Network Inference from Co-Occurrences

The recovery of network structure from experimental data is a basic and fundamental problem. Unfortunately, experimental data often do not directly reveal structure due to inherent limitations such as imprecision in timing or other observation mechanisms. We consider the problem of inferring network structure in the form of a directed graph from co-occurrence observations. Each observation arises from a transmission made over the network and indicates which vertices carry the transmission without explicitly conveying their order in the path. Without order information, there are an exponential number of feasible graphs which agree with the observed data equally well. Yet, the basic physical principles underlying most networks strongly suggest that all feasible graphs are not equally likely. In particular, vertices that co-occur in many observations are probably closely connected. Previous approaches to this problem are based on ad hoc heuristics. We model the experimental observations as independent realizations of a random walk on the underlying graph, subjected to a random permutation which accounts for the lack of order information. Treating the permutations as missing data, we derive an exact expectation-maximization (EM) algorithm for estimating the random walk parameters. For long transmission paths the exact E-step may be computationally intractable, so we also describe an efficient Monte Carlo EM (MCEM) algorithm and derive conditions which ensure convergence of the MCEM algorithm with high probability. Simulations and experiments with Internet measurements demonstrate the promise of this approach.Comment: Submitted to IEEE Transactions on Information Theory. An extended version is available as University of Wisconsin Technical Report ECE-06-

Matching and Network Effects

This paper examines the existence and magnitude of network effects in the matching of workteams. We study the formation of co-author relations among economists over a thirty year period. Our principal finding is that a collaboration emerges faster among two authors if they are closer in the social network of economists. This proximity effect on collaboration is strong and robust but only affects initial collaboration. It has no positive influence on subsequent co-authorship. We also provide some evidence that matching depends on experience, junior authors being more likely to collaborate with senior authors.

Resilience in Transportation Networks

The functionality of transportation networks is greatly challenged by risk factors such as increasing climate-related hazards, rising population exposure, and greater city vulnerability. Inevitably, the transportation network cannot withstand the impact of an overwhelming disaster, which results in rapid declines in the performance of road net-work. As a next step, the authorities need to restore the performance of the road net-work to an acceptable state as soon as possible and rebalance the conflict between the capacity of the road network and travel demand. Resilience is defined as the process of system performance degradation followed by recovery. To improve the transportation network resilience and maintain regular traffic, it is crucial to identify which factors are related to the resilience and investigate how these factors impact resilience. In this thesis, four factors, i.e., road networks, evacuees, disruption types and au-thorities, are identified to analyze resilience mechanisms. Firstly, the change in vehicle speed during a disaster is used as a measure of resilience, and we analyze the quantita-tive relationship between resilience and the structural characteristics and properties of the road network in multiple disruptions in multiple cities. The results show that the connectivity of the road network, the predictability of disruption, and the population density affect the resilience of the road network in different ways. Secondly, as the road connectivity plays a crucial role during the evacuation pe-riod and considering more frequent and extensive bushfires, we explore a practical and challenging problem: are bushfire fatalities related to road network characteristics? Con-nectivity index (CI), a composite metric that takes into account redundancy, connectivi-ty, and population exposure is designed. The statistical analysis of real-world data sug-gests that CI is significantly negatively correlated with historical bushfire fatalities. This parsimonious and simple graph-theoretic measure can provide planners a useful metric to reduce vulnerability and increase resilience among areas that are prone to bushfires. Finally, a modelling framework for optimizing road network pre-disaster invest-ment strategy under different disaster damage levels is proposed. A bi-level multi-objective optimization model is formulated, in which the upper-level aims to maximize the capacity-based functionality and robustness of the road network, and the lower-level is the user equilibrium problem. To efficiently solve the model, the Shapley value is used to select candidate edges and obtain a near-optimal project order. For more reality, the heterogeneity of road segments to hazards and the correlation of road segments in dif-ferent hazard phases are considered. Realistic speed data is used to explore the depend-ency between different disaster states with copula functions. The numerical results illus-trate that the investment strategy is significantly influenced by the road edge character-istics and the level of disaster damage. Critical sections that can significantly improve the overall functionality of the network are identified. Overall, the core contribution of this thesis is to provide insights into the evalua-tion and analysis of resilience in transportation networks, as well as develop modelling frameworks to promote resilience. The results of this work can provide a theoretical ba-sis for road network design, pre-disaster investment and post-disaster emergency rescue

Formalising the multidimensional nature of social networks

Individuals interact with conspecifics in a number of behavioural contexts or dimensions. Here, we formalise this by considering a social network between n individuals interacting in b behavioural dimensions as a nxnxb multidimensional object. In addition, we propose that the topology of this object is driven by individual needs to reduce uncertainty about the outcomes of interactions in one or more dimension. The proposal grounds social network dynamics and evolution in individual selection processes and allows us to define the uncertainty of the social network as the joint entropy of its constituent interaction networks. In support of these propositions we use simulations and natural 'knock-outs' in a free-ranging baboon troop to show (i) that such an object can display a small-world state and (ii) that, as predicted, changes in interactions after social perturbations lead to a more certain social network, in which the outcomes of interactions are easier for members to predict. This new formalisation of social networks provides a framework within which to predict network dynamics and evolution under the assumption that it is driven by individuals seeking to reduce the uncertainty of their social environment.Comment: 16 pages, 4 figure