632 research outputs found
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
Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products
Zipf's power-law distribution is a generic empirical statistical regularity
found in many complex systems. However, rather than universality with a single
power-law exponent (equal to 1 for Zipf's law), there are many reported
deviations that remain unexplained. A recently developed theory finds that the
interplay between (i) one of the most universal ingredients, namely stochastic
proportional growth, and (ii) birth and death processes, leads to a generic
power-law distribution with an exponent that depends on the characteristics of
each ingredient. Here, we report the first complete empirical test of the
theory and its application, based on the empirical analysis of the dynamics of
market shares in the product market. We estimate directly the average growth
rate of market shares and its standard deviation, the birth rates and the
"death" (hazard) rate of products. We find that temporal variations and product
differences of the observed power-law exponents can be fully captured by the
theory with no adjustable parameters. Our results can be generalized to many
systems for which the statistical properties revealed by power law exponents
are directly linked to the underlying generating mechanism
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
Power-law distributions from additive preferential redistributions
We introduce a non-growth model that generates the power-law distribution
with the Zipf exponent. There are N elements, each of which is characterized by
a quantity, and at each time step these quantities are redistributed through
binary random interactions with a simple additive preferential rule, while the
sum of quantities is conserved. The situation described by this model is
similar to those of closed -particle systems when conservative two-body
collisions are only allowed. We obtain stationary distributions of these
quantities both analytically and numerically while varying parameters of the
model, and find that the model exhibits the scaling behavior for some parameter
ranges. Unlike well-known growth models, this alternative mechanism generates
the power-law distribution when the growth is not expected and the dynamics of
the system is based on interactions between elements. This model can be applied
to some examples such as personal wealths, city sizes, and the generation of
scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added
more explanations and changed the order of presentation in Sec.III while
results are the sam
Statistical Analysis of Airport Network of China
Through the study of airport network of China (ANC), composed of 128 airports
(nodes) and 1165 flights (edges), we show the topological structure of ANC
conveys two characteristics of small worlds, a short average path length
(2.067) and a high degree of clustering (0.733). The cumulative degree
distributions of both directed and undirected ANC obey two-regime power laws
with different exponents, i.e., the so-called Double Pareto Law. In-degrees and
out-degrees of each airport have positive correlations, whereas the undirected
degrees of adjacent airports have significant linear anticorrelations. It is
demonstrated both weekly and daily cumulative distributions of flight weights
(frequencies) of ANC have power-law tails. Besides, the weight of any given
flight is proportional to the degrees of both airports at the two ends of that
flight. It is also shown the diameter of each sub-cluster (consisting of an
airport and all those airports to which it is linked) is inversely proportional
to its density of connectivity. Efficiency of ANC and of its sub-clusters are
measured through a simple definition. In terms of that, the efficiency of ANC's
sub-clusters increases as the density of connectivity does. ANC is found to
have an efficiency of 0.484.Comment: 6 Pages, 5 figure
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
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
Zipf law in the popularity distribution of chess openings
We perform a quantitative analysis of extensive chess databases and show that
the frequencies of opening moves are distributed according to a power-law with
an exponent that increases linearly with the game depth, whereas the pooled
distribution of all opening weights follows Zipf's law with universal exponent.
We propose a simple stochastic process that is able to capture the observed
playing statistics and show that the Zipf law arises from the self-similar
nature of the game tree of chess. Thus, in the case of hierarchical
fragmentation the scaling is truly universal and independent of a particular
generating mechanism. Our findings are of relevance in general processes with
composite decisions.Comment: 5 pages, 4 figure
Violations of robustness trade-offs
Biological robustness is a principle that may shed light on system-level characteristics of biological systems. One intriguing aspect of the concept of biological robustness is the possible existence of intrinsic trade-offs among robustness, fragility, performance, and so on. At the same time, whether such trade-offs hold regardless of the situation or hold only under specific conditions warrants careful investigation. In this paper, we reassess this concept and argue that biological robustness may hold only when a system is sufficiently optimized and that it may not be conserved when there is room for optimization in its design. Several testable predictions and implications for cell culture experiments are presented
Breakdown of the mean-field approximation in a wealth distribution model
One of the key socioeconomic phenomena to explain is the distribution of
wealth. Bouchaud and M\'ezard have proposed an interesting model of economy
[Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the
mean-field approximation, the model produces a stationary wealth distribution
with a power-law tail. In this paper we examine characteristic time scales of
the model and show that for any finite number of agents, the validity of the
mean-field result is time-limited and the model in fact has no stationary
wealth distribution. Further analysis suggests that for heterogeneous agents,
the limitations are even stronger. We conclude with general implications of the
presented results.Comment: 11 pages, 3 figure
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