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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.

Published in Mathematical Modelling and Applications (Volume 1, Issue 1)
DOI 10.11648/j.mma.20160101.12
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), 2016. Published by Science Publishing Group

Keywords

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

References
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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://article.sciencepublishinggroup.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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    T1  - On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions
    AU  - Nikolay Kyurkchiev
    AU  - Anton Iliev
    Y1  - 2016/10/14
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    DO  - 10.11648/j.mma.20160101.12
    T2  - Mathematical Modelling and Applications
    JF  - Mathematical Modelling and Applications
    JO  - Mathematical Modelling and Applications
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    PB  - Science Publishing Group
    SN  - 2575-1794
    UR  - https://doi.org/10.11648/j.mma.20160101.12
    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.
    VL  - 1
    IS  - 1
    ER  - 

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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

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