Carter T. Butts

Carter T. Butts, Alexander Murray-Watters

Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes from which the corresponding networks were presumably generated. Here, we build on prior work in this area to present a behavioral micro-foundation for cross-sectional network models, based on a continuous time stochastic choice mechanism, that can accommodate highly general classes of cases (including agents who are not themselves in the network, and multilateral edge control). As we show, the equilibrium behavior of this process under appropriate conditions can be expressed in exponential family form, allowing estimation of individual preferences using existing methods; the graph potential separates naturally into a preference-based term reflecting agent utilities, and an entropic term reflecting the rules of tie formation. We illustrate our approach via an analysis of friendship in a professional organization, and modeling of phase transitions in the structure of small groups.

Alexander Murray-Watters, Cheng Wang, John R. Hipp et al.

Many processes related to status, power, and influence within social networks have been modeled using forced linear diffusion models; examples include the highly successful Friedkin-Johnsen model of social influence, the status/power scores of Katz and Bonacich, and the widely used network autocorrelation model. While a basic assumption of such models is that the impact of one individual on another through any given path falls exponentially with path length, the total impact of the first individual on the second involves contributions from walks of all lengths; thus, while total impact is expected to decline with network distance, the relationship is not trivial. Here, we provide an approximate solution for the total impact of one node on another as a function of network distance, showing that the total impact is given to first order by a product of eigenvector centrality scores together with an expression in terms of the graph spectrum (eigenvalues of the adjacency matrix) that falls exponentially with distance. We also show how this solution can be refined using higher-order eigenvectors of the adjacency matrix. A numerical study on interpersonal networks drawn from educational settings verifies an average exponential decline in impact strength under the linear diffusion model, and shows that the first-order eigenvector approximation can often be a good proxy for total impact as obtained from the exact solution. This suggests a simple model that can be used to approximate total impact for social influence or status processes in a range of settings.

Carter T. Butts

Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent advances in dynamic network modeling with ideas from transition state theory. This framework facilitates both characterizing the process of structural change and, in some cases, predicting it. Notably, this approach allows approximate prediction of network change from cross-sectional models, under limited assumptions regarding the underlying microdynamics. We apply this framework to a simple model of faction realignment in small groups, showing that the process through which realignment occurs can be well-predicted ex ante for a number of different network micro-processes.

Emmanouil Alimpertis, Athina Markopoulou, Carter T. Butts et al.

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 metrics of interest, and posing privacy risks. In this paper, we develop a unified framework for predicting cellular signal maps from limited 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, i.e., coverage and call drop probability. 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 errors are 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 improves prediction (e.g., from 64% to 94% in recall for coverage loss) by removing points with negative values, and can also enable data minimization. We evaluate our methods and demonstrate significant improvement in prediction performance, using several real-world datasets.

Vy Duong, Elizabeth Diessner, Gianmarc Grazioli et al.

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 structure, 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 $μ$s atomistic molecular dynamics trajectory of A$β_{1-40}$, 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.