Mathematics of Digital Hyperspace

Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data supported by continuous streams that stretch standard concep...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Kepner, Jeremy, Davis, Timothy, Gadepally, Vijay, Hayden Jananthan, Milechin, Lauren
Format: Article
Language:English
Subjects:
Arrays
Communications traffic
Digital media
Graph theory
Graphs
Hyperspaces
Lakes
Machine learning
Mathematical analysis
Mathematics
Matrix algebra
Matrix methods
Oceans
Packets (communication)
Rings (mathematics)
Spreadsheets
Tables (data)
Unstructured data
Websites
Online Access:Get full text
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Summary:Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data supported by continuous streams that stretch standard concepts of type and dimension. The unstructured data of digital hyperspace can be elegantly represented, traversed, and transformed via the mathematics of hypergraphs, hypersparse matrices, and associative array algebra. This paper explores a novel mathematical concept, the semilink, that combines pairs of semirings to provide the essential operations for graph analytics, database operations, and machine learning. The GraphBLAS standard currently supports hypergraphs, hypersparse matrices, the mathematics required for semilinks, and seamlessly performs graph, network, and matrix operations. With the addition of key based indices (such as pointers to strings) and semilinks, GraphBLAS can become a richer associative array algebra and be a plug-in replacement for spreadsheets, database tables, and data centric operating systems, enhancing the navigation of unstructured data found in digital hyperspace.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.15203