847 research outputs found
Growing Scale-Free Networks with Small World Behavior
In the context of growing networks, we introduce a simple dynamical model
that unifies the generic features of real networks: scale-free distribution of
degree and the small world effect. While the average shortest path length
increases logartihmically as in random networks, the clustering coefficient
assumes a large value independent of system size. We derive expressions for the
clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and
highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure
Hamiltonian dynamics for Einstein's action in G0 limit
The Hamiltonian analysis for the Einstein's action in limit is
performed. Considering the original configuration space without involve the
usual variables we show that the version for Einstein's action
is devoid of physical degrees of freedom. In addition, we will identify the
relevant symmetries of the theory such as the extended action, the extended
Hamiltonian, the gauge transformations and the algebra of the constraints. As
complement part of this work, we develop the covariant canonical formalism
where will be constructed a closed and gauge invariant symplectic form. In
particular, using the geometric form we will obtain by means of other way the
same symmetries that we found using the Hamiltonian analysis
Generic scale of the "scale-free" growing networks
We show that the connectivity distributions of scale-free growing
networks ( is the network size) have the generic scale -- the cut-off at
. The scaling exponent is related to the exponent
of the connectivity distribution, . We propose the
simplest model of scale-free growing networks and obtain the exact form of its
connectivity distribution for any size of the network. We demonstrate that the
trace of the initial conditions -- a hump at --
may be found for any network size. We also show that there exists a natural
boundary for the observation of the scale-free networks and explain why so few
scale-free networks are observed in Nature.Comment: 4 pages revtex, 3 figure
Line Graphs of Weighted Networks for Overlapping Communities
In this paper, we develop the idea to partition the edges of a weighted graph
in order to uncover overlapping communities of its nodes. Our approach is based
on the construction of different types of weighted line graphs, i.e. graphs
whose nodes are the links of the original graph, that encapsulate differently
the relations between the edges. Weighted line graphs are argued to provide an
alternative, valuable representation of the system's topology, and are shown to
have important applications in community detection, as the usual node partition
of a line graph naturally leads to an edge partition of the original graph.
This identification allows us to use traditional partitioning methods in order
to address the long-standing problem of the detection of overlapping
communities. We apply it to the analysis of different social and geographical
networks.Comment: 8 Pages. New title and text revisions to emphasise differences from
earlier paper
Highly clustered scale-free networks
We propose a model for growing networks based on a finite memory of the
nodes. The model shows stylized features of real-world networks: power law
distribution of degree, linear preferential attachment of new links and a
negative correlation between the age of a node and its link attachment rate.
Notably, the degree distribution is conserved even though only the most
recently grown part of the network is considered. This feature is relevant
because real-world networks truncated in the same way exhibit a power-law
distribution in the degree. As the network grows, the clustering reaches an
asymptotic value larger than for regular lattices of the same average
connectivity. These high-clustering scale-free networks indicate that memory
effects could be crucial for a correct description of the dynamics of growing
networks.Comment: 6 pages, 4 figure
Dynamics in online social networks
An increasing number of today's social interactions occurs using online
social media as communication channels. Some online social networks have become
extremely popular in the last decade. They differ among themselves in the
character of the service they provide to online users. For instance, Facebook
can be seen mainly as a platform for keeping in touch with close friends and
relatives, Twitter is used to propagate and receive news, LinkedIn facilitates
the maintenance of professional contacts, Flickr gathers amateurs and
professionals of photography, etc. Albeit different, all these online platforms
share an ingredient that pervades all their applications. There exists an
underlying social network that allows their users to keep in touch with each
other and helps to engage them in common activities or interactions leading to
a better fulfillment of the service's purposes. This is the reason why these
platforms share a good number of functionalities, e.g., personal communication
channels, broadcasted status updates, easy one-step information sharing, news
feeds exposing broadcasted content, etc. As a result, online social networks
are an interesting field to study an online social behavior that seems to be
generic among the different online services. Since at the bottom of these
services lays a network of declared relations and the basic interactions in
these platforms tend to be pairwise, a natural methodology for studying these
systems is provided by network science. In this chapter we describe some of the
results of research studies on the structure, dynamics and social activity in
online social networks. We present them in the interdisciplinary context of
network science, sociological studies and computer science.Comment: 17 pages, 4 figures, book chapte
Can we avoid high coupling?
It is considered good software design practice to organize source code into modules and to favour within-module connections (cohesion) over between-module connections (coupling), leading to the oft-repeated maxim "low coupling/high cohesion". Prior research into network theory and its application to software systems has found evidence that many important properties in real software systems exhibit approximately scale-free structure, including coupling; researchers have claimed that such scale-free structures are ubiquitous. This implies that high coupling must be unavoidable, statistically speaking, apparently contradicting standard ideas about software structure. We present a model that leads to the simple predictions that approximately scale-free structures ought to arise both for between-module connectivity and overall connectivity, and not as the result of poor design or optimization shortcuts. These predictions are borne out by our large-scale empirical study. Hence we conclude that high coupling is not avoidable--and that this is in fact quite reasonable
Interface Depinning in the Absence of External Driving Force
We study the pinning-depinning phase transition of interfaces in the quenched
Kardar-Parisi-Zhang model as the external driving force goes towards zero.
For a fixed value of the driving force we induce depinning by increasing the
nonlinear term coefficient , which is related to lateral growth, up to
a critical threshold. We focus on the case in which there is no external force
applied (F=0) and find that, contrary to a simple scaling prediction, there is
a finite value of that makes the interface to become depinned. The
critical exponents at the transition are consistent with directed percolation
depinning. Our results are relevant for paper wetting experiments, in which an
interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR
Mechanical mode dependence of bolometric back-action in an AFM microlever
Two back action (BA) processes generated by an optical cavity based detection
device can deeply transform the dynamical behavior of an AFM microlever: the
photothermal force or the radiation pressure. Whereas noise damping or
amplifying depends on optical cavity response for radiation pressure BA, we
present experimental results carried out under vacuum and at room temperature
on the photothermal BA process which appears to be more complex. We show for
the first time that it can simultaneously act on two vibration modes in
opposite direction: noise on one mode is amplified whereas it is damped on
another mode. Basic modeling of photothermal BA shows that dynamical effect on
mechanical mode is laser spot position dependent with respect to mode shape.
This analysis accounts for opposite behaviors of different modes as observed
Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
The master equation approach to Lyapunov spectra for many-particle systems is
applied to non-equilibrium thermostatted systems to discuss the conjugate
pairing rule. We consider iso-kinetic thermostatted systems with a shear flow
sustained by an external restriction, in which particle interactions are
expressed as a Gaussian white randomness. Positive Lyapunov exponents are
calculated by using the Fokker-Planck equation to describe the tangent vector
dynamics. We introduce another Fokker-Planck equation to describe the
time-reversed tangent vector dynamics, which allows us to calculate the
negative Lyapunov exponents. Using the Lyapunov exponents provided by these two
Fokker-Planck equations we show the conjugate pairing rule is satisfied for
thermostatted systems with a shear flow in the thermodynamic limit. We also
give an explicit form to connect the Lyapunov exponents with the
time-correlation of the interaction matrix in a thermostatted system with a
color field.Comment: 10 page
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