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 |
Transmuted Activation Functions, Heaviside Function, Hausdorff Distance, Upper and Lower Bounds, Squashing Function
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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
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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Download@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}
}
TY - JOUR T1 - On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions AU - Nikolay Kyurkchiev AU - Anton Iliev Y1 - 2016/10/14 PY - 2016 N1 - https://doi.org/10.11648/j.mma.20160101.12 DO - 10.11648/j.mma.20160101.12 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 8 EP - 12 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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