175 research outputs found
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
Link Prediction Based on Local Random Walk
The problem of missing link prediction in complex networks has attracted much
attention recently. Two difficulties in link prediction are the sparsity and
huge size of the target networks. Therefore, the design of an efficient and
effective method is of both theoretical interests and practical significance.
In this Letter, we proposed a method based on local random walk, which can give
competitively good prediction or even better prediction than other
random-walk-based methods while has a lower computational complexity.Comment: 6 pages, 2 figure
Emergence of linguistic laws in human voice
Submitted for publicationSubmitted for publicatio
Non-crossing dependencies: Least effort, not grammar
The use of null hypotheses (in a statistical sense) is common in hard sciences but not in theoretical linguistics. Here the null hypothesis that the low frequency of syntactic dependency crossings is expected by an arbitrary ordering of words is rejected. It is shown that this would require star dependency structures, which are both unrealistic and too restrictive. The hypothesis of the limited resources of the human brain is revisited. Stronger null hypotheses taking into account actual dependency lengths for the likelihood of crossings are presented. Those hypotheses suggests that crossings are likely to reduce when dependencies are shortened. A hypothesis based on pressure to reduce dependency lengths is more parsimonious than a principle of minimization of crossings or a grammatical ban that is totally dissociated from the general and non-linguistic principle of economy.Postprint (author's final draft
Testing the robustness of laws of polysemy and brevity versus frequency
The pioneering research of G.K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. Here we focus on a couple of them: the meaning-frequency law, i.e. the tendency of more frequent words to be more polysemous, and the law of abbreviation, i.e. the tendency of more frequent words to be shorter. Here we evaluate the robustness of these laws in contexts where they have not been explored yet to our knowledge. The recovery of the laws again in new conditions provides support for the hypothesis that they originate from abstract mechanisms.Peer ReviewedPostprint (author's final draft
Subgraphs in random networks
Understanding the subgraph distribution in random networks is important for
modelling complex systems. In classic Erdos networks, which exhibit a
Poissonian degree distribution, the number of appearances of a subgraph G with
n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However,
many natural networks have a non-Poissonian degree distribution. Here we
present approximate equations for the average number of subgraphs in an
ensemble of random sparse directed networks, characterized by an arbitrary
degree sequence. We find new scaling rules for the commonly occurring case of
directed scale-free networks, in which the outgoing degree distribution scales
as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree
distribution, \gamma, as a control parameter, we show that random networks
exhibit transitions between three regimes. In each regime the subgraph number
of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where
\alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and
\alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and
\gamma_c=s+1. We find that certain subgraphs appear much more frequently than
in Erdos networks. These results are in very good agreement with numerical
simulations. This has implications for detecting network motifs, subgraphs that
occur in natural networks significantly more than in their randomized
counterparts.Comment: 8 pages, 5 figure
Hierarchical Organization in Complex Networks
Many real networks in nature and society share two generic properties: they
are scale-free and they display a high degree of clustering. We show that these
two features are the consequence of a hierarchical organization, implying that
small groups of nodes organize in a hierarchical manner into increasingly large
groups, while maintaining a scale-free topology. In hierarchical networks the
degree of clustering characterizing the different groups follows a strict
scaling law, which can be used to identify the presence of a hierarchical
organization in real networks. We find that several real networks, such as the
World Wide Web, actor network, the Internet at the domain level and the
semantic web obey this scaling law, indicating that hierarchy is a fundamental
characteristic of many complex systems
Point-occurrence self-similarity in crackling-noise systems and in other complex systems
It has been recently found that a number of systems displaying crackling
noise also show a remarkable behavior regarding the temporal occurrence of
successive events versus their size: a scaling law for the probability
distributions of waiting times as a function of a minimum size is fulfilled,
signaling the existence on those systems of self-similarity in time-size. This
property is also present in some non-crackling systems. Here, the uncommon
character of the scaling law is illustrated with simple marked renewal
processes, built by definition with no correlations. Whereas processes with a
finite mean waiting time do not fulfill a scaling law in general and tend
towards a Poisson process in the limit of very high sizes, processes without a
finite mean tend to another class of distributions, characterized by double
power-law waiting-time densities. This is somehow reminiscent of the
generalized central limit theorem. A model with short-range correlations is not
able to escape from the attraction of those limit distributions. A discussion
on open problems in the modeling of these properties is provided.Comment: Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon),
topic: crackling nois
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