15,418 research outputs found
Phase transitions for scaling of structural correlations in directed networks
Analysis of degree-degree dependencies in complex networks, and their impact
on processes on networks requires null models, i.e. models that generate
uncorrelated scale-free networks. Most models to date however show structural
negative dependencies, caused by finite size effects. We analyze the behavior
of these structural negative degree-degree dependencies, using rank based
correlation measures, in the directed Erased Configuration Model. We obtain
expressions for the scaling as a function of the exponents of the
distributions. Moreover, we show that this scaling undergoes a phase
transition, where one region exhibits scaling related to the natural cut-off of
the network while another region has scaling similar to the structural cut-off
for uncorrelated networks. By establishing the speed of convergence of these
structural dependencies we are able to asses statistical significance of
degree-degree dependencies on finite complex networks when compared to networks
generated by the directed Erased Configuration Model
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks
Structural balance in social network theory starts from signed networks with
active relationships (friendly or hostile) to establish a hierarchy between
four different types of triadic relationships. The lack of an active link also
provides information about the network. To exploit the information that remains
uncovered by structural balance, we introduce the inactive relationship that
accounts for both neutral and nonexistent ties between two agents. This
addition results in ten types of triads, with the advantage that the network
analysis can be done with complete networks. To each type of triadic
relationship, we assign an energy that is a measure for its average occupation
probability. Finite temperatures account for a persistent form of disorder in
the formation of the triadic relationships. We propose a Hamiltonian with three
interaction terms and a chemical potential (capturing the cost of edge
activation) as an underlying model for the triadic energy levels. Our model is
suitable for empirical analysis of political networks and allows to uncover
generative mechanisms. It is tested on an extended data set for the standings
between two classes of alliances in a massively multi-player on-line game
(MMOG) and on real-world data for the relationships between countries during
the Cold War era. We find emergent properties in the triadic relationships
between the nodes in a political network. For example, we observe a persistent
hierarchy between the ten triadic energy levels across time and networks. In
addition, the analysis reveals consistency in the extracted model parameters
and a universal data collapse of a derived combination of global properties of
the networks. We illustrate that the model has predictive power for the
transition probabilities between the different triadic states.Comment: 21 pages, 10 figure
Critical dynamics on a large human Open Connectome network
Extended numerical simulations of threshold models have been performed on a
human brain network with N=836733 connected nodes available from the Open
Connectome project. While in case of simple threshold models a sharp
discontinuous phase transition without any critical dynamics arises, variable
thresholds models exhibit extended power-law scaling regions. This is
attributed to fact that Griffiths effects, stemming from the
topological/interaction heterogeneity of the network, can become relevant if
the input sensitivity of nodes is equalized. I have studied the effects effects
of link directness, as well as the consequence of inhibitory connections.
Non-universal power-law avalanche size and time distributions have been found
with exponents agreeing with the values obtained in electrode experiments of
the human brain. The dynamical critical region occurs in an extended control
parameter space without the assumption of self organized criticality.Comment: 7 pages, 6 figures, accepted version to appear in PR
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Emergent complex neural dynamics
A large repertoire of spatiotemporal activity patterns in the brain is the
basis for adaptive behaviour. Understanding the mechanism by which the brain's
hundred billion neurons and hundred trillion synapses manage to produce such a
range of cortical configurations in a flexible manner remains a fundamental
problem in neuroscience. One plausible solution is the involvement of universal
mechanisms of emergent complex phenomena evident in dynamical systems poised
near a critical point of a second-order phase transition. We review recent
theoretical and empirical results supporting the notion that the brain is
naturally poised near criticality, as well as its implications for better
understanding of the brain
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks,
have recently been suggested to provide a mechanism, rid of fine parameter
tuning, to explain the critical behavior of complex systems. One conjectured
requirement for systems with modular structures was that the network of modules
must be hierarchically organized and possess finite dimension. We investigate
the dynamical behavior of an activity spreading model, evolving on
heterogeneous random networks with highly modular structure and organized
non-hierarchically. We observe that loosely coupled modules act as effective
rare-regions, slowing down the extinction of activation. As a consequence, we
find extended control parameter regions with continuously changing dynamical
exponents for single network realizations, preserved after finite size
analyses, as in a real GP. The avalanche size distributions of spreading events
exhibit robust power-law tails. Our findings relax the requirement of
hierarchical organization of the modular structure, which can help to
rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure
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