Arturo Tozzi

University of North Texas

(8 January 2019)


The groundbreaking paper from Miri and Alù, apart from the mentioned fields of quantum resonance, optics and photonics, paves also the way for fully-novel applications of non-Hermitian systems’ singularities. Indeed, non-Hermitian systems have been recently assessed in biological and neural networks too (1,2). In particular, the brain exhibits the ingredients required by Miri and Alù’s framework:

1) nonconservative elements with gain and loss fit very well with the dynamic inhibitory/excitatory balance occurring in the neocortical neurons (3).

2) The imaginary values required by non-Hamiltonian systems (able however to support entirely real eigenvalue spectra) have been recently found in the human brain of healthy subjects (4).

3) The occurrence of abrupt phase transitions that dramatically alter the overall response take place both in optic/photonic dissipative systems and in neural ones (5).

4) In both physical and biological systems, completeness and orthogonality of the eigenbasis of the governing operators are broken and no longer diagonalized when introducing small perturbations.

5) The peculiar topology of eigenvalue surfaces near exceptional points described by (6) might correspond to the oscillations of sharp frequency produced by the brain activity.

6) Non-Hermitian components can be currently extracted from neurodata, e.g., from EEG traces (7).


Therefore, the insights provided by Miri et Alù might lead to fruitful applications not just in the fields of coupled-cavity laser sources, sensors, absorbers, nonlinear resonators, spatial mode converters and isolators, but also in revising fundamental concepts in nonconservative BIOLOGICAL systems, such as the human brain.





1) A. Amir, N. Hatano, D.R. Nelson, 2016. Non-Hermitian localization in biological networks. Phys. Rev. E 93, 042310. doi: :

2) H. Tanaka, D.R. Nelson, 2018. Non-Hermitian Quasi-Localization and Ring Attractor Neural Networks. arXiv:1811.07433.

3) B. Haider, A. Duque, A.R. Hasenstaub, D.A. McCormick, 2006. Neocortical network activity in vivo is generated through a dynamic balance of excitation and inhibition. J. Neurosci. 26, 4535-45. doi: 10.1523/JNEUROSCI.5297-05.2006.

4) A. Tozzi, J.F. Peters, N. Jausovec, 2016. A repetitive modular oscillation underlies human brain electric activity. Neurosci. Lett. 653, 234-238. 10.1016/j.neulet.2017.05.051.

5) E. Tognoli, J.A. Scott Kelso, 2014. Enlarging the scope: grasping brain complexity. Front. Syst. Neurosci. doi: 10.3389/fnsys.2014.00122.

6) Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, M. Ueda, 2018. Topological phases of non-Hermitian systems. Phys. Rev. X 8, 031079.

7) L. Marzetti, C. Del Gratta, G. Nolte, 2008. Understanding brain connectivity from EEG data by identifying systems composed of interacting sources. Neuroimage 42, 87-98 (2008). doi: 10.1016/j.neuroimage.2008.04.250.





Tozzi A.  2019.  RE: towards applications for exceptional points also in non- hermitian biological networks.  (electronic response to: Miri M-A, Alù A.  2019.  Exceptional points in optics and photonics.  Science, 363 (6422), eaar7709. 

DOI: 10.1126/science.aar7709.