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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.
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Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate further research in this area.
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existence of objects from which no direct information can be obtained
experimentally or observationally. A well known example is to
ascertain the existence of black holes of various masses in different
parts of the universe from indirect evidence, such as X-ray emissions.
In the field of complex networks, the problem of detecting
hidden nodes can be stated, as follows. Consider a network whose
topology is completely unknown but whose nodes consist of two types:
one accessible and another inaccessible from the outside world. The
accessible nodes can be observed or monitored, and it is assumed that time
series are available from each node in this group. The inaccessible
nodes are shielded from the outside and they are essentially
``hidden.'' The question is, based solely on the
available time series from the accessible nodes, can the existence and
locations of the hidden nodes be inferred? A completely data-driven,
compressive-sensing based method is developed to address this issue by utilizing
complex weighted networks of nonlinear oscillators, evolutionary game
and geospatial networks.
Both microbes and multicellular organisms actively regulate their cell
fate determination to cope with changing environments or to ensure
proper development. Here, the synthetic biology approaches are used to
engineer bistable gene networks to demonstrate that stochastic and
permanent cell fate determination can be achieved through initializing
gene regulatory networks (GRNs) at the boundary between dynamic
attractors. This is experimentally realized by linking a synthetic GRN
to a natural output of galactose metabolism regulation in yeast.
Combining mathematical modeling and flow cytometry, the
engineered systems are shown to be bistable and that inherent gene expression
stochasticity does not induce spontaneous state transitioning at
steady state. By interfacing rationally designed synthetic
GRNs with background gene regulation mechanisms, this work
investigates intricate properties of networks that illuminate possible
regulatory mechanisms for cell differentiation and development that
can be initiated from points of instability.
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Although eusociality evolved independently within several orders of insects, research into the molecular underpinnings of the transition towards social complexity has been confined primarily to Hymenoptera (for example, ants and bees). Here we sequence the genome and stage-specific transcriptomes of the dampwood termite Zootermopsis nevadensis (Blattodea) and compare them with similar data for eusocial Hymenoptera, to better identify commonalities and differences in achieving this significant transition. We show an expansion of genes related to male fertility, with upregulated gene expression in male reproductive individuals reflecting the profound differences in mating biology relative to the Hymenoptera. For several chemoreceptor families, we show divergent numbers of genes, which may correspond to the more claustral lifestyle of these termites. We also show similarities in the number and expression of genes related to caste determination mechanisms. Finally, patterns of DNA methylation and alternative splicing support a hypothesized epigenetic regulation of caste differentiation.
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