Related papers: The Hierarchical Graphene model
Graph Neural Networks (GNN) have gained significant traction in the forecasting domain, especially for their capacity to simultaneously account for intra-series temporal correlations and inter-series relationships. This paper introduces a…
The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to…
Graph neural networks (GNNs) are powerful graph-based machine-learning models that are popular in various domains, e.g., social media, transportation, and drug discovery. However, owing to complex data representations, GNNs do not easily…
Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism,…
We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…
In this article we investigate the possibility of generating piezoelectric orbital polarization in graphene-like systems which are deformed periodically. We start with discrete two-level models which depend on control parameters; in this…
While heterophily has been widely studied in node-level tasks, its impact on graph-level tasks remains unclear. We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation.…
Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…
In this work, we focus on the fermionic structure of the low-energy excitations of graphene (a monolayer of carbon atoms) to propose a new supersymmetric field-theoretic model for this physical system. In the current literature, other…
Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open…
In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a…
Multilevel modeling extends traditional modeling techniques with a potentially unlimited number of abstraction levels. Multilevel models can be formally represented by multilevel typed graphs whose manipulation and transformation are…
We perform an exact renormalization-group analysis of one-dimensional 4-state clock models with complex interactions. Our aim is to provide a simple explicit illustration of the behavior of the renormalization-group flow in a system…
In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first…
Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but…
Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriad graph analytic tasks and applications. Most GNNs rely on the homophily assumption that nodes belonging to the same class are more…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
How does neural connectivity in autistic children differ from neural connectivity in healthy children or autistic youths? What patterns in global trade networks are shared across classes of goods, and how do these patterns change over time?…