Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie

Simultaneous Measurement Imputation and Outcome Prediction for Achilles Tendon Rupture Rehabilitation

Achilles Tendon Rupture (ATR) is one of the typical soft tissue injuries. Rehabilitation after such a musculoskeletal injury remains a prolonged process with a very variable outcome. Accurately predicting rehabilitation outcome is crucial for treatment decision support. However, it is challenging to train an automatic method for predicting the ATR rehabilitation outcome from treatment data, due to a massive amount of missing entries in the data recorded from ATR patients, as well as complex nonlinear relations between measurements and outcomes. In this work, we design an end-to-end probabilistic framework to impute missing data entries and predict rehabilitation outcomes simultaneously. We evaluate our model on a real-life ATR clinical cohort, comparing with various baselines. The proposed method demonstrates its clear superiority over traditional methods which typically perform imputation and prediction in two separate stages

Estimation of the vertical wavelength of atmospheric gravity waves from airglow imagery

Abstract In the summer of 2010, two imagers were installed in New Mexico with the objective of making stereoscopic observations of atmospheric gravity waves (AGWs). As AGWs propagate vertically, they spatially perturb the airglow emission layers in all three dimensions. Estimates of the vertical wavelength, horizontal wavelength, and the intrinsic frequency are needed to characterize an AGW and quantify its effects on upper atmospheric dynamics. The dispersion relation describes the relationship between vertical and horizontal wavelengths as a function of the intrinsic frequency. Thus, any two of the three aforementioned parameters can be used to determine the third. Mesospheric winds are hard to measure and consequently the intrinsic frequency is difficult to estimate. However, the horizontal wavelength can be directly measured from airglow imagery once the three-dimensional imager field of view is projected onto the two-dimensional image plane. This thesis presents a method to estimate the vertical wavelength using an airglow perturbation model proposed by Anderson et al. (2009). The model is subsequently validated using the observations from ground-based imagers installed in New Mexico. Abstract The perturbed airglow is modeled as a quasi-monochromatic wave and thus, it can be characterized using only a few parameters, one of which is the vertical wavelength. Because the vertical wavelength is embedded in both the phase and the magnitude of this model, two values of the vertical wavelength are estimated by applying two different parameter estimation techniques on the phase and magnitude. The estimation of the vertical wavelength from the phase of the model entails solving an overdetermined system of linear equations by minimizing the sum of the squared residuals. This estimate is then compared to that obtained by iteratively finding the best approximation to the roots of a function, representing the magnitude of the perturbation model. These two techniques are applied on three nights in 2010, and the estimates for the vertical wavelength match to within a few kilometers. Thus, the perturbation model is validated using real data

Neural ODEs with stochastic vector field mixtures

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to the set that baseline methods cannot solve, and proposes mixtures of stochastic vector fields as a model class that is capable of solving these essential problems. Dynamic vector field selection is of critical importance for our model, and our approach is to propagate component uncertainty over the integration interval with a technique based on forward filtering. We also formalise several loss functions that encourage desirable properties on the trajectory paths, and of particular interest are those that directly encourage fewer expected function evaluations. Experimentally, we demonstrate that our model class is capable of capturing the natural dynamics of human behaviour; a notoriously volatile application area. Baseline approaches cannot adequately model this problem

Computational Methods for Probabilistic Inference of Sector Congestion in Air Traffic Management

This article addresses the issue of computing the expected cost functions from a probabilistic model of the air traffic flow and capacity management. The Clenshaw-Curtis quadrature is compared to Monte-Carlo algorithms defined specifically for this problem. By tailoring the algorithms to this model, we reduce the computational burden in order to simulate real instances. The study shows that the Monte-Carlo algorithm is more sensible to the amount of uncertainty in the system, but has the advantage to return a result with the associated accuracy on demand. The performances for both approaches are comparable for the computation of the expected cost of delay and the expected cost of congestion. Finally, this study shows some evidences that the simulation of the proposed probabilistic model is tractable for realistic instances.Comment: Interdisciplinary Science for Innovative Air Traffic Management (2013

Routing in Mobile Ad-Hoc Networks using Social Tie Strengths and Mobility Plans

We consider the problem of routing in a mobile ad-hoc network (MANET) for which the planned mobilities of the nodes are partially known a priori and the nodes travel in groups. This situation arises commonly in military and emergency response scenarios. Optimal routes are computed using the most reliable path principle in which the negative logarithm of a node pair's adjacency probability is used as a link weight metric. This probability is estimated using the mobility plan as well as dynamic information captured by table exchanges, including a measure of the social tie strength between nodes. The latter information is useful when nodes deviate from their plans or when the plans are inaccurate. We compare the proposed routing algorithm with the commonly-used optimized link state routing (OLSR) protocol in ns-3 simulations. As the OLSR protocol does not exploit the mobility plans, it relies on link state determination which suffers with increasing mobility. Our simulations show considerably better throughput performance with the proposed approach as compared with OLSR at the expense of increased overhead. However, in the high-throughput regime, the proposed approach outperforms OLSR in terms of both throughput and overhead