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Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), that generalizes…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
Knowledge Graph Embedding (KGE) methods have gained enormous attention from a wide range of AI communities including Natural Language Processing (NLP) for text generation, classification and context induction. Embedding a huge number of…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
Many empirical networks are intrinsically polyadic, with interactions occurring within groups of agents of arbitrary size. There are, however, few flexible null models that can support statistical inference for such polyadic networks. We…
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable…
Multi-label learning poses significant challenges in extracting reliable supervisory signals from the label space. Existing approaches often employ continuous pseudo-labels to replace binary labels, improving supervisory information…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
The discussion of how to apply geometric algebra to euclidean $n$-space has been clouded by a number of conceptual misunderstandings which we first identify and resolve, based on a thorough review of crucial but largely forgotten themes…
Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…
Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…
Link Prediction on Hyper-relational Knowledge Graphs (HKG) is a worthwhile endeavor. HKG consists of hyper-relational facts (H-Facts), composed of a main triple and several auxiliary attribute-value qualifiers, which can effectively…
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
Survival prediction is a complex ordinal regression task that aims to predict the survival coefficient ranking among a cohort of patients, typically achieved by analyzing patients' whole slide images. Existing deep learning approaches…
Graph generative models have shown strong results in molecular design but struggle to scale to large, complex structures. While hierarchical methods improve scalability, they usually ignore node and edge features, which are critical in…
While Graph Foundation Models (GFMs) have achieved remarkable success in homogeneous graphs, extending them to multi-domain heterogeneous graphs (MDHGs) remains a formidable challenge due to cross-type feature shifts and intra-domain…
We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing…