351 research outputs found
Statistics of Lead Changes in Popularity-Driven Systems
We study statistical properties of the highest degree, or most popular, nodes
in growing networks. We show that the number of lead changes increases
logarithmically with network size N, independent of the details of the growth
mechanism. The probability that the first node retains the lead approaches a
finite constant for popularity-driven growth, and decays as N^{-phi}(ln
N)^{-1/2}, with phi=0.08607..., for growth with no popularity bias.Comment: 4 pages, 4 figures, 2 column revtex format. Minor changes in response
to referee comments. For publication in 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
A Group-Based Yule Model for Bipartite Author-Paper Networks
This paper presents a novel model for author-paper networks, which is based
on the assumption that authors are organized into groups and that, for each
research topic, the number of papers published by a group is based on a
success-breeds-success model. Collaboration between groups is modeled as random
invitations from a group to an outside member. To analyze the model, a number
of different metrics that can be obtained in author-paper networks were
extracted. A simulation example shows that this model can effectively mimic the
behavior of a real-world author-paper network, extracted from a collection of
900 journal papers in the field of complex networks.Comment: 13 pages (preprint format), 7 figure
A Yule-Simon process with memory
The Yule-Simon model has been used as a tool to describe the growth of
diverse systems, acquiring a paradigmatic character in many fields of research.
Here we study a modified Yule-Simon model that takes into account the full
history of the system by means of an hyperbolic memory kernel. We show how the
memory kernel changes the properties of preferential attachment and provide an
approximate analytical solution for the frequency distribution density as well
as for the frequency-rank distribution.Comment: 7 pages, 5 figures; accepted for publication in Europhysics Letter
Power Law Distribution of Wealth in a Money-Based Model
A money-based model for the power law distribution (PLD) of wealth in an
economically interacting population is introduced. The basic feature of our
model is concentrating on the capital movements and avoiding the complexity of
micro behaviors of individuals. It is proposed as an extension of the Equiluz
and Zimmermann's (EZ) model for crowding and information transmission in
financial markets. Still, we must emphasize that in EZ model the PLD without
exponential correction is obtained only for a particular parameter, while our
pattern will give it within a wide range. The Zipf exponent depends on the
parameters in a nontrivial way and is exactly calculated in this paper.Comment: 5 pages and 4 figure
Critical and Near-Critical Branching Processes
Scale-free dynamics in physical and biological systems can arise from a
variety of causes. Here, we explore a branching process which leads to such
dynamics. We find conditions for the appearance of power laws and study
quantitatively what happens to these power laws when such conditions are
violated. From a branching process model, we predict the behavior of two
systems which seem to exhibit near scale-free behavior--rank-frequency
distributions of number of subtaxa in biology, and abundance distributions of
genotypes in an artificial life system. In the light of these, we discuss
distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results
from non-critical sandpile simulations that were excised from the published
versio
Rank Statistics in Biological Evolution
We present a statistical analysis of biological evolution processes.
Specifically, we study the stochastic replication-mutation-death model where
the population of a species may grow or shrink by birth or death, respectively,
and additionally, mutations lead to the creation of new species. We rank the
various species by the chronological order by which they originate. The average
population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu}
k^{-mu}, where M is the average total population. The characteristic exponent
mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the
replication, mutation, and death rates. Furthermore, the average population P_k
of all descendants of the kth species has a universal algebraic behavior, P_k ~
M/k.Comment: 4 pages, 3 figure
Exact Scale Invariance in Mixing of Binary Candidates in Voting Model
We introduce a voting model and discuss the scale invariance in the mixing of
candidates. The Candidates are classified into two categories
and are called as `binary' candidates. There are in total
candidates, and voters vote for them one by one. The probability that a
candidate gets a vote is proportional to the number of votes. The initial
number of votes (`seed') of a candidate is set to be . After
infinite counts of voting, the probability function of the share of votes of
the candidate obeys gamma distributions with the shape exponent
in the thermodynamic limit . Between the
cumulative functions of binary candidates, the power-law relation
with the critical exponent
holds in the region . In the double
scaling limit and with
fixed, the relation holds
exactly over the entire range . We study the data on
horse races obtained from the Japan Racing Association for the period 1986 to
2006 and confirm scale invariance.Comment: 19 pages, 8 figures, 2 table
Semi-Markov Graph Dynamics
In this paper, we outline a model of graph (or network) dynamics based on two
ingredients. The first ingredient is a Markov chain on the space of possible
graphs. The second ingredient is a semi-Markov counting process of renewal
type. The model consists in subordinating the Markov chain to the semi-Markov
counting process. In simple words, this means that the chain transitions occur
at random time instants called epochs. The model is quite rich and its possible
connections with algebraic geometry are briefly discussed. Moreover, for the
sake of simplicity, we focus on the space of undirected graphs with a fixed
number of nodes. However, in an example, we present an interbank market model
where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON
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