80 research outputs found
Statistical analysis of 22 public transport networks in Poland
Public transport systems in 22 Polish cities have been analyzed. Sizes of
these networks range from N=152 to N=2881. Depending on the assumed definition
of network topology the degree distribution can follow a power law or can be
described by an exponential function. Distributions of paths in all considered
networks are given by asymmetric, unimodal functions. Clustering, assortativity
and betweenness are studied. All considered networks exhibit small world
behavior and are hierarchically organized. A transition between dissortative
small networks N=500 is observed.Comment: 11 pages, 17 figures, 2 tables, REVTEX4 forma
Universal scaling of distances in complex networks
Universal scaling of distances between vertices of Erdos-Renyi random graphs,
scale-free Barabasi-Albert models, science collaboration networks, biological
networks, Internet Autonomous Systems and public transport networks are
observed. A mean distance between two nodes of degrees k_i and k_j equals to
=A-B log(k_i k_j). The scaling is valid over several decades. A simple
theory for the appearance of this scaling is presented. Parameters A and B
depend on the mean value of a node degree _nn calculated for the nearest
neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl
Estimation of a Noise Level Using Coarse-Grained Entropy of Experimental Time Series of Internal Pressure in a Combustion Engine
We report our results on non-periodic experimental time series of pressure in
a single cylinder spark ignition engine. The experiments were performed for
different levels of loading. We estimate the noise level in internal pressure
calculating the coarse-grained entropy from variations of maximal pressures in
successive cycles. The results show that the dynamics of the combustion is a
nonlinear multidimensional process mediated by noise. Our results show that so
defined level of noise in internal pressure is not monotonous function of
loading.Comment: 12 pages, 6 figure
Supremacy distribution in evolving networks
We study a supremacy distribution in evolving Barabasi-Albert networks. The
supremacy of a node is defined as a total number of all nodes that
are younger than and can be connected to it by a directed path. For a
network with a characteristic parameter the supremacy of an
individual node increases with the network age as in an
appropriate scaling region. It follows that there is a relation between a node degree and its supremacy and the supremacy
distribution scales as . Analytic calculations basing on
a continuum theory of supremacy evolution and on a corresponding rate equation
have been confirmed by numerical simulations.Comment: 4 pages, 4 figure
Log-periodic oscillations due to discrete effects in complex networks
We show that discretization of internode distribution in complex networks
affects internode distances l_ij calculated as a function of degrees (k_i k_j)
and an average path length as function of network size N. For dense
networks there are log-periodic oscillations of above quantities. We present
real-world examples of such a behavior as well as we derive analytical
expressions and compare them to numerical simulations. We consider a simple
case of network optimization problem, arguing that discrete effects can lead to
a nontrivial solution.Comment: 5 pages, 5 figures, REVTE
Ferromagnetic fluid as a model of social impact
The paper proposes a new model of spin dynamics which can be treated as a
model of sociological coupling between individuals. Our approach takes into
account two different human features: gregariousness and individuality. We will
show how they affect a psychological distance between individuals and how the
distance changes the opinion formation in a social group. Apart from its
sociological aplications the model displays the variety of other interesting
phenomena like self-organizing ferromagnetic state or a second order phase
transition and can be studied from different points of view, e.g. as a model of
ferromagnetic fluid, complex evolving network or multiplicative random process.Comment: 8 pages, 5 figure
Thermodynamic forces, flows, and Onsager coefficients in complex networks
We present Onsager formalism applied to random networks with arbitrary degree
distribution. Using the well-known methods of non-equilibrium thermodynamics we
identify thermodynamic forces and their conjugated flows induced in networks as
a result of single node degree perturbation. The forces and the flows can be
understood as a response of the system to events, such as random removal of
nodes or intentional attacks on them. Finally, we show that cross effects (such
as thermodiffusion, or thermoelectric phenomena), in which one force may not
only give rise to its own corresponding flow, but to many other flows, can be
observed also in complex networks.Comment: 4 pages, 2 figure
Scaling of human behavior during portal browsing
We investigate transitions of portals users between different subpages. A
weighted network of portals subpages is reconstructed where edge weights are
numbers of corresponding transitions. Distributions of link weights and node
strengths follow power laws over several decades. Node strength increases
faster than linearly with node degree. The distribution of time spent by the
user at one subpage decays as power law with exponent around 1.3. Distribution
of numbers P(z) of unique subpages during one visit is exponential. We find a
square root dependence between the average z and the total number of
transitions n during a single visit. Individual path of portal user resembles
of self-attracting walk on the weighted network. Analytical model is developed
to recover in part the collected data.Comment: 6 pages, 7 figure
Volatility clustering and scaling for financial time series due to attractor bubbling
A microscopic model of financial markets is considered, consisting of many
interacting agents (spins) with global coupling and discrete-time thermal bath
dynamics, similar to random Ising systems. The interactions between agents
change randomly in time. In the thermodynamic limit the obtained time series of
price returns show chaotic bursts resulting from the emergence of attractor
bubbling or on-off intermittency, resembling the empirical financial time
series with volatility clustering. For a proper choice of the model parameters
the probability distributions of returns exhibit power-law tails with scaling
exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or
Mean-field theory for clustering coefficients in Barabasi-Albert networks
We applied a mean field approach to study clustering coefficients in
Barabasi-Albert networks. We found that the local clustering in BA networks
depends on the node degree. Analytic results have been compared to extensive
numerical simulations finding a very good agreement for nodes with low degrees.
Clustering coefficient of a whole network calculated from our approach
perfectly fits numerical data.Comment: 8 pages, 3 figure
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