Mathematical Modelling and Applications

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On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions

Received: 18 August 2016    Accepted: 12 October 2016    Published: 14 October 2016
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Abstract

In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.

DOI 10.11648/j.mma.20160101.12
Published in Mathematical Modelling and Applications (Volume 1, Issue 1, October 2016)
Page(s) 8-12
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Transmuted Activation Functions, Heaviside Function, Hausdorff Distance, Upper and Lower Bounds, Squashing Function

References
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Author Information
  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria; Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, Plovdiv, Bulgaria

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  • APA Style

    Nikolay Kyurkchiev, Anton Iliev. (2016). On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions. Mathematical Modelling and Applications, 1(1), 8-12. https://doi.org/10.11648/j.mma.20160101.12

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    ACS Style

    Nikolay Kyurkchiev; Anton Iliev. On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions. Math. Model. Appl. 2016, 1(1), 8-12. doi: 10.11648/j.mma.20160101.12

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    AMA Style

    Nikolay Kyurkchiev, Anton Iliev. On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions. Math Model Appl. 2016;1(1):8-12. doi: 10.11648/j.mma.20160101.12

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  • @article{10.11648/j.mma.20160101.12,
      author = {Nikolay Kyurkchiev and Anton Iliev},
      title = {On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions},
      journal = {Mathematical Modelling and Applications},
      volume = {1},
      number = {1},
      pages = {8-12},
      doi = {10.11648/j.mma.20160101.12},
      url = {https://doi.org/10.11648/j.mma.20160101.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.mma.20160101.12},
      abstract = {In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.},
     year = {2016}
    }
    

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    AB  - In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.
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