Faculty and Staff

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. We implement some realistic extensions to the basic model to offer more accurate predictions for cities of various scaling behaviours and the Zipf distribution reported in the literature and observed in our empirical studies. All of the empirical results can be precisely recovered by our model with analytical predictions of all major properties. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems.

The emergence of the disease chytridiomycosis caused by the chytrid fungus Batrachochytrium dendrobatidis (Bd) has been implicated in dramatic global amphibian declines. Although many species have undergone catastrophic declines and/or extinctions, others appear to be unaffected or persist at reduced frequencies after Bd outbreaks. The reasons behind this variance in disease outcomes are poorly understood: differences in host immune responses have been proposed, yet previous studies suggest a lack of robust immune responses to Bd in susceptible species. Here, we sequenced transcriptomes from clutch-mates of a highly susceptible amphibian, Atelopus zeteki, with different infection histories. We found significant changes in expression of numerous genes involved in innate and inflammatory responses in infected frogs despite high susceptibility to chytridiomycosis.

We show evidence of acquired immune responses generated against Bd, including increased expression of immunoglobulins and major histocompatibility complex genes. In addition, fungal-killing genes had significantly greater expression in frogs previously exposed to Bd compared with Bd-naïve frogs, including chitinase and serine-type proteases. However, our results appear to confirm recent in vitro evidence of immune suppression by Bd, demonstrated by decreased expression of lymphocyte genes in the spleen of infected compared with control frogs. We propose susceptibility to chytridiomycosis is not due to lack of Bd-specific immune responses but instead is caused by failure of those responses to be effective. Ineffective immune pathway activation and timing of antibody production are discussed as potential mechanisms. However, in light of our findings, suppression of key immune responses by Bd is likely an important factor in the lethality of this fungus.

Amphibians vary in their response to infection by the amphibian-killing chytrid fungus, Batrachochytrium dendrobatidis (Bd). Highly susceptible species are the first to decline and/or disappear once Bd arrives at a site. These competent hosts likely facilitate Bd proliferation because of ineffective innate and/or acquired immune defenses. We show that Atelopus zeteki, a highly susceptible species that has undergone substantial population declines throughout its range, rapidly and exponentially increases skin Bd infection intensity, achieving intensities that are several orders of magnitude greater than most other species reported. We experimentally infected individuals that were never exposed to Bd (n = 5) or previously exposed to an attenuated Bd strain (JEL427-P39; n = 3). Within seven days post-inoculation, the average Bd infection intensity was 18,213 zoospores (SE: 9,010; range: 0 to 66,928).

Both average Bd infection intensity and zoospore output (i.e., the number of zoospores released per minute by an infected individual) increased exponentially until time of death (t₅₀ = 7.018, p<0.001, t₄₆ = 3.164, p = 0.001, respectively). Mean Bd infection intensity and zoospore output at death were 4,334,422 zoospores (SE: 1,236,431) and 23.55 zoospores per minute (SE: 22.78), respectively, with as many as 9,584,158 zoospores on a single individual. The daily percent increases in Bd infection intensity and zoospore output were 35.4% (SE: 0.05) and 13.1% (SE: 0.04), respectively. We also found that Bd infection intensity and zoospore output were positively correlated (t₄₃ = 3.926, p<0.001). All animals died between 22 and 33 days post-inoculation (mean: 28.88; SE: 1.58). Prior Bd infection had no effect on survival, Bd infection intensity, or zoospore output. We conclude that A. zeteki, a highly susceptible amphibian species, may be an acute supershedder. Our results can inform epidemiological models to estimate Bd outbreak probability, especially as they relate to reintroduction programs.

Laboratory investigations into the amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), have accelerated recently, given the pathogen’s role in causing the global decline and extinction of amphibians. Studies in which host animals were exposed to Bd have largely assumed that lab-maintained pathogen cultures retained the infective and pathogenic properties of wild isolates. Attenuated pathogenicity is common in artificially maintained cultures of other pathogenic fungi, but to date, it is unknown whether, and to what degree, Bd might change in culture. We compared zoospore production over time in two samples of a single Bd isolate having different passage histories: one maintained in artificial media for more than six years (JEL427-P39), and one recently thawed from cryopreserved stock (JEL427-P9). In a common garden experiment, we then exposed two different amphibian species, Eleutherodactylus coqui and Atelopus zeteki, to both cultures to test whether Bd attenuates in pathogenicity with in vitro passages. The culture with the shorter passage history, JEL427-P9, had significantly greater zoospore densities over time compared to JEL427-P39. This difference in zoospore production was associated with a difference in pathogenicity for a susceptible amphibian species, indicating that fecundity may be an important virulence factor for Bd. In the 130-day experiment, Atelopus zeteki frogs exposed to the JEL427-P9 culture experienced higher average infection intensity and 100% mortality, compared with 60% mortality for frogs exposed to JEL427-P39. This effect was not observed with Eleutherodactylus coqui, which was able to clear infection. We hypothesize that the differences in phenotypic performance observed with Atelopus zeteki are rooted in changes of the Bd genome. Future investigations enabled by this study will focus on the underlying mechanisms of Bd pathogenicity.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

Recent works revealed that the energy required to control a complex network depends on the number of driving signals and the energy distribution follows an algebraic scaling law. If one implements control using a small number of drivers, e.g. as determined by the structural controllability theory, there is a high probability that the energy will diverge. We develop a physical theory to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy. Based on the LCCs, we articulate a strategy to drastically reduce the control energy (e.g. in a large number of real-world networks). Owing to their structural nature, the LCCs may shed light on energy issues associated with control of nonlinear dynamical networks.

A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.

Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.

Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.