1,613,489 research outputs found
Hidden communication aspects in the exponent of Zipf's law
This article focuses on communication systems following Zipf’s law, in a study of the rel-ationship between the properties of those communication systems and the exponent of the law. The properties of communication systems are described using quantitative measures of semantic vagueness and the cost of word use. The precision and the economy of a communication system is reduced to a function of the exponent of Zipf’s law and the size of the communication system. Taking the exponent of the frequency spectrum, it is demonstrated that semantic precision grows with the exponent, where-as the cost of word use reaches a global minimum between 1.5 and 2, if the size of the communication system remains constant. The exponent of Zipf’s law is shown to be a key aspect for knowing about the number of stimuli handled by a communication system, and determining which of two systems is less vague or less expensive. The ideal exponent of Zipf’s law, it is therefore argued, should be very slightly above 2.Peer ReviewedPostprint (published version
Scaling laws of human interaction activity
Even though people in our contemporary, technological society are depending
on communication, our understanding of the underlying laws of human
communicational behavior continues to be poorly understood. Here we investigate
the communication patterns in two social Internet communities in search of
statistical laws in human interaction activity. This research reveals that
human communication networks dynamically follow scaling laws that may also
explain the observed trends in economic growth. Specifically, we identify a
generalized version of Gibrat's law of social activity expressed as a scaling
law between the fluctuations in the number of messages sent by members and
their level of activity. Gibrat's law has been essential in understanding
economic growth patterns, yet without an underlying general principle for its
origin. We attribute this scaling law to long-term correlation patterns in
human activity, which surprisingly span from days to the entire period of the
available data of more than one year. Further, we provide a mathematical
framework that relates the generalized version of Gibrat's law to the long-term
correlated dynamics, which suggests that the same underlying mechanism could be
the source of Gibrat's law in economics, ranging from large firms, research and
development expenditures, gross domestic product of countries, to city
population growth. These findings are also of importance for designing
communication networks and for the understanding of the dynamics of social
systems in which communication plays a role, such as economic markets and
political systems.Comment: 20+7 pages, 4+2 figure
Node similarity as a basic principle behind connectivity in complex networks
How are people linked in a highly connected society? Since in many networks a
power-law (scale-free) node-degree distribution can be observed, power-law
might be seen as a universal characteristics of networks. But this study of
communication in the Flickr social online network reveals that power-law
node-degree distributions are restricted to only sparsely connected networks.
More densely connected networks, by contrast, show an increasing divergence
from power-law. This work shows that this observation is consistent with the
classic idea from social sciences that similarity is the driving factor behind
communication in social networks. The strong relation between communication
strength and node similarity could be confirmed by analyzing the Flickr
network. It also is shown that node similarity as a network formation model can
reproduce the characteristics of different network densities and hence can be
used as a model for describing the topological transition from weakly to
strongly connected societies.Comment: 6 pages in Journal of Data Mining & Digital Humanities (2015)
jdmdh:3
Emergence of Zipf's Law in the Evolution of Communication
Zipf's law seems to be ubiquitous in human languages and appears to be a
universal property of complex communicating systems. Following the early
proposal made by Zipf concerning the presence of a tension between the efforts
of speaker and hearer in a communication system, we introduce evolution by
means of a variational approach to the problem based on Kullback's Minimum
Discrimination of Information Principle. Therefore, using a formalism fully
embedded in the framework of information theory, we demonstrate that Zipf's law
is the only expected outcome of an evolving, communicative system under a
rigorous definition of the communicative tension described by Zipf.Comment: 7 pages, 2 figure
Search in Power-Law Networks
Many communication and social networks have power-law link distributions,
containing a few nodes which have a very high degree and many with low degree.
The high connectivity nodes play the important role of hubs in communication
and networking, a fact which can be exploited when designing efficient search
algorithms. We introduce a number of local search strategies which utilize high
degree nodes in power-law graphs and which have costs which scale sub-linearly
with the size of the graph. We also demonstrate the utility of these strategies
on the Gnutella peer-to-peer network.Comment: 17 pages, 14 figure
Duality, Time-asymmetry and the Condensation of Vacuum
A variant of the divergence theory for vacuum-condensation developed in a
previous communication is analyzed from the viewpoint of a 'time' asymmetric
law in vacuum. This law is found to establish a substantial distinction between
dynamically allowed vacuum-configurations related by signature changing duality
transformations.Comment: 6 pages, latex fil
The meaning-frequency law in Zipfian optimization models of communication
According to Zipf's meaning-frequency law, words that are more frequent tend
to have more meanings. Here it is shown that a linear dependency between the
frequency of a form and its number of meanings is found in a family of models
of Zipf's law for word frequencies. This is evidence for a weak version of the
meaning-frequency law. Interestingly, that weak law (a) is not an inevitable of
property of the assumptions of the family and (b) is found at least in the
narrow regime where those models exhibit Zipf's law for word frequencies
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