969 research outputs found
Universality of Zipf's Law
We introduce a simple and generic model that reproduces Zipf's law. By
regarding the time evolution of the model as a random walk in the logarithmic
scale, we explain theoretically why this model reproduces Zipf's law. The
explanation shows that the behavior of the model is very robust and universal.Comment: 5 eps files included. To be published in J. Phys. Soc. Jp
Bug propagation and debugging in asymmetric software structures
Software dependence networks are shown to be scale-free and asymmetric. We
then study how software components are affected by the failure of one of them,
and the inverse problem of locating the faulty component. Software at all
levels is fragile with respect to the failure of a random single component.
Locating a faulty component is easy if the failures only affect their nearest
neighbors, while it is hard if the failures propagate further.Comment: 4 pages, 4 figure
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
Universal scaling in sports ranking
Ranking is a ubiquitous phenomenon in the human society. By clicking the web
pages of Forbes, you may find all kinds of rankings, such as world's most
powerful people, world's richest people, top-paid tennis stars, and so on and
so forth. Herewith, we study a specific kind, sports ranking systems in which
players' scores and prize money are calculated based on their performances in
attending various tournaments. A typical example is tennis. It is found that
the distributions of both scores and prize money follow universal power laws,
with exponents nearly identical for most sports fields. In order to understand
the origin of this universal scaling we focus on the tennis ranking systems. By
checking the data we find that, for any pair of players, the probability that
the higher-ranked player will top the lower-ranked opponent is proportional to
the rank difference between the pair. Such a dependence can be well fitted to a
sigmoidal function. By using this feature, we propose a simple toy model which
can simulate the competition of players in different tournaments. The
simulations yield results consistent with the empirical findings. Extensive
studies indicate the model is robust with respect to the modifications of the
minor parts.Comment: 8 pages, 7 figure
Zipf's Law in Gene Expression
Using data from gene expression databases on various organisms and tissues,
including yeast, nematodes, human normal and cancer tissues, and embryonic stem
cells, we found that the abundances of expressed genes exhibit a power-law
distribution with an exponent close to -1, i.e., they obey Zipf's law.
Furthermore, by simulations of a simple model with an intra-cellular reaction
network, we found that Zipf's law of chemical abundance is a universal feature
of cells where such a network optimizes the efficiency and faithfulness of
self-reproduction. These findings provide novel insights into the nature of the
organization of reaction dynamics in living cells.Comment: revtex, 11 pages, 3 figures, submitted to Phys. Rev. Let
Interacting Individuals Leading to Zipf's Law
We present a general approach to explain the Zipf's law of city distribution.
If the simplest interaction (pairwise) is assumed, individuals tend to form
cities in agreement with the well-known statisticsComment: 4 pages 2 figure
Bidding process in online auctions and winning strategy:rate equation approach
Online auctions have expanded rapidly over the last decade and have become a
fascinating new type of business or commercial transaction in this digital era.
Here we introduce a master equation for the bidding process that takes place in
online auctions. We find that the number of distinct bidders who bid times,
called the -frequent bidder, up to the -th bidding progresses as
. The successfully transmitted bidding rate by the
-frequent bidder is obtained as , independent of
for large . This theoretical prediction is in agreement with empirical data.
These results imply that bidding at the last moment is a rational and effective
strategy to win in an eBay auction.Comment: 4 pages, 6 figure
Complex network analysis of literary and scientific texts
We present results from our quantitative study of statistical and network
properties of literary and scientific texts written in two languages: English
and Polish. We show that Polish texts are described by the Zipf law with the
scaling exponent smaller than the one for the English language. We also show
that the scientific texts are typically characterized by the rank-frequency
plots with relatively short range of power-law behavior as compared to the
literary texts. We then transform the texts into their word-adjacency network
representations and find another difference between the languages. For the
majority of the literary texts in both languages, the corresponding networks
revealed the scale-free structure, while this was not always the case for the
scientific texts. However, all the network representations of texts were
hierarchical. We do not observe any qualitative and quantitative difference
between the languages. However, if we look at other network statistics like the
clustering coefficient and the average shortest path length, the English texts
occur to possess more clustered structure than do the Polish ones. This result
was attributed to differences in grammar of both languages, which was also
indicated in the Zipf plots. All the texts, however, show network structure
that differs from any of the Watts-Strogatz, the Barabasi-Albert, and the
Erdos-Renyi architectures
Scaling laws of strategic behaviour and size heterogeneity in agent dynamics
The dynamics of many socioeconomic systems is determined by the decision
making process of agents. The decision process depends on agent's
characteristics, such as preferences, risk aversion, behavioral biases, etc..
In addition, in some systems the size of agents can be highly heterogeneous
leading to very different impacts of agents on the system dynamics. The large
size of some agents poses challenging problems to agents who want to control
their impact, either by forcing the system in a given direction or by hiding
their intentionality. Here we consider the financial market as a model system,
and we study empirically how agents strategically adjust the properties of
large orders in order to meet their preference and minimize their impact. We
quantify this strategic behavior by detecting scaling relations of allometric
nature between the variables characterizing the trading activity of different
institutions. We observe power law distributions in the investment time
horizon, in the number of transactions needed to execute a large order and in
the traded value exchanged by large institutions and we show that heterogeneity
of agents is a key ingredient for the emergence of some aggregate properties
characterizing this complex system.Comment: 6 pages, 3 figure
Time-Varying Priority Queuing Models for Human Dynamics
Queuing models provide insight into the temporal inhomogeneity of human
dynamics, characterized by the broad distribution of waiting times of
individuals performing tasks. We study the queuing model of an agent trying to
execute a task of interest, the priority of which may vary with time due to the
agent's "state of mind." However, its execution is disrupted by other tasks of
random priorities. By considering the priority of the task of interest either
decreasing or increasing algebraically in time, we analytically obtain and
numerically confirm the bimodal and unimodal waiting time distributions with
power-law decaying tails, respectively. These results are also compared to the
updating time distribution of papers in the arXiv.org and the processing time
distribution of papers in Physical Review journals. Our analysis helps to
understand human task execution in a more realistic scenario.Comment: 8 pages, 6 figure
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