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Feedforward CNN models have proven themselves in recent years as state-of-the-art models for predicting single-neuron responses to natural images in early visual cortical neurons. In this paper, we extend these models with recurrent…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special…
Graph neural networks (GNNs), especially dynamic GNNs, have become a research hotspot in spatio-temporal forecasting problems. While many dynamic graph construction methods have been developed, relatively few of them explore the causal…
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn…
Understanding the dynamic reorganization of brain networks is critical for predicting cognitive decline, neurological progression, and individual variability in clinical outcomes. This work proposes a multimodal graph neural network…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
Research on information diffusion generally assumes complete knowledge of the underlying network. However, in the presence of factors such as increasing privacy awareness, restrictions on application programming interfaces (APIs) and…
Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here we…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
Standard diffusion models are flexible estimators of complex distributions, but they do not encode causal structures and therefore do not by themselves support causal analysis. We propose a causality-encoded diffusion framework that…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…
This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Recent advances in Neural Variational Inference allowed for a renaissance in latent variable models in a variety of domains involving high-dimensional data. While traditional variational methods derive an analytical approximation for the…