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One of the most interesting scientific challenges nowadays deals with the analysis and the understanding of complex networks' dynamics and how their processes lead to emergence according to the interactions among their components. In this…

Hidden Markov jump processes are an attractive approach for modeling clinical disease progression data because they are explainable and capable of handling both irregularly sampled and noisy data. Most applications in this context consider…

There has been an increasing interest in modeling continuous-time dynamics of temporal graph data. Previous methods encode time-evolving relational information into a low-dimensional representation by specifying discrete layers of neural…

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other nonlinear phenomena in complex human and natural systems. Increasing amounts…

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…

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…

Event skeleton generation, aiming to induce an event schema skeleton graph with abstracted event nodes and their temporal relations from a set of event instance graphs, is a critical step in the temporal complex event schema induction task.…

Analysis of sequential event data has been recognized as one of the essential tools in data modeling and analysis field. In this paper, after the examination of its technical requirements and issues to model complex but practical situation,…

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the…

Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it…

Dynamic networks have intrinsic structural, computational, and multidisciplinary advantages. Link prediction estimates the next relationship in dynamic networks. However, in the current link prediction approaches, only bipartite or…

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections…

We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other…

We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…

We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs…

Recent technological advances have made it easier to collect large and complex networks of time-stamped relational events connecting two or more entities. Relational hyper-event models (RHEMs) aim to explain the dynamics of these events by…