The orthogonality between input and output mode preserves chaotic fluctuations by preventing feedback loops.
Itamar Daniel Landau, Haim Sompolinsky 2018, 'Coherent chaos in a recurrent neural network with structured connectivity.', PLoS Computational Biologyhttp://europepmc.org/articles/PMC6307850?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Moreover, eigenstructure, orthogonality, and eigenfunctions expansion are studied.
Villanueva Rafael J, Jódar Lucas 2005, 'Eigenstructure of nonselfadjoint complex discrete vector Sturm-Liouville problems',Advances in Difference Equationshttp://www.advancesindifferenceequations.com/content/2005/101430. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The reality of the corresponding eigenvalues and the orthogonality of the eigenfunctions areproved.
Pisamai Kittipoom 2017, 'Fractional singular Sturm-Liouville problems on the half-line', Advances in Difference Equationshttp://link.springer.com/article/10.1186/s13662-017-1370-4. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Their orthogonality properties are shown, with respect to classical weights.
Clemente Cesarano, Paolo Emilio Ricci 2019, 'Orthogonality Properties of the Pseudo-Chebyshev Functions (Variations on a Chebyshev'sTheme)', Mathematicshttps://www.mdpi.com/2227-7390/7/2/180. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Nonlinear amplification introduces degradation of bit error performance and destroys the orthogonality among subcarriers.
P. Galajda, J. Gazda, D. Kocur, P. Drotar 2009, 'Effects of Spreading Sequences on the Performance of MC-CDMA System with NonlinearModels of HPA', Radioengineeringwww.radioeng.cz/fulltexts/2009/09_01_048_054.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Orthogonality to the lactose-based expression system was also confirmed.
Kentaro Miyazaki 2018, 'Molecular engineering of the salicylate-inducible transcription factor Sal7AR fororthogonal and high gene expression in Escherichia coli', PLOS ONE10.1371/journal.pone.0194090. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)