517 research outputs found
Reshuffling spins with short range interactions: When sociophysics produces physical results
Galam reshuffling introduced in opinion dynamics models is investigated under
the nearest neighbor Ising model on a square lattice using Monte Carlo
simulations. While the corresponding Galam analytical critical temperature T_C
\approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different
from both values, not reshuffled (T_C=2/arcsinh(1) \approx 2.27 [J/k_B]) and
mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as
function of 0 \leq p \leq 1 where p measures the probability of spin
reshuffling after each Monte Carlo step. The variation of T_C as function of p
is obtained and exhibits a non-linear behavior. The simplest Solomon network
realization is noted to reproduce Galam p=1 result. Similarly to the critical
temperature, critical exponents are found to differ from both, the classical
Ising case and the mean-field values.Comment: 11 pages, 5 figures in 6 eps files, to appear in IJMP
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
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
Blockbusters, Bombs and Sleepers: The income distribution of movies
The distribution of gross earnings of movies released each year show a
distribution having a power-law tail with Pareto exponent .
While this offers interesting parallels with income distributions of
individuals, it is also clear that it cannot be explained by simple asset
exchange models, as movies do not interact with each other directly. In fact,
movies (because of the large quantity of data available on their earnings)
provide the best entry-point for studying the dynamics of how ``a hit is born''
and the resulting distribution of popularity (of products or ideas). In this
paper, we show evidence of Pareto law for movie income, as well as, an analysis
of the time-evolution of income.Comment: 5 pages, 3 figures, to appear in Proceedings of International
Workshop on Econophysics of Wealth Distributions (Econophys-Kolkata I), March
15-19, 200
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
Zipf's law in Nuclear Multifragmentation and Percolation Theory
We investigate the average sizes of the largest fragments in nuclear
multifragmentation events near the critical point of the nuclear matter phase
diagram. We perform analytic calculations employing Poisson statistics as well
as Monte Carlo simulations of the percolation type. We find that previous
claims of manifestations of Zipf's Law in the rank-ordered fragment size
distributions are not born out in our result, neither in finite nor infinite
systems. Instead, we find that Zipf-Mandelbrot distributions are needed to
describe the results, and we show how one can derive them in the infinite size
limit. However, we agree with previous authors that the investigation of
rank-ordered fragment size distributions is an alternative way to look for the
critical point in the nuclear matter diagram.Comment: 8 pages, 11 figures, submitted to PR
Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend
We have translated fractional Brownian motion (FBM) signals into a text based
on two ''letters'', as if the signal fluctuations correspond to a constant
stepsize random walk. We have applied the Zipf method to extract the
exponent relating the word frequency and its rank on a log-log plot. We have
studied the variation of the Zipf exponent(s) giving the relationship between
the frequency of occurrence of words of length made of such two letters:
is varying as a power law in terms of . We have also searched how
the exponent of the Zipf law is influenced by a linear trend and the
resulting effect of its slope. We can distinguish finite size effects, and
results depending whether the starting FBM is persistent or not, i.e. depending
on the FBM Hurst exponent . It seems then numerically proven that the Zipf
exponent of a persistent signal is more influenced by the trend than that of an
antipersistent signal. It appears that the conjectured law
only holds near . We have also introduced considerations based on the
notion of a {\it time dependent Zipf law} along the signal.Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys
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
Computing the set of Epsilon-efficient solutions in multiobjective space mission design
In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose
Asymptotic analysis of the model for distribution of high-tax payers
The z-transform technique is used to investigate the model for distribution
of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and
others. Our analysis shows an asymptotic power-law of this model with the
exponent -5/2 when a total ``mass'' has a certain critical value. Below the
critical value, the system exhibits an ordinary critical behavior, and scaling
relations hold. Above the threshold, numerical simulations show that a
power-law distribution coexists with a huge ``monopolized'' member. It is
argued that these behaviors are observed universally in conserved aggregation
processes, by analizing an extended model.Comment: 5pages, 3figure
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