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The edge partition model (EPM) is a generative model for extracting an overlapping community structure from static graph-structured data. In the EPM, the gamma process (GaP) prior is adopted to infer the appropriate number of latent…

Due to the irregular nature of connections in most graph datasets, partitioning graph analysis algorithms across multiple computational nodes that do not share a common memory inevitably leads to large amounts of interconnect traffic.…

Complex systems with multiple processes evolving on different temporal scales are naturally described by multilayer networks, where each layer represents a different timescale. In this work, we show how the multilayer structure shapes the…

Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…

The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…

Network epidemic simulation holds the promise of enabling fine-grained understanding of epidemic behavior, beyond that which is possible with coarse-grained compartmental models. Key inputs to these epidemic simulations are the networks…

This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…

We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…

Analytical explorations on complex networks and cubes (i.e., multi-dimensional datasets) are currently two separate research fields with different strategies. To gain more insights into cube dynamics via unique network-domain methodologies…

Information on social media spreads through an underlying diffusion network that connects people of common interests and opinions. This diffusion network often comprises multiple layers, each capturing the spreading dynamics of a certain…

The study of meme propagation and the prediction of meme trajectory are emerging areas of interest in the field of complex networks research. In addition to the properties of the meme itself, the structural properties of the underlying…

Many systems of scientific interest can be conceptualized as multipartite networks. Examples include the spread of sexually transmitted infections, scientific collaborations, human friendships, product recommendation systems, and metabolic…

Information, ideas, and diseases, or more generally, contagions, spread over space and time through individual transmissions via social networks, as well as through external sources. A detailed picture of any diffusion process can be…

Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have…

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…

Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time…