Related Info Links
More by Authors Links
Journal Browser
Volume | Year
Issue
News and Announcements
RESEARCH ARTICLE
Activation functions based on Sincπ(xn) transform of sigmoids: Definitions and properties
Show Less
1 Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia , Bulgaria
JASMC, 026330001 https://doi.org/10.36922/JASMC026330001
Received: 16 August 2026 | Revised: 24 August 2026 | Accepted: 25 August 2026 | Published online: 22 September 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
The creation of activation functions via the nonlinear Sincπ(πXn) transformation of sigmoids, including both basic (logistic-type) and more intricate variants employing Mittag-Leffler functions, was proposed and elaborated through examples and calculations using Maple. The findings are encouraging and illustrate the potential to regulate the behaviors of the activation functions through the implemented fractional order α and the exponent value n of the nonlinear transformation.
Keywords
Sigmoids
Sinc function
Activation function
Nonlinear transform
Funding
None.
Conflict of interest
The author declares he has no competing interests.
References
- Jamone L, Natale L, Nori F. Autonomous online learning of reaching behavior in a humanoid robot. Int J Humanoid Robot. 2012;9(3):1250017. doi: 10.1142/S0219843612500176
- Vásárhelyi G, Virágh C, Somorjai G, Nepusz T, Eiben AE, Vicsek T. Optimized flocking of autonomous drones in confined environments. Sci Robot. 2018;3:eaat3536. doi: 10.1126/scirobotics.aat3536
- Qamar S, Khan SH, Arshad MA, Qamar M, Gwak J, Khan A. Autonomous drone swarm navigation and multitarget tracking with island policy-based optimization framework. IEEE Access. 2022;10:91073-91091. doi: 10.1109/ACCESS.2022.3201530
- Deng J. Dynamic neural networks with hybrid structures for nonlinear system identification. Eng Appl Artif Intell. 2013;26(1):281-292. doi: 10.1016/j.engappai.2012.07.005
- Ivanov R, Carpenter TJ, Weimer J, Alur R, Pappas GJ, Lee I. Verifying the safety of autonomous systems with neural network controllers. ACM Trans Embed Comput Syst. 2020;20(1):Article 7. doi: 10.1145/3419742
- Kocak Y, Siray GU. New activation function for single layer feedforward neural network. Expert Syst Appl. 2021;164:113977. doi: 10.1016/j.eswa.2020.113977
- Kunc V, Klema J. Three decades of activations: A comprehensive survey of 400 activation functions for neural networks. arXiv. 2024. Accessed August 6, 2026. https://arxiv.org/abs/2402.09092.
- Bueno S, Salmeron JL. Benchmarking main activation functions in fuzzy cognitive maps. Expert Syst Appl. 2009;36(3):5221-5229. doi: 10.1016/j.eswa.2008.06.045
- Zhao Y, Wang R, Sun J, Liu C, Li J, Chen D. Sigmoid function based modelling and route tracking of obstacle avoidance for ship in restricted water. MATEC Web Conf. 2018;232:02025. doi: 10.1051/matecconf/201823202025
- Cococcioni M, Rossi F, Ruffaldi E, Saponara S. Fast approximations of activation functions in deep neural networks when using posit arithmetics. Sensors. 2020;20(5):1515. doi: 10.3390/s20051515
- Hristov J. The logistic models and sigmoid functions: A variety of models and solution perspectives. Trans Comput Model Intell Syst. 2025;1(1):10002. doi: 10.65112/tcmis.10002
- Verhulst P. Recherches mathématiques sur la loi de d'accroissement de la population. Nouv Mem Acad R Soc Belle-Lettr Bruxelles. 1845;18:1-38.
- Hristov J. Sigmoids based on Mittag-Leffler functions: Ideas, modeling, and computational experiments. Trans Comput Model Intell Syst. 2026;3(2):10073. doi: 10.65112/tcmis.10073
- Hristov J. A non-linear diffusion problem with power-law diffusivity: An approximate solution experimenting with a modified sinc function. Math Model Numer Simul Appl. 2024;4(5):6-44. doi: 10.53391/mmnsa.1531086
- Stenger F. Numerical methods based on Whittaker cardinal, or sinc functions. SIAM Rev. 1981;23(2):165-224. doi: 10.1137/1023037
- Bradley DM. Note on Dirichlet sinc integral. Am Sci Mon. 2021;128(3):273-274. doi: 10.2307/48615205
- Bercu G. Sharp bounds on the sinc function via the Fourier series method. J Math Inequal. 2019;13(2):495-504. doi: 10.7153/jmi-2019-13-36
- Hu Y, Mortici C. A lower bound of the sinc function and its applications. Sci World J. 2014;571218. doi: 10.1155/2014/571218
- Selariu ME, Smarandache F, Nitu M. Cardinal functions and integral functions. Int J Geom. 2012;1(1):54-66.
- Wang Y. Sinc sum function and its application on FIR filter design. Acta Appl Math. 2010;110:1037-1056. doi: 10.1007/s10440-009-9480-y
- Gomopoulos N, Cheng W, Efremov M, Nealey PF, Fytas G. Out-of-plane longitudinal elastic modulus of supported polymer thin films. Macromolecules. 2009;42:7164-7167. doi: 10.1021/ma901317q
- Abrarov AM, Quine BQ. A rational approximation of the sinc function based on sampling and the Fourier transforms. Appl Numer Math. 2020;150:65-75. doi: 10.1016/j.apnum.2019.08.012
- Stenger F. Numerical Methods Based on Sinc and Analytic Functions. Berlin, Germany: Springer-Verlag; 1993. doi: 10.1007/978-1-4613-8336-7
- Morlet AC. Convergence of the sinc-method for a fourth-order ordinary differential equation with application. SIAM J Numer Anal. 1995;32(5):1475-1503. doi: 10.1137/0732082
- Stenger F. Fourier series for zeta function via sinc. Linear Algebra Appl. 2008;429:2636-2639. doi: 10.1016/j.laa.2008.01.037
- Mescia L, Bia P, Caratelli D. Fractional-calculus-based electromagnetic tool to study pulse propagation in arbitrary dispersive dielectrics. Phys Status Solidi A. 2018;2018:1800557. doi: 10.1002/pssa.201800557
- Cattani C. Sinc-fractional operator on Shannon wavelet space. Front Phys. 2018;6:118. doi: 10.3389/fphy.2018.00118
- Slavnov NA. Integral operators with the generalized sine kernel on the real axis. Theor Math Phys. 2010;165(1):1262-1274. doi: 10.1007/s11232-010-0121-4
- Yang XJ, Cao F, Machado JA, Baleanu D. A new fractional derivative involving the normalized sinc function without singular kernel. Eur Phys J Spec Top. 2018;226:3567-3575. doi: 10.1140/epjst/e2018-00020-2
- Yavuz M. Characterizations of two different fractional operators without singular kernel. Math Model Nat Phenom. 2019;14:302. doi: 10.1051/mmnp/2019007
- Odibat Z, Baleanu D. A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulations. Math Comput Simul. 2023;212:224-233. doi: 10.1016/j.matcom.2023.05.010
- Odibat Z, Al-Refai M, Baleanu D. On some properties of generalized cardinal sine kernel fractional operators: Advantages and applications of the extended operators. Chin J Phys. 2024;91:349-360. doi: 10.1016/j.cjph.2024.07.018