Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown
that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited;
communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to
vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions.
Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts
method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and
Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.
KEYWORDS: Social networks, Modeling, Radon, Systems modeling, Data modeling, Physics, Human-computer interaction, Stochastic processes, Complex systems, Detection and tracking algorithms
The structure of social networks influences dynamic processes of human interaction and communication, such
as opinion formation and spreading of information or infectious diseases. To facilitate simulation studies of
such processes, we have developed a weighted network model to resemble the structure of real social networks, in
particular taking into account recent observations on weight-topology correlations. The model iterates on a fixed
size network, reaching a steady state through processes of weighted local searches, global random attachment, and
random deletion of nodes. There are essentially two parameters which can be used to tune network properties.
The generated networks display community structure, with strong internal links and weak links connecting the
communities. Similarly to empirical observations, strong ties correlate with overlapping neighbourhoods, and
under edge removal, the network becomes fragmented faster when weak ties are removed first. As an example
of the effects that such structural properties have on dynamic processes, we present early results from studies of
social dynamics describing the competition of two non-excluding opinions in a society, showing that the weighted
community structure slows down the dynamics as compared to randomized references.
Space charge build-up in the well is shown to be the cause of the inductive effects in double- barrier diodes. A new impedance model for the diode is presented, built on a static model of coherent tunneling in a selfconsistent electron potential. The corresponding equivalent circuit is made up of two capacitances--related to the charge accumulations in the emitter and in the well--, and two conductances--one for each barrier. The numerical results of this circuit model are in qualitative agreement with experimental data. The success of the earlier quantum inductance model of Brown et al. is explained in terms of the presented model, without the need of introducing such a quantum inductance.
Conference Committee Involvement (1)
Noise and Stochastics in Complex Systems and Finance
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