small-world effect. We derive some basic properties for
random walks on the Koch network family, based on which we calculate
analytically the partial mean first-passage time (PMFPT) defined as the average
of MFPTs from a hub node to all other nodes, excluding the hub itself. The
obtained closed-form expression displays that in large networks the PMFPT grows
with network order as , which is larger than the linear scaling of
SMFPT to the hub from other nodes. On the other hand, we also address the case
with the information sender distributed uniformly among the Koch networks, and
derive analytically the entire mean first-passage time (EMFPT), namely, the
average of MFPTs between all couples of nodes, the leading scaling of which is
identical to that of PMFPT. From the obtained results, we present that although
hub nodes are more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as non-hub nodes.
Moreover, we show that the location of information sender has little effect on
the transmission efficiency. The present findings are helpful for better
understanding random walks performed on scale-free small-world networks.Comment: Definitive version published in European Physical Journal
Jamming and correlation patterns in traffic of information on sparse modular networks
89.75.Hc Networks and genealogical trees, 05.40.Ca Noise, 02.70.-c Computational techniques; simulations,
Networks and emotion-driven user communities at popular blogs
Online communications at web portals represents technology-mediated user interactions, leading to massive data and potentially new techno-social phenomena not seen in real social mixing. Apart from being dynamically driven, the user interactions via posts is indirect, suggesting the importance of the contents of the posted material. We present a systematic way to study Blog data by combined approaches of physics of complex networks and computer science methods of text analysis. We are mapping the Blog data onto a bipartite network where users and posts with comments are two natural partitions. With the machine learning methods we classify the texts of posts and comments for their emotional contents as positive or negative, or otherwise objective (neutral). Using the spectral methods of weighted bipartite graphs, we identify topological communities featuring the users clustered around certain popular posts, and underly the role of emotional contents in the emergence and evolution of these communities. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010