Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition

Editorial Material Computer Science, Theory & Methods

Special issue on Algebraic Geometry and Machine Learning

Jonathan D. Hauenstein et al.

JOURNAL OF SYMBOLIC COMPUTATION (2023)

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Article Computer Science, Theory & Methods

Machine learning the real discriminant locus

Edgar A. Bernal et al.

JOURNAL OF SYMBOLIC COMPUTATION (2022)

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Article Mathematics, Interdisciplinary Applications

Exotic Bifurcations in Three Connected Populations with Allee Effect

Gergely Rost et al.

Summary: The study investigates the steady state structure of three connected populations with strong Allee effect, showing that increasing the dispersal rate between patches does not always simplify the system and may temporarily increase the number of steady states. The research also identifies various bifurcation patterns, including triple-transcritical bifurcations and a sun-ray shaped bifurcation where twelve steady states meet at a single point and then disappear. The main tool used in the investigation is a novel algorithm that decomposes the parameter space and finds bifurcation values using cylindrical algebraic decomposition.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2021)

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Article Multidisciplinary Sciences

Advancing mathematics by guiding human intuition with AI

Alex Davies et al.

Summary: This study demonstrates the application of machine learning in assisting mathematicians to discover new conjectures and theorems, providing examples of new fundamental results in pure mathematics. It outlines a process of using machine learning to discover potential patterns and relations between mathematical objects, guiding intuition and proposing conjectures. Leveraging strengths of mathematicians and machine learning can lead to surprising results in the collaboration between mathematics and artificial intelligence.

NATURE (2021)

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Article Computer Science, Theory & Methods