Related papers: Mathematics of Digital Hyperspace
Digital twins, used to represent physical systems, have been lauded as tools for understanding reality. Complex system behavior is typically captured in domain-specific models crafted by subject experts. Contemporary methods for employing…
Low-power small form factor data processing units (DPUs) enable offloading and acceleration of a broad range of networking and security services. DPUs have accelerated the transition to programmable networking by enabling the replacement of…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
This paper presents HyperGraphOS, an innovative Operating System designed for the scientific and engineering domains. It combines model based engineering, graph modeling, data containers, and computational tools, offering users a dynamic…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
Unstructured data, such as text, images, audio, and video, comprises the vast majority of the world's information, yet it remains poorly supported by traditional data systems that rely on structured formats for computation. We argue for a…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…
Machine Learning (ML) techniques are indispensable in a wide range of fields. Unfortunately, the exponential increase of dataset sizes are rapidly extending the runtime of sequential algorithms and threatening to slow future progress in ML.…
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
Hypersparse matrices are a powerful enabler for a variety of network, health, finance, and social applications. Hierarchical hypersparse GraphBLAS matrices enable rapid streaming updates while preserving algebraic analytic power and…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are…
Modern advances in transportation and communication technology from airplanes to the internet alongside global expansions of media, migration, and trade have made the modern world more connected than ever before. But what does this bode for…
While social network analysis often focuses on graph structure of social actors, an increasing number of communication networks now provide textual content within social activity (email, instant messaging, blogging, collaboration networks).…
Hyperatlas is an open standard intended to facilitate the large-scale federation of image-based data. The subject of hyperatlas is the space of sphere-to-plane projection mappings (the FITS-WCS information), and the standard consists of…