920 research outputs found

### Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional
random resistor network at the percolation threshold. We consider two ways of
applying the voltage difference: (i) two parallel bars, and (ii) two points.
Our numerical results suggest that in the infinite system limit, the
probability distribution behaves for small current i as P(i) ~ 1/i. As a
consequence, the moments of i of order q less than q_c=0 do not exist and all
current of value below the most probable one have the fractal dimension of the
backbone. The backbone can thus be described in terms of only (i) blobs of
fractal dimension d_B and (ii) high current carrying bonds of fractal dimension
going from $1/\nu$ to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E
(Rapid Comm

### The Emergence of El-Ni\~{n}o as an Autonomous Component in the Climate Network

We construct and analyze a climate network which represents the
interdependent structure of the climate in different geographical zones and
find that the network responds in a unique way to El-Ni\~{n}o events. Analyzing
the dynamics of the climate network shows that when El-Ni\~{n}o events begin,
the El-Ni\~{n}o basin partially loses its influence on its surroundings. After
typically three months, this influence is restored while the basin loses almost
all dependence on its surroundings and becomes \textit{autonomous}. The
formation of an autonomous basin is the missing link to understand the
seemingly contradicting phenomena of the afore--noticed weakening of the
interdependencies in the climate network during El-Ni\~{n}o and the known
impact of the anomalies inside the El-Ni\~{n}o basin on the global climate
system.Comment: 5 pages,10 figure

### Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks

Many real-world networks exhibit degree-assortativity, with nodes of similar
degree more likely to link to one another. Particularly in social networks, the
contribution to the total assortativity varies with degree, featuring a
distinctive peak slightly past the average degree. The way traditional models
imprint assortativity on top of pre-defined topologies is via degree-preserving
link permutations, which however destroy the particular graph's hierarchical
traits of clustering. Here, we propose the first generative model which creates
heterogeneous networks with scale-free-like properties and tunable realistic
assortativity. In our approach, two distinct populations of nodes are added to
an initial network seed: one (the followers) that abides by usual preferential
rules, and one (the potential leaders) connecting via anti-preferential
attachments, i.e. selecting lower degree nodes for their initial links. The
latter nodes come to develop a higher average degree, and convert eventually
into the final hubs. Examining the evolution of links in Facebook, we present
empirical validation for the connection between the initial anti-preferential
attachment and long term high degree. Thus, our work sheds new light on the
structure and evolution of social networks

### Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a
certain magnitude M$in California. We find that the distribution of the
recurrence times strongly depends on the previous recurrence time$\tau_0$. As
a consequence, the conditional mean recurrence time$\hat \tau(\tau_0)$between
two events increases monotonically with$\tau_0$. For$\tau_0$well below the
average recurrence time$\ov{\tau}, \hat\tau(\tau_0)$is smaller than$\ov{\tau}$, while for$\tau_0>\ov{\tau}$,$\hat\tau(\tau_0)$is greater than$\ov{\tau}$. Also the mean residual time until the next earthquake does not
depend only on the elapsed time, but also strongly on$\tau_0$. The larger$\tau_0$ is, the larger is the mean residual time. The above features should be
taken into account in any earthquake prognosis.Comment: 5 pages, 3 figures, submitted to Physica

### Robustness of interdependent networks under targeted attack

When an initial failure of nodes occurs in interdependent networks, a cascade
of failure between the networks occurs. Earlier studies focused on random
initial failures. Here we study the robustness of interdependent networks under
targeted attack on high or low degree nodes. We introduce a general technique
and show that the {\it targeted-attack} problem in interdependent networks can
be mapped to the {\it random-attack} problem in a transformed pair of
interdependent networks. We find that when the highly connected nodes are
protected and have lower probability to fail, in contrast to single scale free
(SF) networks where the percolation threshold $p_c=0$, coupled SF networks are
significantly more vulnerable with $p_c$ significantly larger than zero. The
result implies that interdependent networks are difficult to defend by
strategies such as protecting the high degree nodes that have been found useful
to significantly improve robustness of single networks.Comment: 11 pages, 2 figure

### Dynamics of Surface Roughening with Quenched Disorder

We study the dynamical exponent $z$ for the directed percolation depinning
(DPD) class of models for surface roughening in the presence of quenched
disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent
$d_{\rm min}$ characterizing the shortest path between two sites in an
isotropic percolation cluster in $d$ dimensions. To test the argument, we
perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for
percolation, from $d = 1$ to $d = 6$.Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via
email [email protected]

### A lattice Boltzmann model with random dynamical constraints

In this paper we introduce a modified lattice Boltzmann model (LBM) with the
capability of mimicking a fluid system with dynamic heterogeneities. The
physical system is modeled as a one-dimensional fluid, interacting with
finite-lifetime moving obstacles. Fluid motion is described by a lattice
Boltzmann equation and obstacles are randomly distributed semi-permeable
barriers which constrain the motion of the fluid particles. After a lifetime
delay, obstacles move to new random positions. It is found that the
non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous
patterns in fluid density and non-exponential relaxation of two-time
autocorrelation function.Comment: 10 pages, 9 figures, to be published in Eur. Phys. J.

### On the Tomography of Networks and Multicast Trees

In this paper we model the tomography of scale free networks by studying the
structure of layers around an arbitrary network node. We find, both
analytically and empirically, that the distance distribution of all nodes from
a specific network node consists of two regimes. The first is characterized by
rapid growth, and the second decays exponentially. We also show that the nodes
degree distribution at each layer is a power law with an exponential cut-off.
We obtain similar results for the layers surrounding the root of multicast
trees cut from such networks, as well as the Internet. All of our results were
obtained both analytically and on empirical Interenet data

### Generalized Shortest Path Kernel on Graphs

We consider the problem of classifying graphs using graph kernels. We define
a new graph kernel, called the generalized shortest path kernel, based on the
number and length of shortest paths between nodes. For our example
classification problem, we consider the task of classifying random graphs from
two well-known families, by the number of clusters they contain. We verify
empirically that the generalized shortest path kernel outperforms the original
shortest path kernel on a number of datasets. We give a theoretical analysis
for explaining our experimental results. In particular, we estimate
distributions of the expected feature vectors for the shortest path kernel and
the generalized shortest path kernel, and we show some evidence explaining why
our graph kernel outperforms the shortest path kernel for our graph
classification problem.Comment: Short version presented at Discovery Science 2015 in Banf

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