S.Yu. Eremenko − Dr.Sc. (Eng.), Professor, Director of Soliton Scientific Pty Ltd (Sydney, Australia) 

E-mail: sergei@solitonscientific.com

It is shown how the theory of Atomic functions known since 1970th  and their AString generalizations can be expanded to Machine Learning algorithms to represent atomic kernels in Support Vector Machines, Density Estimation, Principal Component Analysis, LOESS regression, and be the foundation of atomic regression, atomic activation function for Neural Networks and atomic computer. Representing a probabilistic weighted uniform distribution, these functions are related to Prouhet–Thue–Morse ‘fair game’ sequence and offer a fast calculation of derivatives. Multiple Matlab, R and Python examples calculate complex regressions, decision boundaries and precise target clusters important for medical, military and engineering applications. In combination, these methods compose Atomic Machine Learning theory which extends the 50 years’ history of atomic functions and their generalisations to new scientific domains.

1. Eremenko S.Yu. Atomic Strings and Fabric of Spacetime. Foreign Radioelectronics: Achievements of modern radioelectronics. 2018, Accepted for publication. https://www.researchgate.net/publication/320457739.
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10. Eremenko S.Yu. Finite Element Methods in Mechanics of Deformable Bodies. Kharkov: Osnova. 1991. 272p. https://www.researchgate.net/publication/321171685. 
11. Eremenko S.Yu. Natural Vibrations and Dynamics of Composite Materials and Constructions. Kiev: Naukova Dumka. 1992. 182 p. 
12. Eremenko S.Yu., Rvachev V.L. A survey of variants of the structural finite-element method // Journal of Mathematical Sciences. 1998. V. 90. № 2. P. 1917–1922.
13. Eremenko S.Yu. Combined Non-Archimedean Calculi. Foreign Radioelectronics // Achievements of modern radioelectronics. 1996. № 8. P. 57–65. https://www.researchgate.net/publication/320616255. 
14. Eremenko S.Yu., Kravchenko V.F., Rvachev V.L. Combined Non-Archimedean Calculi and New Models of Relativistic Mechanics. Foreign Radioelectronics // Achievements of modern radioelectronics. 1997. № 9. P. 26–38. https://www.researchgate.net/publication/320616269.

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