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Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
Individuals or companies in a large social or financial network often display rather heterogeneous behaviors for various reasons. In this work, we propose a network vector autoregressive model with a latent group structure to model…
Prediction algorithms typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors,…
We propose a novel method of detecting directed interactions of a general dynamic network from measured data. By repeating random state variable resetting of a target node and appropriately averaging over the measurable data, the pairwise…
Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Previously, most network comparison methods that rely on topological properties have been restricted to measuring…
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…
The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…
This paper describes a novel approach to modeling homphily, i.e. the tendency of nodes that share (or differ in) certain attributes to be linked; we consider dynamic networks in which nodes can be added over time but not removed. Our…
Network autocorrelation models are widely used to evaluate the impact of social influence on some variable of interest. This is a large class of models that parsimoniously accounts for how one's neighbors influence one's own behaviors or…
We investigate the impact of network heterogeneity on synergistic contagion dynamics. By extending a synergistic contagion model to diverse heterogeneous network topologies, we uncover the emergence of novel dynamical regimes characterized…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Social networks inherently exhibit complex relationships that can be positive or negative, as well as directional. Understanding balance in these networks is crucial for unraveling social dynamics, yet traditional theories struggle to…
As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of…
The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale we consider the coherence of overall network dynamics. We show that such \emph{global coherence}…