Related papers: Towards a Quantitative Theory of Digraph-Based Com…

This paper introduces a new neural network model that aims to mimic the biological brain more closely by structuring the network as a complete directed graph that processes continuous data for each timestep. Current neural networks have…

Brain networks/graphs derived from resting-state functional MRI (fMRI) help study underlying pathophysiology of neurocognitive disorders by measuring neuronal activities in the brain. Some studies utilize learning-based methods for brain…

The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…

We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…

Brain connectivity analysis based on magnetic resonance imaging is crucial for understanding neurological mechanisms. However, edge-based connectivity inference faces significant challenges, particularly the curse of dimensionality when…

Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…

The human brain can be considered as complex networks, composed of various regions that continuously exchange their information with each other, forming the brain network graph, from which nodes and edges are extracted using resting-state…

We consider the problem of distilling efficient network topologies for collective communications. We provide an algorithmic framework for constructing direct-connect topologies optimized for the latency vs. bandwidth trade-off associated…

Temporal Graph Neural Networks (TGNNs) have gained growing attention for modeling and predicting structures in temporal graphs. However, existing TGNNs primarily focus on pairwise interactions while overlooking higher-order structures that…

In this thesis, we present robust and fully-automated methods for the subdivision of the entire human cerebral cortex based on connectivity information. Our contributions are four-fold: First, we propose a clustering approach to delineate a…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats…

The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver. Significant success has been obtained in applying the…

Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…

Brain networks characterize complex connectivities among brain regions as graph structures, which provide a powerful means to study brain connectomes. In recent years, graph neural networks have emerged as a prevalent paradigm of learning…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…

The connectome, a map of the structural and/or functional connections in the brain, provides a complex representation of the neurobiological phenotypes on which it supervenes. This information-rich data modality has the potential to…