ASU Scholarship Showcase

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.

Resource allocation takes place in various types of real-world complex systems such as urban traffic, social services institutions, economical and ecosystems. Mathematically, the dynamical process of resource allocation can be modeled as minority games. Spontaneous evolution of the resource allocation dynamics, however, often leads to a harmful herding behavior accompanied by strong fluctuations in which a large majority of agents crowd temporarily for a few resources, leaving many others unused. Developing effective control methods to suppress and eliminate herding is an important but open problem. Here we develop a pinning control method, that the fluctuations of the system consist of intrinsic and systematic components allows us to design a control scheme with separated control variables. A striking finding is the universal existence of an optimal pinning fraction to minimize the variance of the system, regardless of the pinning patterns and the network topology. We carry out a generally applicable theory to explain the emergence of optimal pinning and to predict the dependence of the optimal pinning fraction on the network topology. Our work represents a general framework to deal with the broader problem of controlling collective dynamics in complex systems with potential applications in social, economical and political systems.

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the structurally and dynamically identical oscillators in a coupled networked system spontaneously break into two groups, one exhibiting coherent motion and another incoherent. This phenomenon was typically studied in the setting of non-local coupling configurations. We ask what can happen to chimera states under systematic changes to the network structure when links are removed from the network in an orderly fashion but the local coupling topology remains invariant with respect to an index shift. We find the emergence of multicluster chimera states. Remarkably, as a parameter characterizing the amount of link removal is increased, chimera states of distinct numbers of clusters emerge and persist in different parameter regions. We develop a phenomenological theory, based on enhanced or reduced interactions among oscillators in different spatial groups, to explain why chimera states of certain numbers of clusters occur in certain parameter regions. The theoretical prediction agrees well with numerics.

We investigate the emergence of extreme events in interdependent networks. We introduce an inter-layer traffic resource competing mechanism to account for the limited capacity associated with distinct network layers. A striking finding is that, when the number of network layers and/or the overlap among the layers are increased, extreme events can emerge in a cascading manner on a global scale. Asymptotically, there are two stable absorption states: a state free of extreme events and a state of full of extreme events, and the transition between them is abrupt. Our results indicate that internal interactions in the multiplex system can yield qualitatively distinct phenomena associated with extreme events that do not occur for independent network layers. An implication is that, e.g., public resource competitions among different service providers can lead to a higher resource requirement than naively expected. We derive an analytical theory to understand the emergence of global-scale extreme events based on the concept of effective betweenness. We also articulate a cost-effective control scheme through increasing the capacity of very few hubs to suppress the cascading process of extreme events so as to protect the entire multi-layer infrastructure against global-scale breakdown.

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.