27,997 research outputs found
Universal data-based method for reconstructing complex networks with binary-state dynamics
ACKNOWLEDGMENTS W.-X.W. was supported by NSFC under Grant No. 61573064, No. 61074116, and No. 71631002, as well as the Fundamental Research Funds for the Central Universities, Beijing Nova Programme. Y.-C.L. was supported by ARO under Grant No. W911NF-14-1-0504. W.-X.W. designed research; J.L. and Z.S. performed research; all analyzed data; J.L., W.-X.W., and Y.-C.L. wrote the paper; all edited the paper. The authors declare no competing financial interests.Peer reviewedPublisher PD
Reconstructing propagation networks with natural diversity and identifying hidden sources
Our ability to uncover complex network structure and dynamics from data is
fundamental to understanding and controlling collective dynamics in complex
systems. Despite recent progress in this area, reconstructing networks with
stochastic dynamical processes from limited time series remains to be an
outstanding problem. Here we develop a framework based on compressed sensing to
reconstruct complex networks on which stochastic spreading dynamics take place.
We apply the methodology to a large number of model and real networks, finding
that a full reconstruction of inhomogeneous interactions can be achieved from
small amounts of polarized (binary) data, a virtue of compressed sensing.
Further, we demonstrate that a hidden source that triggers the spreading
process but is externally inaccessible can be ascertained and located with high
confidence in the absence of direct routes of propagation from it. Our approach
thus establishes a paradigm for tracing and controlling epidemic invasion and
information diffusion in complex networked systems.Comment: 20 pages and 5 figures. For Supplementary information, please see
http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Nearly extensive sequential memory lifetime achieved by coupled nonlinear neurons
Many cognitive processes rely on the ability of the brain to hold sequences
of events in short-term memory. Recent studies have revealed that such memory
can be read out from the transient dynamics of a network of neurons. However,
the memory performance of such a network in buffering past information has only
been rigorously estimated in networks of linear neurons. When signal gain is
kept low, so that neurons operate primarily in the linear part of their
response nonlinearity, the memory lifetime is bounded by the square root of the
network size. In this work, I demonstrate that it is possible to achieve a
memory lifetime almost proportional to the network size, "an extensive memory
lifetime", when the nonlinearity of neurons is appropriately utilized. The
analysis of neural activity revealed that nonlinear dynamics prevented the
accumulation of noise by partially removing noise in each time step. With this
error-correcting mechanism, I demonstrate that a memory lifetime of order
can be achieved.Comment: 21 pages, 5 figures, the manuscript has been accepted for publication
in Neural Computatio
Reconstructing dynamical networks via feature ranking
Empirical data on real complex systems are becoming increasingly available.
Parallel to this is the need for new methods of reconstructing (inferring) the
topology of networks from time-resolved observations of their node-dynamics.
The methods based on physical insights often rely on strong assumptions about
the properties and dynamics of the scrutinized network. Here, we use the
insights from machine learning to design a new method of network reconstruction
that essentially makes no such assumptions. Specifically, we interpret the
available trajectories (data) as features, and use two independent feature
ranking approaches -- Random forest and RReliefF -- to rank the importance of
each node for predicting the value of each other node, which yields the
reconstructed adjacency matrix. We show that our method is fairly robust to
coupling strength, system size, trajectory length and noise. We also find that
the reconstruction quality strongly depends on the dynamical regime
Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
The autoregressive neural networks are emerging as a powerful computational
tool to solve relevant problems in classical and quantum mechanics. One of
their appealing functionalities is that, after they have learned a probability
distribution from a dataset, they allow exact and efficient sampling of typical
system configurations. Here we employ a neural autoregressive distribution
estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a
paradigmatic classical model of spin-glass theory, namely the two-dimensional
Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately
mimic the Boltzmann distribution using unsupervised learning from system
configurations generated using standard MCMC algorithms. The trained NADE is
then employed as smart proposal distribution for the Metropolis-Hastings
algorithm. This allows us to perform efficient MCMC simulations, which provide
unbiased results even if the expectation value corresponding to the probability
distribution learned by the NADE is not exact. Notably, we implement a
sequential tempering procedure, whereby a NADE trained at a higher temperature
is iteratively employed as proposal distribution in a MCMC simulation run at a
slightly lower temperature. This allows one to efficiently simulate the
spin-glass model even in the low-temperature regime, avoiding the divergent
correlation times that plague MCMC simulations driven by local-update
algorithms. Furthermore, we show that the NADE-driven simulations quickly
sample ground-state configurations, paving the way to their future utilization
to tackle binary optimization problems.Comment: 13 pages, 14 figure
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