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Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

Reasoning about images/objects and their hierarchical interactions is a key concept for the next generation of computer vision approaches. Here we present a new framework to deal with it through a visual hierarchical context-based…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

An interchange ring,(R,+,*)is an abelian group with a second binary operation defined so that the interchange law (x+y)*(u+v)=(x*u)+(y*v)holds. An interchange near ring is the same structure based on a group which may not be abelian. It is…

Two recent streams of work suggest that pairwise interactions may be sufficient to capture the complexity of biological systems ranging from protein structure to networks of neurons. In one approach, possible amino acid sequences in a…

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…

The growth of science and technology is a recombinative process, wherein new discoveries and inventions are built from prior knowledge. Yet relatively little is known about the manner in which scientific and technological knowledge develop…

Scientific knowledge is growing rapidly, making it difficult to track progress and high-level conceptual links across broad disciplines. While tools like citation networks and search engines help retrieve related papers, they lack the…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing…

We introduce a nested family of Bayesian nonparametric models for network and interaction data with a hierarchical granularity structure that naturally arises through finer and coarser population labelings. In the case of network data, the…

Adverse drug reactions (ADRs) are a major barrier to safe and effective pharmacotherapy and increasingly reflect higher order interactions between drugs, genetic background, and clinical phenotypes. Existing graph based approaches usually…

Collective decision-making is a widespread phenomenon in both biological and artificial systems, where individuals reach a consensus through social interactions. While traditional models of opinion dynamics and contagion focus on pairwise…

With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are…

In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical…

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…

Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…