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Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…

Regulatory networks depict promoting or inhibiting interactions between molecules in a biochemical system. We introduce a category-theoretic formalism for regulatory networks, using signed graphs to model the networks and signed functors to…

How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these…

Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been…

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…

Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…

Complex biological functions are carried out by the interaction of genes and proteins. Uncovering the gene regulation network behind a function is one of the central themes in biology. Typically, it involves extensive experiments of…

Scene graphs are powerful representations that parse images into their abstract semantic elements, i.e., objects and their interactions, which facilitates visual comprehension and explainable reasoning. On the other hand, commonsense…

Graph Neural Networks have revolutionized many machine learning tasks in recent years, ranging from drug discovery, recommendation systems, image classification, social network analysis to natural language understanding. This paper shows…

Machine learning methods can detect complex relationships between variables, but usually do not exploit domain knowledge. This is a limitation because in many scientific disciplines, such as systems biology, domain knowledge is available in…

In this paper, we review recent developments and the role of Graph Neural Networks (GNNs) in computational drug discovery, including molecule generation, molecular property prediction, and drug-drug interaction prediction. By summarizing…

Biological foundation models have shown strong performance in single-cell representation learning by applying transformer architectures directly to gene-expression matrices. However, these approaches predominantly operate in static settings…

The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…

GNNs are powerful models based on node representation learning that perform particularly well in many machine learning problems related to graphs. The major obstacle to the deployment of GNNs is mostly a problem of societal acceptability…

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…

Graphs as a type of data structure have recently attracted significant attention. Representation learning of geometric graphs has achieved great success in many fields including molecular, social, and financial networks. It is natural to…

Humans learn complex latent structures from their environments (e.g., natural language, mathematics, music, social hierarchies). In cognitive science and cognitive neuroscience, models that infer higher-order structures from sensory or…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…