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Keywords = online encyclopedia of integer sequences (OEIS)

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22 pages, 418 KiB  
Article
Discovery of Exact Equations for Integer Sequences
by Boštjan Gec, Sašo Džeroski and Ljupčo Todorovski
Mathematics 2024, 12(23), 3745; https://doi.org/10.3390/math12233745 - 28 Nov 2024
Cited by 1 | Viewed by 1413
Abstract
Equation discovery, also known as symbolic regression, is the field of machine learning that studies algorithms for discovering quantitative laws, expressed as closed-form equations or formulas, in collections of observed data. The latter is expected to come from measurements of physical systems and, [...] Read more.
Equation discovery, also known as symbolic regression, is the field of machine learning that studies algorithms for discovering quantitative laws, expressed as closed-form equations or formulas, in collections of observed data. The latter is expected to come from measurements of physical systems and, therefore, noisy, moving the focus of equation discovery algorithms towards discovering approximate equations. These loosely match the noisy observed data, rendering them inappropriate for applications in mathematics. In this article, we introduce Diofantos, an algorithm for discovering equations in the ring of integers that exactly match the training data. Diofantos is based on a reformulation of the equation discovery task into the task of solving linear Diophantine equations. We empirically evaluate the performance of Diofantos on reconstructing known equations for more than 27,000 sequences from the online encyclopedia of integer sequences, OEIS. Diofantos successfully reconstructs more than 90% of these equations and clearly outperforms SINDy, a state-of-the-art method for discovering approximate equations, that achieves a reconstruction rate of less than 70%. Full article
7 pages, 389 KiB  
Article
A New Record of Graph Enumeration Enabled by Parallel Processing
by Zhipeng Xu, Xiaolong Huang, Fabian Jimenez and Yuefan Deng
Mathematics 2019, 7(12), 1214; https://doi.org/10.3390/math7121214 - 10 Dec 2019
Cited by 7 | Viewed by 3830
Abstract
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, [...] Read more.
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, while discovering several regular graphs with minimum average shortest path lengths (ASPL) that can be used as interconnection networks for parallel computers. The enumeration of 4-regular graphs and the discovery of minimal-ASPL graphs are extremely time consuming. We accomplish them by adapting GENREG, a classical regular graph generator, to three supercomputers with thousands of processor cores. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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