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Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case. 

The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme. 

Signal maps are essential for the planning and operation of cellular networks. However, the measurements needed to create such maps are expensive, often biased, not always reflecting the performance metrics of interest, and posing privacy risks. In this paper, we develop a unified framework for predicting cellular performance maps from limited available measurements. Our framework builds on a state-of-the-art random-forest predictor, or any other base predictor. We propose and combine three mechanisms that deal with the fact that not all measurements are equally important for a particular prediction task. First, we design quality-of-service functions (Q), including signal strength (RSRP) but also other metrics of interest to operators, such as number of bars, coverage (improving recall by 76%-92%) and call drop probability (reducing error by as much as 32%). By implicitly altering the loss function employed in learning, quality functions can also improve prediction for RSRP itself where it matters (e.g., MSE reduction up to 27% in the low signal strength regime, where high accuracy is critical). Second, we introduce weight functions (W) to specify the relative importance of prediction at different locations and other parts of the feature space. We propose re-weighting based on importance sampling to obtain unbiased estimators when the sampling and target distributions are different. This yields improvements up to 20% for targets based on spatially uniform loss or losses based on user population density. Third, we apply the Data Shapley framework for the first time in this context: to assign values (ϕ) to individual measurement points, which capture the importance of their contribution to the prediction task. This can improve prediction (e.g., from 64% to 94% in recall for coverage loss) by removing points with negative values and storing only the remaining data points (i.e., as low as 30%), which also has the side-benefit of helping privacy. We evaluate our methods and demonstrate significant improvement in prediction performance, using several real-world datasets. 

The uneven spread of COVID-19 has resulted in disparate experiences for marginalized populations in urban centers. Using computational models, we examine the effects of local cohesion on COVID-19 spread in social contact networks for the city of San Francisco, finding that more early COVID-19 infections occur in areas with strong local cohesion. This spatially correlated process tends to affect Black and Hispanic communities more than their non-Hispanic White counterparts. Local social cohesion thus acts as a potential source of hidden risk for COVID-19 infection. 

Low‐dimensional parametric models for network dynamics have been successful as inferentially efficient and interpretable tools for modelling network evolution but have difficulty in settings with strong time inhomogeneity (particularly when sharp variation in parameters is possible and covariates are limited). Here, we propose to address this problem via a novel family of block‐structured dynamic exponential‐family random graph models (ERGMs), where the time domain is divided into consecutive blocks and the network parameters are assumed to evolve smoothly within each block. In particular, we let the latent ERGM parameters follow a piecewise polynomial model with an unknown block structure (e.g., change points). We propose an iterative estimation procedure that involves estimating the block structure using trend filtering and fitting ERGMs for networks belonging to the same time block. We demonstrate the utility of the proposed approach using simulation studies and applications to interbank transaction networks and citations among political blogs over the course of an electoral cycle.

 

Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structures, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail—an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This “neural upscaling” procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 μs atomistic molecular dynamics trajectory of Aβ1–40, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs.