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.

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.

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.

Background: Many studies used the older ActiGraph (7164) for physical activity measurement, but this model has been replaced with newer ones (e.g., GT3X+). The assumption that new generation models are more accurate has been questioned, especially for measuring lower intensity levels. The low-frequency extension (LFE) increases the low-intensity sensitivity of newer models, but its comparability with older models is unknown. This study compared step counts and physical activity collected with the 7164 and GT3X + using the Normal Filter and the LFE (GT3X+N and GT3X+LFE, respectively).

Findings: Twenty-five adults wore 2 accelerometer models simultaneously for 3Âdays and were instructed to engage in typical behaviors. Average daily step counts and minutes per day in nonwear, sedentary, light, moderate, and vigorous activity were calculated. Repeated measures ANOVAs with post-hoc pairwise comparisons were used to compare mean values. Means for the GT3X+N and 7164 were significantly different in 4 of the 6 categories (p < .05). The GT3X+N showed 2041 fewer steps per day and more sedentary, less light, and less moderate than the 7164 (+25.6, -31.2, -2.9 mins/day, respectively). The GT3X+LFE showed non-significant differences in 5 of 6 categories but recorded significantly more steps (+3597 steps/day; p < .001) than the 7164.

Conclusion: Studies using the newer ActiGraphs should employ the LFE for greater sensitivity to lower intensity activity and more comparable activity results with studies using the older models. Newer generation ActiGraphs do not produce comparable step counts to the older generation devices with the Normal filter or the LFE.

Background: Advancements in geographic information systems over the past two decades have increased the specificity by which an individual’s neighborhood environment may be spatially defined for physical activity and health research. This study investigated how different types of street network buffering methods compared in measuring a set of commonly used built environment measures (BEMs) and tested their performance on associations with physical activity outcomes.

Methods: An internationally-developed set of objective BEMs using three different spatial buffering techniques were used to evaluate the relative differences in resulting explanatory power on self-reported physical activity outcomes. BEMs were developed in five countries using ‘sausage,’ ‘detailed-trimmed,’ and ‘detailed,’ network buffers at a distance of 1 km around participant household addresses (n = 5883).

Results: BEM values were significantly different (p < 0.05) for 96% of sausage versus detailed-trimmed buffer comparisons and 89% of sausage versus detailed network buffer comparisons. Results showed that BEM coefficients in physical activity models did not differ significantly across buffering methods, and in most cases BEM associations with physical activity outcomes had the same level of statistical significance across buffer types. However, BEM coefficients differed in significance for 9% of the sausage versus detailed models, which may warrant further investigation.

Conclusions: Results of this study inform the selection of spatial buffering methods to estimate physical activity outcomes using an internationally consistent set of BEMs. Using three different network-based buffering methods, the findings indicate significant variation among BEM values, however associations with physical activity outcomes were similar across each buffering technique. The study advances knowledge by presenting consistently assessed relationships between three different network buffer types and utilitarian travel, sedentary behavior, and leisure-oriented physical activity outcomes.

Background: The World Health Organization recommends strategies to improve urban design, public transportation, and recreation facilities to facilitate physical activity for non-communicable disease prevention for an increasingly urbanized global population. Most evidence supporting environmental associations with physical activity comes from single countries or regions with limited variation in urban form. This paper documents variation in comparable built environment features across countries from diverse regions.

Methods: The International Physical Activity and the Environment Network (IPEN) study of adults aimed to measure the full range of variation in the built environment using geographic information systems (GIS) across 12 countries on 5 continents. Investigators in Australia, Belgium, Brazil, Colombia, the Czech Republic, Denmark, China, Mexico, New Zealand, Spain, the United Kingdom, and the United States followed a common research protocol to develop internationally comparable measures. Using detailed instructions, GIS-based measures included features such as walkability (i.e., residential density, street connectivity, mix of land uses), and access to public transit, parks, and private recreation facilities around each participant’s residential address using 1-km and 500-m street network buffers.

Results: Eleven of 12 countries and 15 cities had objective GIS data on built environment features. We observed a 38-fold difference in median residential densities, a 5-fold difference in median intersection densities and an 18-fold difference in median park densities. Hong Kong had the highest and North Shore, New Zealand had the lowest median walkability index values, representing a difference of 9 standard deviations in GIS-measured walkability.

Conclusions: Results show that comparable measures can be created across a range of cultural settings revealing profound global differences in urban form relevant to physical activity. These measures allow cities to be ranked more precisely than previously possible. The highly variable measures of urban form will be used to explain individuals’ physical activity, sedentary behaviors, body mass index, and other health outcomes on an international basis. Present measures provide the ability to estimate dose–response relationships from projected changes to the built environment that would otherwise be impossible.