14,981 research outputs found
Disentangling different types of El Ni\~no episodes by evolving climate network analysis
Complex network theory provides a powerful toolbox for studying the structure
of statistical interrelationships between multiple time series in various
scientific disciplines. In this work, we apply the recently proposed climate
network approach for characterizing the evolving correlation structure of the
Earth's climate system based on reanalysis data of surface air temperatures. We
provide a detailed study on the temporal variability of several global climate
network characteristics. Based on a simple conceptual view on red climate
networks (i.e., networks with a comparably low number of edges), we give a
thorough interpretation of our evolving climate network characteristics, which
allows a functional discrimination between recently recognized different types
of El Ni\~no episodes. Our analysis provides deep insights into the Earth's
climate system, particularly its global response to strong volcanic eruptions
and large-scale impacts of different phases of the El Ni\~no Southern
Oscillation (ENSO).Comment: 20 pages, 12 figure
Complex Networks from Simple Rewrite Systems
Complex networks are all around us, and they can be generated by simple
mechanisms. Understanding what kinds of networks can be produced by following
simple rules is therefore of great importance. We investigate this issue by
studying the dynamics of extremely simple systems where are `writer' moves
around a network, and modifies it in a way that depends upon the writer's
surroundings. Each vertex in the network has three edges incident upon it,
which are colored red, blue and green. This edge coloring is done to provide a
way for the writer to orient its movement. We explore the dynamics of a space
of 3888 of these `colored trinet automata' systems. We find a large variety of
behaviour, ranging from the very simple to the very complex. We also discover
simple rules that generate forms which are remarkably similar to a wide range
of natural objects. We study our systems using simulations (with appropriate
visualization techniques) and analyze selected rules mathematically. We arrive
at an empirical classification scheme which reveals a lot about the kinds of
dynamics and networks that can be generated by these systems
Evolution of networks
We review the recent fast progress in statistical physics of evolving
networks. Interest has focused mainly on the structural properties of random
complex networks in communications, biology, social sciences and economics. A
number of giant artificial networks of such a kind came into existence
recently. This opens a wide field for the study of their topology, evolution,
and complex processes occurring in them. Such networks possess a rich set of
scaling properties. A number of them are scale-free and show striking
resilience against random breakdowns. In spite of large sizes of these
networks, the distances between most their vertices are short -- a feature
known as the ``small-world'' effect. We discuss how growing networks
self-organize into scale-free structures and the role of the mechanism of
preferential linking. We consider the topological and structural properties of
evolving networks, and percolation in these networks. We present a number of
models demonstrating the main features of evolving networks and discuss current
approaches for their simulation and analytical study. Applications of the
general results to particular networks in Nature are discussed. We demonstrate
the generic connections of the network growth processes with the general
problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted
to Adv. Phy
Rounding of first-order phase transitions and optimal cooperation in scale-free networks
We consider the ferromagnetic large- state Potts model in complex evolving
networks, which is equivalent to an optimal cooperation problem, in which the
agents try to optimize the total sum of pair cooperation benefits and the
supports of independent projects. The agents are found to be typically of two
kinds: a fraction of (being the magnetization of the Potts model) belongs
to a large cooperating cluster, whereas the others are isolated one man's
projects. It is shown rigorously that the homogeneous model has a strongly
first-order phase transition, which turns to second-order for random
interactions (benefits), the properties of which are studied numerically on the
Barab\'asi-Albert network. The distribution of finite-size transition points is
characterized by a shift exponent, , and by a different
width exponent, , whereas the magnetization at the transition
point scales with the size of the network, , as: , with
.Comment: 8 pages, 6 figure
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Evolving graphs: dynamical models, inverse problems and propagation
Applications such as neuroscience, telecommunication, online social networking,
transport and retail trading give rise to connectivity patterns that change over time.
In this work, we address the resulting need for network models and computational
algorithms that deal with dynamic links. We introduce a new class of evolving
range-dependent random graphs that gives a tractable framework for modelling and
simulation. We develop a spectral algorithm for calibrating a set of edge ranges from
a sequence of network snapshots and give a proof of principle illustration on some
neuroscience data. We also show how the model can be used computationally and
analytically to investigate the scenario where an evolutionary process, such as an
epidemic, takes place on an evolving network. This allows us to study the cumulative
effect of two distinct types of dynamics
The spread of infections on evolving scale-free networks
We study the contact process on a class of evolving scale-free networks,
where each node updates its connections at independent random times. We give a
rigorous mathematical proof that there is a transition between a phase where
for all infection rates the infection survives for a long time, at least
exponential in the network size, and a phase where for sufficiently small
infection rates extinction occurs quickly, at most like the square root of the
network size. The phase transition occurs when the power-law exponent crosses
the value four. This behaviour is in contrast to that of the contact process on
the corresponding static model, where there is no phase transition, as well as
that of a classical mean-field approximation, which has a phase transition at
power-law exponent three. The new observation behind our result is that
temporal variability of networks can simultaneously increase the rate at which
the infection spreads in the network, and decrease the time which the infection
spends in metastable states.Comment: 17 pages, 1 figur
A simple asymmetric evolving random network
We introduce a new oriented evolving graph model inspired by biological
networks. A node is added at each time step and is connected to the rest of the
graph by random oriented edges emerging from older nodes. This leads to a
statistical asymmetry between incoming and outgoing edges. We show that the
model exhibits a percolation transition and discuss its universality. Below the
threshold, the distribution of component sizes decreases algebraically with a
continuously varying exponent depending on the average connectivity. We prove
that the transition is of infinite order by deriving the exact asymptotic
formula for the size of the giant component close to the threshold. We also
present a thorough analysis of aging properties. We compute local-in-time
profiles for the components of finite size and for the giant component, showing
in particular that the giant component is always dense among the oldest nodes
but invades only an exponentially small fraction of the young nodes close to
the threshold.Comment: 33 pages, 3 figures, to appear in J. Stat. Phy
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