656 research outputs found
Optimization in Networks
The recent surge in the network modeling of complex systems has set the stage
for a new era in the study of fundamental and applied aspects of optimization
in collective behavior. This Focus Issue presents an extended view of the state
of the art in this field and includes articles from a large variety of domains
where optimization manifests itself, including physical, biological, social,
and technological networked systems.Comment: Opening article of the CHAOS Focus Issue "Optimization in Networks",
available at http://link.aip.org/link/?CHA/17/2/htmlto
Synchronization is optimal in non-diagonalizable networks
We consider the problem of maximizing the synchronizability of oscillator
networks by assigning weights and directions to the links of a given
interaction topology. We first extend the well-known master stability formalism
to the case of non-diagonalizable networks. We then show that, unless some
oscillator is connected to all the others, networks of maximum
synchronizability are necessarily non-diagonalizable and can always be obtained
by imposing unidirectional information flow with normalized input strengths.
The extension makes the formalism applicable to all possible network
structures, while the maximization results provide insights into hierarchical
structures observed in complex networks in which synchronization plays a
significant role.Comment: 4 pages, 1 figure; minor revisio
Cascade control and defense in complex networks
Complex networks with heterogeneous distribution of loads may undergo a
global cascade of overload failures when highly loaded nodes or edges are
removed due to attacks or failures. Since a small attack or failure has the
potential to trigger a global cascade, a fundamental question regards the
possible strategies of defense to prevent the cascade from propagating through
the entire network. Here we introduce and investigate a costless strategy of
defense based on a selective further removal of nodes and edges, right after
the initial attack or failure. This intentional removal of network elements is
shown to drastically reduce the size of the cascade.Comment: 4 pages, 2 figures, Revte
(Non)Invariance of dynamical quantities for orbit equivalent flows
We study how dynamical quantities such as Lyapunov exponents, metric entropy,
topological pressure, recurrence rates, and dimension-like characteristics
change under a time reparameterization of a dynamical system. These quantities
are shown to either remain invariant, transform according to a multiplicative
factor or transform through a convoluted dependence that may take the form of
an integral over the initial local values. We discuss the significance of these
results for the apparent non-invariance of chaos in general relativity and
explore applications to the synchronization of equilibrium states and the
elimination of expansions
How big is too big? Critical Shocks for Systemic Failure Cascades
External or internal shocks may lead to the collapse of a system consisting
of many agents. If the shock hits only one agent initially and causes it to
fail, this can induce a cascade of failures among neighoring agents. Several
critical constellations determine whether this cascade remains finite or
reaches the size of the system, i.e. leads to systemic risk. We investigate the
critical parameters for such cascades in a simple model, where agents are
characterized by an individual threshold \theta_i determining their capacity to
handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents
fail, they redistribute their load equally to K neighboring agents in a regular
network. For three different threshold distributions P(\theta), we derive
analytical results for the size of the cascade, X(t), which is regarded as a
measure of systemic risk, and the time when it stops. We focus on two different
regimes, (i) EEE, an external extreme event where the size of the shock is of
the order of the total capacity of the network, and (ii) RIE, a random internal
event where the size of the shock is of the order of the capacity of an agent.
We find that even for large extreme events that exceed the capacity of the
network finite cascades are still possible, if a power-law threshold
distribution is assumed. On the other hand, even small random fluctuations may
lead to full cascades if critical conditions are met. Most importantly, we
demonstrate that the size of the "big" shock is not the problem, as the
systemic risk only varies slightly for changes of 10 to 50 percent of the
external shock. Systemic risk depends much more on ingredients such as the
network topology, the safety margin and the threshold distribution, which gives
hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure
Dispensability of Escherichia coli's latent pathways
Gene-knockout experiments on single-cell organisms have established that
expression of a substantial fraction of genes is not needed for optimal growth.
This problem acquired a new dimension with the recent discovery that
environmental and genetic perturbations of the bacterium Escherichia coli are
followed by the temporary activation of a large number of latent metabolic
pathways, which suggests the hypothesis that temporarily activated reactions
impact growth and hence facilitate adaptation in the presence of perturbations.
Here we test this hypothesis computationally and find, surprisingly, that the
availability of latent pathways consistently offers no growth advantage, and
tends in fact to inhibit growth after genetic perturbations. This is shown to
be true even for latent pathways with a known function in alternate conditions,
thus extending the significance of this adverse effect beyond apparently
nonessential genes. These findings raise the possibility that latent pathway
activation is in fact derivative of another, potentially suboptimal, adaptive
response
Enhancing complex-network synchronization
Heterogeneity in the degree (connectivity) distribution has been shown to
suppress synchronization in networks of symmetrically coupled oscillators with
uniform coupling strength (unweighted coupling). Here we uncover a condition
for enhanced synchronization in directed networks with weighted coupling. We
show that, in the optimum regime, synchronizability is solely determined by the
average degree and does not depend on the system size and the details of the
degree distribution. In scale-free networks, where the average degree may
increase with heterogeneity, synchronizability is drastically enhanced and may
become positively correlated with heterogeneity, while the overall cost
involved in the network coupling is significantly reduced as compared to the
case of unweighted coupling.Comment: 4 pages, 3 figure
Can aerosols be trapped in open flows?
The fate of aerosols in open flows is relevant in a variety of physical
contexts. Previous results are consistent with the assumption that such
finite-size particles always escape in open chaotic advection. Here we show
that a different behavior is possible. We analyze the dynamics of aerosols both
in the absence and presence of gravitational effects, and both when the
dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent
trapping of aerosols much heavier than the advecting fluid is shown to occur in
all these cases. This phenomenon is determined by the occurrence of multiple
vortices in the flow and is predicted to happen for realistic particle-fluid
density ratios.Comment: Animation available at
http://www.pks.mpg.de/~rdvilela/leapfrogging.htm
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