Yan Wan

Designing spatially heterogeneous strategies for control of virus spread

The spread of a virus--whether in a human population, computer network or cell-to-cell--is closely tied to the spatial (graph) topology of the interactions among the possible infectives. The authors study the problem of allocating limited control resources (e.g. quarantine or recovery resources) in these networks in a way that exploits the topological structure, so as to maximise the speed at which the virus is eliminated. For both multi-group and contact-network models for spread, these problems can be abstracted to a particular decentralised control problem for which the goal is to minimise the dominant eigenvalue of a system matrix. Explicit solutions to these problems are provided, using eigenvalue sensitivity ideas together with constrained optimisation methods employing Lagrange multipliers. The proposed design method shows that the optimal strategy is to allocate resources so as to equalise the propagation impact of each network component, as best as possible within the constraints on the resource. Finally, we show that this decentralised control approach can provide significant advantage over a homogeneous control strategy, in the context of a model for SARS transmission in Hong Kong.

A Scalable Methodology for Evaluating and Designing Coordinated Air-Traffic Flow Management Strategies Under Uncertainty

As congestion in the United States National Airspace System (NAS) increases, coordination of en route and terminal-area traffic flow management procedures is becoming increasingly necessary to prevent controller workload excesses without imposing excessive delay on aircraft. Here, we address the coordination of flow management procedures in the presence of realistic uncertainties by developing a family of abstractions for implementable flow restrictions (e.g., miles-in-trail restrictions, ground delay programs, and slot-based policies). Using these abstractions, we are able to evaluate the impact of multiple restrictions on generic (uncertain) traffic flows and, hence, to design practical flow management strategies. We use the developed methodology to address several common design problems, including the design of multiple restrictions along a single major traffic stream and the design of multiple flows entering a congested terminal area or sector. For instance, we find that multiple restrictions along a stream can be used to split the backlog resulting from a single restriction and use this observation to develop low-congestion designs. We conclude the discussion by posing a tractable NAS-wide flow management problem using a simple algebraic model for a restriction.

A Network Model for Activity-Dependent Sleep Regulation

We develop and characterize a dynamical network model for activity-dependent sleep regulation. Specifically, in accordance with the activity-dependent theory for sleep, we view organism sleep as emerging from the local sleep states of functional units known as cortical columns; these local sleep states evolve through integration of local activity inputs, loose couplings with neighboring cortical columns, and global regulation (e.g. by the circadian clock). We model these cortical columns as coupled or networked activity-integrators that transition between sleep and waking states based on thresholds on the total activity. The model dynamics for three canonical experiments (which we have studied both through simulation and system-theoretic analysis) match with experimentally-observed characteristics of the cortical-column network. Most notably, assuming connectedness of the network graph, our model predicts the recovery of the columns to a synchronized state upon temporary overstimulation of a single column and/or randomization of the initial sleep and activity-integration states. In analogy with other models for networked oscillators, our model also predicts the possibility for such phenomena as mode-locking.

A new focus in the science of networks: towards methods for design

In recent years, a realization that networks are ubiquitous in the natural and engineered worlds has led to a burgeoning interest in finding commonalities in their structures and dynamics. Here, we introduce a new design focus in this science of networks by proposing generic methods for synthesizing network controllers that exploit the topological structure. That is, we motivate a canonical controller synthesis problem for networks that has applications in such diverse areas as virus-spreading control and air traffic flow management. We address this design problem by using new techniques from decentralized control theory. Specifically, we mesh optimization machinery together with eigenvalue sensitivity and graph theory notions to identify general structural features of optimally actuated networks. From these features, we are in turn able to explicitly construct high-performance controllers, i.e. the ones that best exploit the networks topological structure. Our general approach for controller design is important because it both provides a broad insight into the structure of well-designed networks and contributes engineering solutions in numerous application areas (e.g. reduction in management delays and human-controller workload in air traffic systems).

Network design problems for controlling virus spread

The spread of viruses in human populations (e.g., SARS) or computer networks is closely related to the networks topological structure. In this paper, we study the problem of allocating limited control resources (e.g., quarantine or recovery resources) in these networks to maximize the speed at which the virus is eliminated, by exploiting the topological structure. This problem can be abstracted to that of designing diagonal K or D to minimize the dominant eigenvalue of one of the system matrices KG, D + KG or D + G under constraints on K and D (where G is a square matrix that captures the network topology). We give explicit solutions to these problems, using eigenvalue sensitivity ideas together with constrained optimization methods employing Lagrange multipliers. Finally, we show that this decentralized control approach can provide significant advantage over a homogeneous control strategy, using a model for SARS transmission in Hong Kong derived from real data.

A Survey and Analysis of Mobility Models for Airborne Networks

Mobility models serve as the foundation for evaluating and designing airborne networks (ANs). Due to the significant impact of mobility models on the networking performance, the mobility models must realistically capture the attributes of ANs. In this paper, we present a comprehensive survey and comparative analysis of mobility models that are either adapted to or developed for AN evaluation purposes. We evaluate these mobility models based on the following metrics: adaptability, networking performance, and ability to realistically capture the mobility attributes of ANs (including high mobility, mechanical and aerodynamic constraint, and safety requirements). To provide a deeper understanding and facilitate the selection and configuration of these mobility models, we also evaluate them based on randomness levels and associated applications.

A smooth-turn mobility model for airborne networks

The design of effective routing protocols in airborne networks (ANs) relies on suitable mobility models that capture the movement patterns of airborne vehicles. As airborne vehicles cannot make sharp turns as easily as ground vehicles do, the widely used ground-based mobile ad hoc network (MANET) mobility models are not appropriate to use as the analytical frameworks for airborne networking. In this paper, we introduce a novel mobility model, which is called the smooth-turn (ST) mobility model, that captures the correlation of acceleration of airborne vehicles across temporal and spatial coordinates. The proposed model is realistic in capturing the tendency of airborne vehicles toward making straight trajectories and STs with large radii, yet is tractable enough for analysis and design. We first describe the mathematics of this model and then prove that the stationary node distribution is uniform. Furthermore, we introduce a metric to quantify the degree of model randomness, and using this, we compare and classify several mobility models in the literature. We conclude this paper with several possible variations to the basic ST mobility model.

A Stochastic Network Model for Uncertain Spatiotemporal Weather Impact at the Strategic Time Horizon

Motivated by challenges in flow-contingency management, we introduce a stochastic network model for the spatiotemporal evolution of weather impact at a strategic time horizon. Specifically, we argue that a model that represents weather-impact propagation using local probabilistic influences can capture the rich dynamics and inherent variability in weather impact at the spatial and temporal resolution of interest. We then illustrate that such an influence model for weather impact is simple enough to permit a family of analyses that are needed for decision-support, including 1) model parameterization to meet probabilistic forecasts at time snapshots, 2) fast simulation of representative weather trajectories and impact probabilities, and 3) computation of correlations and higher-order statistics in weather impact. Also, lower-order representation of the stochastic dynamics at critical locations in the airspace is considered. Finally, a brief exploratory discussion is given on how the weather-impact model may eventually be used in tandem with network flow models to study flow contingency management. 1. Motivation and Goals As the Next Generation Air Transportation System (NextGen) comes into operation, a wide array of new decision-support tools for traffic flow management (TFM) are needed, in order to meet the performance requirements of the new system and to take advantage of its new hardware capabilities. Although decision-support for tactical TFM has been advanced significantly during the last few years, TFM design at the strategic and planning time horizons (2hrs – 1day, and days – months/years, respectively) remains challenging. A major obstacle in current TFM operations is the often overly conservative actions taken when demand exceeds capacity in either predicted or impending operations. A lack of information availability and integration, as well as grave limitations in decision support systems that assist decision makers in identifying and alleviating potential congestion in a way that minimizes the impact on the National Airspace System (NAS), are understood to be current deficits in the system. However, the details on exactly what decision support system capabilities are necessary, and the resulting products from these decision support systems, are not clearly defined. The work that we present here is motivated by this need for decision-support at the strategic time frame.

On inference of network time constants from impulse response data: graph-theoretic Cramer-Rao bounds

We examine the role played by a linear dynamical networks topology in inference of its eigenvalues from noisy impulse-response data. Specifically, for a canonical linear time-invariant network dynamics, we relate the Cramer-Rao bounds on eigenvalue estimator performance (from impulse-response data) to structural properties of the transfer function, and in turn to the networks topological structure. We focus especially on networks with a slow-coherence structure, in which case we find that stimulus and observation in each strongly-connected network component is needed for high-fidelity estimation.

A network control theory approach to modeling and optimal control of zoonoses: case study of brucellosis transmission in sub-Saharan Africa.

Background Developing control policies for zoonotic diseases is challenging, both because of the complex spread dynamics exhibited by these diseases, and because of the need for implementing complex multi-species surveillance and control efforts using limited resources. Mathematical models, and in particular network models, of disease spread are promising as tools for control-policy design, because they can provide comprehensive quantitative representations of disease transmission. Methodology/Principal Findings A layered dynamical network model for the transmission and control of zoonotic diseases is introduced as a tool for analyzing disease spread and designing cost-effective surveillance and control. The model development is achieved using brucellosis transmission among wildlife, cattle herds, and human sub-populations in an agricultural system as a case study. Precisely, a model that tracks infection counts in interacting animal herds of multiple species (e.g., cattle herds and groups of wildlife for brucellosis) and in human subpopulations is introduced. The model is then abstracted to a form that permits comprehensive targeted design of multiple control capabilities as well as model identification from data. Next, techniques are developed for such quantitative design of control policies (that are directed to both the animal and human populations), and for model identification from snapshot and time-course data, by drawing on recent results in the network control community. Conclusions/Significance The modeling approach is shown to provide quantitative insight into comprehensive control policies for zoonotic diseases, and in turn to permit policy design for mitigation of these diseases. For the brucellosis-transmission example in particular, numerous insights are obtained regarding the optimal distribution of resources among available control capabilities (e.g., vaccination, surveillance and culling, pasteurization of milk) and points in the spread network (e.g., transhumance vs. sedentary herds). In addition, a preliminary identification of the network model for brucellosis is achieved using historical data, and the robustness of the obtained model is demonstrated. As a whole, our results indicate that network modeling can aid in designing control policies for zoonotic diseases.