105 research outputs found
Transitions from trees to cycles in adaptive flow networks
Transport networks are crucial to the functioning of natural and
technological systems. Nature features transport networks that are adaptive
over a vast range of parameters, thus providing an impressive level of
robustness in supply. Theoretical and experimental studies have found that
real-world transport networks exhibit both tree-like motifs and cycles. When
the network is subject to load fluctuations, the presence of cyclic motifs may
help to reduce flow fluctuations and, thus, render supply in the network more
robust. While previous studies considered network topology via optimization
principles, here, we take a dynamical systems approach and study a simple model
of a flow network with dynamically adapting weights (conductances). We assume a
spatially non-uniform distribution of rapidly fluctuating loads in the sinks
and investigate what network configurations are dynamically stable. The network
converges to a spatially non-uniform stable configuration composed of both
cyclic and tree-like structures. Cyclic structures emerge locally in a
transcritical bifurcation as the amplitude of the load fluctuations is
increased. The resulting adaptive dynamics thus partitions the network into two
distinct regions with cyclic and tree-like structures. The location of the
boundary between these two regions is determined by the amplitude of the
fluctuations. These findings may explain why natural transport networks display
cyclic structures in the micro-vascular regions near terminal nodes, but
tree-like features in the regions with larger veins
Tree decompositions of real-world networks from simulated annealing
Decompositions of networks are useful not only for structural exploration.
They also have implications and use in analysis and computational solution of
processes (such as the Ising model, percolation, SIR model) running on a given
network. Tree and branch decompositions considered here directly represent
network structure as trees for recursive computation of network properties.
Unlike coarse-graining approximations in terms of community structure or
metapopulations, tree decompositions of sufficiently small width allow for
exact results on equilibrium processes. Here we use simulated annealing to find
tree decompositions of narrow width for a set of medium-size empirical
networks. Rather than optimizing tree decompositions directly, we employ a
search space constituted by so-called elimination orders being permutations on
the network's node set. For each in a database of empirical networks with up to
1000 edges, we find a tree decomposition of low width.Comment: 11 pages, 2 figures, 1 tabl
Competition in the presence of aging: order, disorder, and synchronized collective behavior
We study the stochastic dynamics of coupled states with transition
probabilities depending on local persistence, this is, the time since a state
has changed. When the population has a preference to adopt older states the
system orders quickly due to the dominance of the old state. When preference
for new states prevails, the system can show coexistence of states or
synchronized collective behavior resulting in long ordering times. In this
case, the magnetization of the system oscillates around .
Implications for social systems are discussed.Comment: 5 pages, 5 figures, lette
Cover-Encodings of Fitness Landscapes
The traditional way of tackling discrete optimization problems is by using
local search on suitably defined cost or fitness landscapes. Such approaches
are however limited by the slowing down that occurs when the local minima that
are a feature of the typically rugged landscapes encountered arrest the
progress of the search process. Another way of tackling optimization problems
is by the use of heuristic approximations to estimate a global cost minimum.
Here we present a combination of these two approaches by using cover-encoding
maps which map processes from a larger search space to subsets of the original
search space. The key idea is to construct cover-encoding maps with the help of
suitable heuristics that single out near-optimal solutions and result in
landscapes on the larger search space that no longer exhibit trapping local
minima. We present cover-encoding maps for the problems of the traveling
salesman, number partitioning, maximum matching and maximum clique; the
practical feasibility of our method is demonstrated by simulations of adaptive
walks on the corresponding encoded landscapes which find the global minima for
these problems.Comment: 15 pages, 4 figure
Temporal networks: slowing down diffusion by long lasting interactions
Interactions among units in complex systems occur in a specific sequential
order thus affecting the flow of information, the propagation of diseases, and
general dynamical processes. We investigate the Laplacian spectrum of temporal
networks and compare it with that of the corresponding aggregate network.
First, we show that the spectrum of the ensemble average of a temporal network
has identical eigenmodes but smaller eigenvalues than the aggregate networks.
In large networks without edge condensation, the expected temporal dynamics is
a time-rescaled version of the aggregate dynamics. Even for single sequential
realizations, diffusive dynamics is slower in temporal networks. These
discrepancies are due to the noncommutability of interactions. We illustrate
our analytical findings using a simple temporal motif, larger network models
and real temporal networks.Comment: 5 pages, 2 figures, v2: minor revision + supplemental materia
Stable and unstable attractors in Boolean networks
Boolean networks at the critical point have been a matter of debate for many
years as, e.g., scaling of number of attractor with system size. Recently it
was found that this number scales superpolynomially with system size, contrary
to a common earlier expectation of sublinear scaling. We here point to the fact
that these results are obtained using deterministic parallel update, where a
large fraction of attractors in fact are an artifact of the updating scheme.
This limits the significance of these results for biological systems where
noise is omnipresent. We here take a fresh look at attractors in Boolean
networks with the original motivation of simplified models for biological
systems in mind. We test stability of attractors w.r.t. infinitesimal
deviations from synchronous update and find that most attractors found under
parallel update are artifacts arising from the synchronous clocking mode. The
remaining fraction of attractors are stable against fluctuating response
delays. For this subset of stable attractors we observe sublinear scaling of
the number of attractors with system size.Comment: extended version, additional figur
Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Data of physical contacts and face-to-face communications suggest temporally
varying networks as the media on which infections take place among humans and
animals. Epidemic processes on temporal networks are complicated by complexity
of both network structure and temporal dimensions. Theoretical approaches are
much needed for identifying key factors that affect dynamics of epidemics. In
particular, what factors make some temporal networks stronger media of
infection than other temporal networks is under debate. We develop a theory to
understand the susceptible-infected-susceptible epidemic model on arbitrary
temporal networks, where each contact is used for a finite duration. We show
that temporality of networks lessens the epidemic threshold such that
infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times is a key determinant of the epidemic threshold in
temporal networks. The effect of temporality on the epidemic threshold, which
depends on a data set, is approximately predicted by the magnitude of a
commutator norm.Comment: 8 figures, 1 tabl
- …