32,384 research outputs found
Universally Optimal Noisy Quantum Walks on Complex Networks
Transport properties play a crucial role in several fields of science, as
biology, chemistry, sociology, information science, and physics. The behavior
of many dynamical processes running over complex networks is known to be
closely related to the geometry of the underlying topology, but this connection
becomes even harder to understand when quantum effects come into play. Here, we
exploit the Kossakoski-Lindblad formalism of quantum stochastic walks to
investigate the capability to quickly and robustly transmit energy (or
information) between two distant points in very large complex structures,
remarkably assisted by external noise and quantum features as coherence. An
optimal mixing of classical and quantum transport is, very surprisingly, quite
universal for a large class of complex networks. This widespread behaviour
turns out to be also extremely robust with respect to geometry changes. These
results might pave the way for designing optimal bio-inspired geometries of
efficient transport nanostructures that can be used for solar energy and also
quantum information and communication technologies.Comment: 17 pages, 12 figure
Walks on Apollonian networks
We carry out comparative studies of random walks on deterministic Apollonian
networks (DANs) and random Apollonian networks (RANs). We perform computer
simulations for the mean first passage time, the average return time, the
mean-square displacement, and the network coverage for unrestricted random
walk. The diffusions both on DANs and RANs are proved to be sublinear. The
search efficiency for walks with various strategies and the influence of the
topology of underlying networks on the dynamics of walks are discussed.
Contrary to one's intuition, it is shown that the self-avoiding random walk,
which has been verified as an optimal strategy for searching on scale-free and
small-world networks, is not the best strategy for the DAN in the thermodynamic
limit.Comment: 5 pages, 4 figure
Exploring complex networks by walking on them
We carry out a comparative study on the problem for a walker searching on
several typical complex networks. The search efficiency is evaluated for
various strategies. Having no knowledge of the global properties of the
underlying networks and the optimal path between any two given nodes, it is
found that the best search strategy is the self-avoid random walk. The
preferentially self-avoid random walk does not help in improving the search
efficiency further. In return, topological information of the underlying
networks may be drawn by comparing the results of the different search
strategies.Comment: 5 pages, 5 figure
Information transfer in community structured multiplex networks
The study of complex networks that account for different types of
interactions has become a subject of interest in the last few years, specially
because its representational power in the description of users interactions in
diverse online social platforms (Facebook, Twitter, Instagram, etc.). The
mathematical description of these interacting networks has been coined under
the name of multilayer networks, where each layer accounts for a type of
interaction. It has been shown that diffusive processes on top of these
networks present a phenomenology that cannot be explained by the naive
superposition of single layer diffusive phenomena but require the whole
structure of interconnected layers. Nevertheless, the description of diffusive
phenomena on multilayer networks has obviated the fact that social networks
have strong mesoscopic structure represented by different communities of
individuals driven by common interests, or any other social aspect. In this
work, we study the transfer of information in multilayer networks with
community structure. The final goal is to understand and quantify, if the
existence of well-defined community structure at the level of individual
layers, together with the multilayer structure of the whole network, enhances
or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure
Exploring Complex Graphs by Random Walks
We present an algorithm to grow a graph with scale-free structure of {\it
in-} and {\it out-links} and variable wiring diagram in the class of the
world-wide Web. We then explore the graph by intentional random walks using
local next-near-neighbor search algorithm to navigate through the graph. The
topological properties such as betweenness are determined by an ensemble of
independent walkers and efficiency of the search is compared on three different
graph topologies. In addition we simulate interacting random walks which are
created by given rate and navigated in parallel, representing transport with
queueing of information packets on the graph.Comment: Latex, 4 figure
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