58 research outputs found
Maximal-entropy random walks in complex networks with limited information
J.G.-G. was supported by MICINN through the Ramon y Cajal program and by grants FIS2008-01240 and MTM2009-13848
Nonintegrable Schrodinger Discrete Breathers
In an extensive numerical investigation of nonintegrable translational motion
of discrete breathers in nonlinear Schrodinger lattices, we have used a
regularized Newton algorithm to continue these solutions from the limit of the
integrable Ablowitz-Ladik lattice. These solutions are shown to be a
superposition of a localized moving core and an excited extended state
(background) to which the localized moving pulse is spatially asymptotic. The
background is a linear combination of small amplitude nonlinear resonant plane
waves and it plays an essential role in the energy balance governing the
translational motion of the localized core. Perturbative collective variable
theory predictions are critically analyzed in the light of the numerical
results.Comment: 42 pages, 28 figures. to be published in CHAOS (December 2004
Fear induced explosive transitions in the dynamics of corruption
In this article, we analyze a compartmental model aimed at mimicking the role of imitation and delation of corruption in social systems. In particular, the model relies on a compartmental dynamics in which individuals can transit between three states: honesty, corruption, and ostracism. We model the transitions from honesty to corruption and from corruption to ostracism as pairwise interactions. In particular, honest agents imitate corrupt peers while corrupt individuals pass to ostracism due to the delation of honest acquaintances. Under this framework, we explore the effects of introducing social intimidation in the delation of corrupt people. To this aim, we model the probability that an honest delates a corrupt agent as a decreasing function of the number of corrupt agents, thus mimicking the fear of honest individuals to reprisals by those corrupt ones. When this mechanism is absent or weak, the phase diagram of the model shows three equilibria [(i) full honesty, (ii) full corruption, and (iii) a mixed state] that are connected via smooth transitions. However, when social intimidation is strong, the transitions connecting these states turn explosive leading to a bistable phase in which a stable full corruption phase coexists with either mixed or full honesty stable equilibria. To shed light on the generality of these transitions, we analyze the model in different network substrates by means of Monte Carlo simulations and deterministic microscopic Markov chain equations. This latter formulation allows us to derive analytically the different bifurcation points that separate the different phases of the system
Spreading of sexually transmitted diseases in heterosexual populations
The spread of sexually transmitted diseases (e.g. Chlamydia, Syphilis,
Gonorrhea, HIV) across populations is a major concern for scientists and health
agencies. In this context, both data collection on sexual contact networks and
the modeling of disease spreading, are intensively contributing to the search
for effective immunization policies. Here, the spreading of sexually
transmitted diseases on bipartite scale-free graphs, representing heterosexual
contact networks, is considered. We analytically derive the expression for the
epidemic threshold and its dependence with the system size in finite
populations. We show that the epidemic outbreak in bipartite populations, with
number of sexual partners distributed as in empirical observations from
national sex surveys, takes place for larger spreading rates than for the case
in which the bipartite nature of the network is not taken into account.
Numerical simulations confirm the validity of the theoretical results. Our
findings indicate that the restriction to crossed infections between the two
classes of individuals (males and females) has to be taken into account in the
design of efficient immunization strategies for sexually transmitted diseases.Comment: 7 pages, 3 figures and 2 table
Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem
Elements composing complex systems usually interact in several different ways
and as such the interaction architecture is well modelled by a multiplex
network. However often this architecture is hidden, as one usually only has
experimental access to an aggregated projection. A fundamental challenge is
thus to determine whether the hidden underlying architecture of complex systems
is better modelled as a single interaction layer or results from the
aggregation and interplay of multiple layers. Here we show that using local
information provided by a random walker navigating the aggregated network one
can decide in a robust way if the underlying structure is a multiplex or not
and, in the former case, to determine the most probable number of hidden
layers. As a byproduct, we show that the mathematical formalism also provides a
principled solution for the optimal decomposition and projection of complex,
non-Markovian dynamics into a Markov switching combination of diffusive modes.
We validate the proposed methodology with numerical simulations of both (i)
random walks navigating hidden multiplex networks (thereby reconstructing the
true hidden architecture) and (ii) Markovian and non-Markovian continuous
stochastic processes (thereby reconstructing an effective multiplex
decomposition where each layer accounts for a different diffusive mode). We
also state and prove two existence theorems guaranteeing that an exact
reconstruction of the dynamics in terms of these hidden jump-Markov models is
always possible for arbitrary finite-order Markovian and fully non-Markovian
processes. Finally, we showcase the applicability of the method to experimental
recordings from (i) the mobility dynamics of human players in an online
multiplayer game and (ii) the dynamics of RNA polymerases at the
single-molecule level.Comment: 40 pages, 24 figure
How to suppress undesired synchronization
It is delightful to observe the emergence of synchronization in the blinking
of fireflies to attract partners and preys. Other charming examples of
synchronization can also be found in a wide range of phenomena such as, e.g.,
neurons firing, lasers cascades, chemical reactions, and opinion formation.
However, in many situations the formation of a coherent state is not pleasant
and should be mitigated. For example, the onset of synchronization can be the
root of epileptic seizures, traffic congestion in communication networks, and
the collapse of constructions. Here we propose the use of contrarians to
suppress undesired synchronization. We perform a comparative study of different
strategies, either requiring local or total knowledge of the system, and show
that the most efficient one solely requires local information. Our results also
reveal that, even when the distribution of neighboring interactions is narrow,
significant improvement in mitigation is observed when contrarians sit at the
highly connected elements. The same qualitative results are obtained for
artificially generated networks as well as two real ones, namely, the Routers
of the Internet and a neuronal network
Modelling and analysis of influenza A (H1N1) on networks
Network modelling is a useful tool for studying the transmission of H1N1 in China, capturing the main features of the spread of H1N1. The paper calculates the basic reproduction number and studies the effects of various immunization schemes. The final size relation is derived for the network epidemic model. While a uniform, mass-immunization strategy helps control the prevalence, a targeted immunization strategy focusing on specific groups with given connectivity may better control an epidemic
Spreading to localized targets in complex networks.
As an important type of dynamics on complex networks, spreading is widely used to model many real processes such as the epidemic contagion and information propagation. One of the most significant research questions in spreading is to rank the spreading ability of nodes in the network. To this end, substantial effort has been made and a variety of effective methods have been proposed. These methods usually define the spreading ability of a node as the number of finally infected nodes given that the spreading is initialized from the node. However, in many real cases such as advertising and news propagation, the spreading only aims to cover a specific group of nodes. Therefore, it is necessary to study the spreading ability of nodes towards localized targets in complex networks. In this paper, we propose a reversed local path algorithm for this problem. Simulation results show that our method outperforms the existing methods in identifying the influential nodes with respect to these localized targets. Moreover, the influential spreaders identified by our method can effectively avoid infecting the non-target nodes in the spreading process.We thank an anonymous reviewer for helpful suggestions which improve this paper. This work is supported by the National Natural Science Foundation of China (Nos 61603046 and 11547188), Natural Science Foundation of Beijing (No. 16L00077) and the Young Scholar Program of Beijing Normal University (No. 2014NT38)
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